queensland university of technology school of … · 2010-06-09 · hot water systems (shws). the...

QUEENSLAND UNIVERSITY OF TECHNOLOGY

SCHOOL OF PHYSICAL AND CHEMICAL SCIENCES

NOVEL APPROACHES TO THE DESIGN OF DOMESTIC SOLAR HOT WATER SYSTEMS

Submitted by Raniero Alberto GUARNIERI to the School of Physical and Chemical Sciences,

Queensland University of Technology, in partial fulfilment of the requirements of the degree of

Doctor of Philosophy.

2005

Novel approaches to the design of domestic solar hot water systems iii

Keywords Domestic Solar Hot Water Systems, Concentrating Optics, Compound Parabolic

Collectors, Solar Selective Surface, Self-Pump, Air Heater Panel, Compact Heat

Exchanger, Sun-Earth Geometry

Novel approaches to the design of domestic solar hot water systems v

Abstract

Domestic solar hot water units, if properly designed, are capable of providing all hot water

needs in an environmentally friendly and cost-effective way. Despite 50 years of

development, commercial technology has not yet achieved substantial market penetration

compared to mainstream electric and gas options. Therefore, alternate designs are warranted

if they can offer similar or greater performance for a comparable cost to conventional units.

This study proved that such alternatives are possible by designing and testing two novel solar

hot water systems (SHWS).

The first system used compound parabolic collector (CPC) panels to concentrate solar

energy and produce steam. The steam moved from a rooftop downward into a heat exchange

pipe within a ground level water tank, heating the water, condensing and falling into a

receptacle. The operation was entirely passive, since the condensate was pulled up due to the

partial vacuum that occurred after system cooling. Efficiencies of up to 40% were obtained.

The second system used an air heater panel. Air was circulated in open and closed loop

configuration (air recycling) by means of a fan/blower motor and was forced across a

compact heat exchanger coupled to a water tank. This produced a natural thermosiphon flow

heating the water. Air recycling mode provided higher system efficiencies: 34% vs. 27%.

The concurrent development of an analytical model that reasonably predicted heat transfer

dynamics of these systems allowed 1) performance optimisation for specific input/starting

operating conditions and 2) virtual design improvements. The merit of this model lay in its

acceptable accuracy in spite of its simplicity.

By optimising for operating conditions and parameter design, both systems are capable of

providing over 30 MJ of useful domestic hot water on clear days, which equates roughly to

an increase of 35°C in a 200 L water tank. This will satisfy, on average, daily hot water

requirements for a 4-person household, particularly in low-latitude regions (eg. Queensland).

Preliminary costing for these systems puts them on par with conventional units, with the

passive, remotely coupled, low maintenance, CPC SHWS comparable to higher end models.

The air heater SHWS, by contrast, was much more economical and easier to build and

handle, but at the trade-off cost of 1) the need for an active system, 2) increased maintenance

and running costs and 3) the requirement for a temperature control mechanism that would

protect the panel body by dumping hot air trapped inside if stagnation were to occur.

Novel approaches to the design of domestic solar hot water systems vii

Table of Contents

Keywords ...............................................................................................................iii

Abstract ................................................................................................................... v

Table of Contents ................................................................................................vii

Nomenclature ...................................................................................................... xiv

List of Diagrams, Images and Figures ............................................................. xx

List of Tables ..................................................................................................... xxix

Statement of Original Authorship ................................................................... xxxi

Acknowledgments ..........................................................................................xxxiii

Chapter 1 Introduction ...............................................................1

1.1 Solar energy and domestic solar hot water production .................................... 1

1.2 Conventional SHWS ........................................................................................ 2

1.3 Problems and disadvantages with existing systems ......................................... 5

1.4 Aims and objectives ......................................................................................... 5

1.5 Brief outline of approach to new designs......................................................... 6

1.6 Rationale behind the selection, construction and operation of the designs developed ......................................................................................................... 7

Chapter 2 Solar radiation and solar geometry..........................10

2.1 Introduction .................................................................................................... 10

2.2 Solar energy and solar radiation..................................................................... 10

2.3 Air mass atmospheric transmittance model ................................................... 11

2.4 Sun-earth geometry ........................................................................................ 13

2.5 Solar geometry and panel layout/orientation ................................................. 16

Novel approaches to the design of domestic solar hot water systems viii

Chapter 3 Concentrating devices.............................................23

3.1 Introduction .................................................................................................... 23

3.2 Concentration ................................................................................................. 23

3.2.1 Upper limit for concentration .......................................................... 25

3.3 The Compound Parabolic Collector (CPC).................................................... 26

3.3.1 Conceptualisation of the CPC and the “edge-ray” principle ........... 28

3.4 Exploring CPC orientations and collection times .......................................... 30

Chapter 4 Heat transfer............................................................47

4.1 Introduction .................................................................................................... 47

4.1.1 Conduction heat transfer.................................................................. 47

4.1.2 Convection heat transfer .................................................................. 48

4.1.3 Radiation heat transfer ..................................................................... 49

4.2 Selected heat transfer equations and other relationships................................ 50

4.2.1 Convection in SHWS....................................................................... 51

4.2.1.1 Free convection between a flat plate and the surroundings.... 51

4.2.1.2 Forced convection between a flat plate and the surroundings............................................................................ 52

4.2.1.3 Free convection from horizontal cylinders............................. 53

4.2.1.4 Free convection from vertical cylinders................................. 53

4.2.1.5 Forced convection from horizontal or vertical cylinders ....... 54

4.2.1.6 Free convection between flat plates ....................................... 54

4.2.1.7 Free convection between concentric cylinders....................... 56

4.2.1.8 Forced convection in a corrugated triangular duct................. 56

4.2.2 Radiation in SHWS.......................................................................... 58

4.2.2.1 Radiation exchange between a convex object and a large enclosure ................................................................................. 59

Novel approaches to the design of domestic solar hot water systems ix

4.2.2.2 Radiation exchange between flat plates ................................. 59

4.2.2.3 Radiation exchange between two concentric cylindrical surfaces .............................................................................. 60

4.2.3 Conduction in SHWS ...................................................................... 61

4.2.3.1 Conduction between concentric cylinders ............................. 61

4.3 Thermal network formulation and energy balance equations ........................ 61

4.4 Energy and power in fluid flow and fluid storage.......................................... 64

4.5 Heat exchanger effectiveness-NTU method .................................................. 65

Chapter 5 Fluid mechanics and hydraulics ..............................68

5.1 Introduction .................................................................................................... 68

5.2 Pressure losses................................................................................................ 68

5.2.1 Pressure in fluids ............................................................................. 69

5.2.2 Energy and “head”........................................................................... 69

5.2.3 Head (pressure) losses ..................................................................... 71

5.2.4 Minor losses..................................................................................... 72

5.3 Thermohydraulics .......................................................................................... 74

5.3.1 Poisseuille’s Law for laminar flow.................................................. 74

Chapter 6 Solar Hot Water System with Passive Downward

Vapour Phase Heat Transport.................................75

6.1 Introduction .................................................................................................... 75

6.1.1 Basic design considerations............................................................. 76

6.2 Concentrating systems – a review.................................................................. 80

6.3 Solar Geometry and panel layout/orientation................................................. 83

6.4 Heat transfer ................................................................................................... 85

Novel approaches to the design of domestic solar hot water systems x

6.4.1 Collector panel energy balance equations and relationships for heat transfer modes .......................................................................... 87

6.4.2 Conveyance infrastructure / transfer line......................................... 94

6.4.3 Hot water tank and exchanger ......................................................... 96

6.4.4 Summary of solution process for the entire system......................... 98

6.5 Experimental work: prototype and system construction ................................ 99

6.5.1 System components ......................................................................... 99

6.5.2 First prototype collector panel ....................................................... 105

6.5.3 Second prototype ........................................................................... 107

6.5.4 Third prototype .............................................................................. 109

6.6 Results and discussion.................................................................................. 113

6.6.1 Modelling results ........................................................................... 113

6.6.2 Experimental results from prototypes............................................ 121

6.6.2.1 First Prototype (Figure 6.31) ........................................... 121

6.6.2.2 Second Prototype (Figure 6.32)....................................... 122

6.6.2.3 Third Prototype (Figure 6.33).......................................... 123

6.6.3 Comparison of the 3 prototypes (Figure 6.34)............................... 125

6.6.4 Water tank...................................................................................... 126

6.7 Conclusions and discussion.......................................................................... 128

6.7.1 Performance of the downward vapour heat transport SHWS........ 128

6.7.2 Elements construction and materials used ..................................... 131

6.7.3 Model predictions compared with experimental results. ............... 133

Chapter 7 - Air-to-water heat transfer solar hot water system with

heat exchanger-water tank coupling .....................135

7.1 Introduction .................................................................................................. 135

Novel approaches to the design of domestic solar hot water systems xi

7.1.1 Basic design for the construction and operation of the air-to-water heat exchanger-coupled tank SHWS ................................... 135

7.2 Types of solar air heating panels.................................................................. 139

7.3 Heat transfer ................................................................................................. 142

7.3.1 Air heating collector panel ............................................................. 143

7.3.2 Collector panel energy balance equations and relationships for heat transfer modes ........................................................................ 145

7.3.3 Conveyance system energy balance equations and relationships for heat transfer modes (pipes and bends) ..................................... 149

7.3.4 Heat exchanger energy considerations and power gain in the water .............................................................................................. 151

7.3.5 Centrifugal Fan-Motor ................................................................... 155

7.3.6 Water Tank heat gains and losses .................................................. 157

7.3.7 Summary of solution process for the entire system ....................... 158

7.4 Thermohydraulic assessment of airflow ...................................................... 159

7.4.1 Pressure losses................................................................................ 159

7.5 Experimental work: construction details...................................................... 161

7.5.1 System components........................................................................ 162

7.6 Results ........................................................................................................ 173

7.6.1 First prototype ................................................................................ 173

7.6.2 Second prototype............................................................................ 185

7.6.2.1 Open loop operation mode .............................................. 186

7.6.2.2 Closed loop operation mode............................................ 194

7.6.3 Determination of head loss and pressure drops in the system ....... 200

7.6.4 Thermosiphon effective radius and linear fluid flow approximation................................................................................ 205

7.6.5 Exploring exchanger effectiveness variation under system operation ........................................................................................ 208

7.7 Discussion .................................................................................................... 215

Novel approaches to the design of domestic solar hot water systems xii

7.7.1 Air heater system elements ............................................................ 215

7.7.2 Economics ...................................................................................... 220

7.7.3 Model prediction results................................................................. 220

7.8 Conclusions .................................................................................................. 222

Chapter 8 - Economic analysis..................................................223

8.1 SWHS with passive downward vapour phase heat transport ....................... 224

8.2 SHWS incorporating an air heater collector panel and heat exchanger-water tank coupling ................................................................................................ 227

Chapter 9 General discussion, conclusions and avenues for

future work.............................................................231

9.1 SHWS with passive downward vapour phase heat transport ....................... 233

9.2 SHWS with an air heater collector panel and heat exchanger-water tank coupling ........................................................................................................ 240

Appendix A – Mathematical relationships and calculations in

solar geometry and CPC orientation................... 250

Appendix B – Etendue invariant and optical concentration....... 255

Appendix C – Mathematical formulation for the design of the

CPC shape and the horizontal fin profile ............ 258

Appendix D – Heat transfer parameters and pipe friction .........265

Appendix E – Analytical expressions for the heat transfer

dynamics of the CPC panel SHWS .................... 270

Novel approaches to the design of domestic solar hot water systems xiii

Appendix F – Analytical expressions for the heat transfer

dynamics of the air heater panel SHWS.............275

Appendix G – Polynomial approximations of physical

properties of air and water ..................................284

Appendix H – Air/water heat exchanger and fan-blower motor.290

Appendix I – Anemometer calibration.......................................292

Bibliography ............................................................................295

References ............................................................................296

Novel approaches to the design of domestic solar hot water systems xiv

Nomenclature

α Solar altitude angle / Absorptivity

β Inverse of the temperature

αr Heliz angle of roughness for a pipe with internal corrugation

αt Thermal diffusivity (m2/s)

Γ Total emissive power (W/m2)

γ Specific weight (kg/m2·s2)

δ Declination

Δ Angular surface error for CPC

Δx Thickness of material

ΔΤ Temperature difference

Δp Pressure difference

φ Latitude

Φv Volumetric flow rate

ϕ Panel azimuth angle

ϕS Solar azimuth angle

θ Panel tilt angle

ρ Rotation angle about the normal to the collector panel plane

ω Twist angle

η Dynamic viscosity (kg/m·s) / Efficiency

ε Emissivity / Heat exchanger effectiveness / Pipe wall roughness factor

ε’ Modified heat exchanger effectiveness

ν Kinematic viscosity (m2/s)

σ Stefan-Boltzmmann constant

ρ Reflectivity / Density

τ Transmissivity

τatm Atmospheric transmittance

τod(l) Optical depth for radiation traversing a medium of thickness ‘l’

θa CPC acceptance half-angle

θc CPC collection angle

θinc Incidence angle: the angle between the surface and the solar beam

Novel approaches to the design of domestic solar hot water systems xv

θSN’ Angle between the solar vector and the normal to the panel surface

θSP’ Angle between the solar vector and the vector normal to the panel surface and

to the line-axis of the CPC

θz Zenith angle

a Aperture radius of an optical system

A Area

Arat Area ratio between the surfaces of concentric cylinders

At=Ad Pipe cross-sectional area

C Concentration ratio / combined electrical motor efficiency

Cp Specific heat at constant pressure(kJ/kg·°C)

(also: Cair, Cw for air and water, respectively)

D Diameter

Dh Hydraulic Diameter

Dp Pipe diameter

dr Roughness pitch for a pipe with internal corrugation

dx Element surface length for air panel absorber

er Roughness height for a pipe with internal corrugation

ET Equation of time

f Friction factor / Focal length of parabola

F Force

F’ Collector efficiency factor

Fij Radiation shape factor for radiation exchange from surface i to surface j

g Acceleration of gravity

Gcb Attenuated irradiance on the Earth’s surface after traversing the atmosphere

(Gcb = S = I)

GcbN Attenuated irradiance on a surface for normal solar incidence

Go Extraterrestrial radiation at the boundary of the Earth’s atmosphere

Gr Grashof number

GSC Solar constant

h = lh Hot water column height in the thermosiphon circuit

hf Head losses

hm Minor pressure losses

hn Reduction in cold water column height in the thermosiphon circuit

Novel approaches to the design of domestic solar hot water systems xvi

hs Hour angle

H Head pressure (m)

Hs Plate spacing for double-cover collector panel

hT Heat transfer coefficient

K Overall attenuation factor for solar radiation traversing the atmosphere /

Pressure loss coefficient

k Thermal conductivity

kλ Wavelength dependent extinction coefficient for solar radiation traversing the

atmosphere

KE Kinetic Energy

l Length / Solar panel length / Pipe length / Height

L Characteristic length

l0 Atmosphere thickness for normal solar incidence

LH Enthalpy of vapourisation (kJ/kg)

llocal Local longitude

LST Local standard time

lST Standard time meridian

m Body mass / air mass ratio

m& Mass flow rate

n Day number / Refractive index

Nu Nusselt number

P Perimeter / Power

Pd Wetted perimeter of a duct

p Pressure

PE Pressure Energy

Pr Prandtl number

pr Rib spacing for a pipe with internal ribbed corrugation

Px_act Heat transfer experienced by fluid in heat exchanger

Px_max Maximum possible heat transfer

q Heat flow (W)

Q Total heat flow (W)

r Pipe radius

R Reflectance

Ra Rayleigh number

Novel approaches to the design of domestic solar hot water systems xvii

Re Reynolds number

RT Thermal resistance (W/m4·°C)

ST Solar time

t Thickness of material

T Temperature

Tci Temperature of the cold fluid at input/output port ‘i’ of exhcanger

Thi Temperature of the hot fluid at input/output port ‘i’ of exhcanger

UL Total heat loss coefficient

U(θu) Rotation matrix about an arbitrary vector VU by an angle θu

v Fluid velocity

vm Mean fluid velocity

VN Unit vector normal to panel surface

VN’ Unit vector normal to panel surface after panel orientation

VNpol VN in polar coordinates

VP Unit vector normal to both VN and the line-axis of the collector

VP’ Unit vector normal to both VN’ and the line-axis of the orientated collector

VPpol VP in polar coordinates

VS Solar vector

VSN’ Projection of the solar vector on the axes of VN’

VSP’ Projection of the solar vector on the axes of VP’

VST Projected solar vector on the transverse plane of the CPC panel

V& Volume flow rate

w Width / Aperture width of an optical system

W Body weight (kg)

Ws Slat width for double-cover collector panel

X, Y, Z Rotation matrices about the x, y and z-axes, respectively

ZE Potential Energy

Subscripts and Supersripts

A Related to CPC collector panel absorber

F Related to CPC collector panel absorber sheath

C Related to CPC and Air Heater collector panel cover

Novel approaches to the design of domestic solar hot water systems xviii

V Related to CPC cavity

B Related to back of the air heater absorber panel

Q Related to heat losses from the double cover of the air heater panel to the

environment

amb Related to the ambient, usually temperature (Tamb)

mot Denotes fan/blower motor property or characteristic

ab Related to the air heater absorber

Related to the air streams flowing over or under the air panel absorber

e Related to the side walls of the air heater panel

h Related to the hot fluid

c Related to the cold fluid / Related to convection heat trasfer

k Related to conduction heat trasfer

r Related to radiation heat trasfer

i Related to point, port, or object of measurement

s Related to steam properties or characteristic (ηs)

f Relates to a fluid property or characteristic (Tf)

sky Related to the sky (Tsky)

forced Denotes forced convection mode

free Denotes free convection mode

cond Related to steam condensate

tank_cond Related to condensation occurring in the heat exchanger loop of the tank

tot_cond Related to total steam condensate

stag Related to stagnation temperature

eff Denotes an effective measurement or quality

in Denotes input condition or internal location

out Denotes output condition or external location

w, water Denotes water characteristic

w Denotes internal pipe wall

x Denotes heat exchanger characteristic

f Indicates evaluation of property at film temperature

cyl Related to a cylindrical geometry

opt Related to the optical properties of the CPC

eff Effective

cpc Related to the CPC

iair

Novel approaches to the design of domestic solar hot water systems xix

fin Related to CPC absorber-boiler fin

ins Related to insulation material

T Related to the water storage tank

tube Related to CPC absorber-boiler tube

Novel approaches to the design of domestic solar hot water systems xx

List of Diagrams, Images and Figures

Figure 1.1 A conventional close-coupled thermosiphonic solar hot water system... 2

Figure 1.2 Schematic for the vapour phase downward heat transport SHWS.......... 6

Figure 1.3 Schematic for the air-to-water heat exchanger tank-coupled SHWS...... 7

Figure 2.1 Solar radiation travel distance through the atmosphere ........................ 11

Figure 2.2 Sun path diagrams for seasonal times for a temperate austral latitude.. 13

Figure 2.3 Collection angle comparison between a flat plate and a concentrator .. 15

Figure 2.4 Cartesian coordinate system for collector panel.................................... 17

Figure 2.5 Plane of a CPC before and after azimuth rotation................................. 18

Figure 2.6 Tilt angle for the plane of the CPC........................................................ 18

Figure 2.7 Tilt and twist angles for the plane of a CPC.......................................... 19

Figure 2.8 Effective azimuth and tilt angles for the plane of a CPC and angle of incidence for direct solar radiation ........................................................ 20

Figure 2.9 Radiation collection and acceptance angles for an arbitrary CPC layout ..................................................................................................... 22

Figure 3.1 Magnifying glass ................................................................................... 24

Figure 3.2 Cone concentrator (longitudinal profile) ............................................... 25

Figure 3.3 Off-axis aberrations (coma) for a parabolic trough mirror.................... 26

Figure 3.4 CPC configurations for different absorber types................................... 27

Figure 3.5 Projection of incoming solar ray on transverse CPC plane, normal to the surface.............................................................................................. 28

Figure 3.6 Edge-ray principle for 2D CPC ............................................................. 29

Figure 3.7 The CPC profile as compounded parabolic segments........................... 29

Figure 3.8 Irradiation profile and collection times for east-west orientation and north facing collector, i.e., twisted to the latitude angle........................ 31

Figure 3.9 Irradiation profile and collection times for north-south alignment and north facing collector, i.e., tilted to the latitude angle .................... 32

Novel approaches to the design of domestic solar hot water systems xxi

Figure 3.10 Irradiation profile and collection times for northeast-southwest aligned collector, tilted to the latitude angle ......................................... 33

Figure 3.11 Irradiation profile and collection times for northwest-southeast aligned collector, twisted to the latitude angle ...................................... 34

Figure 3.12 Irradiation profile and collection times for east-west aligned collector, twisted to the latitude angle and tilted east ........................... 35

Figure 3.13 Irradiation profile and collection times for east-west aligned collector, twisted to the latitude angle, tilted east & rotated 5° about its normal............................................................................................... 36




Figure 3.17 Irradiation profile and collection times for east-west aligned collector, with a 30° twist angle and a 20° tilt – summer solstice......... 40

Figure 3.18 Irradiation profile and collection times for east-west aligned collector, with a 30° twist angle and a 20° tilt – winter solstice ........... 41

Figure 3.19 Irradiation profile for a northwest facing collector with a 20° tilt, before and after a +25° ρ-rotation – summer solstice ........................... 42

Figure 3.20 Irradiation profile for a northwest facing collector with a 20° tilt, before and after a +25° ρ-rotation – winter solstice.............................. 43

Figure 4.1 Convection, conduction and radiation heat transfer (qc, qk, qr, respectively) for a hot plate exposed to a cool environment, Tp > Tair.. 47

Figure 4.2 Parallel flat plates with slats for convection suppression...................... 55

Figure 4.3 Corrugation parameters for circular ducts............................................. 58

Figure 4.4 Concentric cylinder arrangement for two radiating surfaces ................ 60

Novel approaches to the design of domestic solar hot water systems xxii

Figure 4.5 Thermal circuit schematics for heat transfer through the roof of a shed........................................................................................................ 62

Figure 4.6 Double pipe heat exchanger .................................................................. 65

Figure 5.1 Fluid element in a pipe section at height ‘h’ above reference level ...... 70

Figure 6.1 Sketch for the downward vapour heat transport SHWS........................ 76

Figure 6.2 CPC main plane rotations...................................................................... 83

Figure 6.3 CPC collection and acceptance angles .................................................. 84

Figure 6.4 CPC cross-section.................................................................................. 85

Figure 6.5 Heat transfer modes............................................................................... 87

Figure 6.6 Double cover model .............................................................................. 87

Figure 6.7 Thermal network resistance for the CPC heat transfer model............... 88

Figure 6.8 Solutions algorithm flow chart for simulation of heat transfer in the system and calculation of relevant parameters ...................................... 92

Figure 6.9 Assessment of heat losses for an experimental transfer line ................. 94

Figure 6.10 Truncated CPC profile used (scale 1:3)............................................... 100

Figure 6.11 Schematic of the fin and tube copper absorber ................................... 100

Figure 6.12 Absorber-boiler array of 7 fins & tubes connected to header/footer tubes and return water pipes prior to blackening (2nd prototype) ........ 101

Figure 6.13 Reservoir tank (from final prototype).................................................. 103

Figure 6.14 Hot water tank ..................................................................................... 104

Figure 6.15 Insulated vapour transfer line (trajectory indicated by red arrows) .... 104

Figure 6.16 CPC modules and 1st prototype ........................................................... 105

Figure 6.17 Vertical fin profile CPC mould before and after aluminium lining .... 105

Figure 6.18 Header tube of the 1st prototype and transfer line connection............. 106

Figure 6.19 Double-panel 2nd prototype with reservoir tank in the centre ............. 107

Figure 6.20 7-CPC module structure with reflective lining in metal case.............. 108

Figure 6.21 Single-module 3rd prototype with reservoir tank to the right .............. 110

Figure 6.22 Fin and tube copper array before and during maxorb layering ........... 110

Novel approaches to the design of domestic solar hot water systems xxiii

Figure 6.23 CPC structure with reflector material Silverlux™ (still covered with protective foil) and maxorb-lined boiler array .................................... 111

Figure 6.24 Steam production from 3rd prototype .................................................. 111

Figure 6.25 Collection and orientation layout for 3rd prototype showing collector and reservoir on the roof and the storage tank at ground level ........... 112

Figure 6.26 Performance plots for variations in CPC wall reflectance .................. 114

Figure 6.27 Performance plots for single- and double-cover collector models...... 115

Figure 6.28 Total steam production for a typical CPC panel over 5 hours ............ 118

Figure 6.29 Steam power produced for various CPC concentration ratios ............ 119

Figure 6.30 Daily steam energy produced for various CPC concentration and emittance values .................................................................................. 120

Figure 6.31 Efficiency results for the 1st CPC prototype........................................ 121

Figure 6.32 Efficiency results for the 2nd CPC prototype....................................... 122

Figure 6.33 Efficiency results for the 3rd CPC prototype ....................................... 124

Figure 6.34 Prototypes performance comparison ................................................... 125

Figure 6.35 Water tank temperature for no-load conditions over 6 consecutive clear days............................................................................................. 126

Figure 6.36 Hot water storage tank, transfer pipe and condensate receptacle........ 128

Figure 6.37 Water tank temperature for no-load conditions over 12 consecutive days showing stagnation water temperature........................................ 133

Figure 7.1 Sketch for the air-to-water heat exchanger-coupled tank SHWS........ 136

Figure 7.2 Longitudinal view for 3 different air-heating flat-plate solar panels .. 140

Figure 7.3 Transverse view for 2 different air-heating solar panels with multi-channel absorber plates ....................................................................... 140

Figure 7.4 Longitudinal view for 2 different air-heating flat-plate solar panels using alternative absorber type............................................................ 141

Figure 7.5 Transverse view of 1st prototype with a V-shaped absorber panel and triangular fins ...................................................................................... 144

Figure 7.6 Heat transfer modes for a) double channel flat and b) V-shaped absorber configurations ....................................................................... 145

Novel approaches to the design of domestic solar hot water systems xxiv

Figure 7.7 Thermal resistance network for absorber panel configurations of Figure 7.6............................................................................................. 148

Figure 7.8 Pipe section / schematic for air pipe heat loses to the environment .... 149

Figure 7.9 Thermosiphon and hot water stratification for the SHWS heat exchanger and tank .............................................................................. 152

Figure 7.10 V-corrugated absorber panel with fins and polystyrene housing ........ 162

Figure 7.11 1st prototype air heater absorber panel with air diffuser sections and double cover ........................................................................................ 162

Figure 7.12 1st prototype air heater panel on movable tilted base .......................... 163

Figure 7.13 1st prototype on work bench with fan blower and variable power supply .................................................................................................. 164

Figure 7.14 Devices used in the determination of airflow rates ............................. 164

Figure 7.15 2nd prototype large scale air heater panel on tilt-adjustable frame ...... 165

Figure 7.16 Absorber panel profile and panel construction.................................... 166

Figure 7.17 Heat exchanger employed in the SHWS ............................................. 167

Figure 7.18 Hot water tank and heat exchanger ..................................................... 168

Figure 7.19 Upper view of centrifugal fan-blower attached to heat exchanger...... 169

Figure 7.20 2nd prototype air heater panel & SHWS in operation .......................... 170

Figure 7.21 Measurement of pressure drop in mm H2O gauge across a pipe section.................................................................................................. 172

Figure 7.22 Output air temperature vs. airflow rate for different panel configurations ...................................................................................... 174

Figure 7.23 Collector efficiency vs. airflow rate for different panel configurations ...................................................................................... 174

Figure 7.24 Output air temperature vs. airflow rate for finned V-corrugated absorbers for an input air temperature of 20°C ................................... 177

Figure 7.25 Efficiency vs. airflow rate for a V-corrugated absorber of various fin lengths.................................................................................................. 177

Figure 7.26 Output air temperature vs. airflow rate for finned V-corrugated absorbers for an input air temperature of 60°C ................................... 178

Novel approaches to the design of domestic solar hot water systems xxv

Figure 7.27 Efficiency vs. airflow rate for a V-corrugated absorber of various fin lengths ................................................................................................. 178

Figure 7.28 Output air temperature vs. airflow rate for input air at 20°C and different panel configurations ............................................................. 179

Figure 7.29 Efficiency vs. airflow rate for input air at 20°C and different panel configurations...................................................................................... 180





Figure 7.34 Variation of the ouput air temperature for 20°C input air based on different D/L ratios.............................................................................. 183

Figure 7.35 Efficiency air temperature for 20 °C input air temperatures based on different D/L ratios.............................................................................. 183

Figure 7.36 Variation of the ouput air temperature for 40°C input air based on different D/L ratios.............................................................................. 184

Figure 7.37 Efficiency air temperature for 40 °C input air temperatures based on different D/L ratios.............................................................................. 184

Figure 7.38 Experimental and numerical temperature variations vs. time of the day for the elements of the 2nd prototype air heater panel and SHWS in open loop mode ............................................................................... 186

Figure 7.39 Experimental results and numerical fit for determination of exchanger effectiveness (eq. 7.24) for an airflow rate of 61 L/s in open loop mode ................................................................................... 187

Figure 7.40 Experimental measurements and numerical predictions for power delivered to the water vs. exchanger output air temperature for various thermosiphon pipe radii (eq. 7.22) and for an airflow of 61 L/s in open loop operation.............................................................. 188

Novel approaches to the design of domestic solar hot water systems xxvi

Figure 7.41 Experimental temperature variations and numerical predictions over a wide range of irradiance values for the 2nd SHWS prototype in open loop mode ................................................................................... 189

Figure 7.42 Experimental and numerical output air temperature variations for the 2nd prototype air heater panel vs. time of the day in open loop mode.191

Figure 7.43 Experimental results and numerical prediction for power delivered to the water vs. time of the day for open loop operation and for 61 L/s airflow ...................................................................................... 192

Figure 7.44 Temperature measurements for a vertical profile of the water in the storage tank for open loop operation of the system and for 61 L/s airflow.................................................................................................. 193

Figure 7.45 Experimental and numerical temperature variations vs. time of the day for the elements of the 2nd prototype air heater panel and SHWS in closed loop mode............................................................................. 194

Figure 7.46 Experimental results and numerical fits for determination of exchanger effectiveness (Equation 7.24) for an airflow rate of 63 L/s in open loop mode ............................................................................... 195

Figure 7.47 Experimental measurements and numerical predictions for power delivered to the water vs. exchanger output air temperature for varius thermosiphon pipe radi (eq. 7.56) and for an airflow of 63 L/s in closed loop operation....................................................................... 196

Figure 7.48 Experimental temperature variations and numerical predictions over a wide range of irradiance values for the 2nd SHWS prototype in closed loop mode................................................................................. 197

Figure 7.49 Experimental results and numerical prediction for power delivered to the water vs. time of the day for 63 L/s airflow in closed loop mode .................................................................................................... 198

Figure 7.50 Temperatre measurements for a vertical profile of the water in the storage tank for 63 L/s airflow in closed loop mode ........................... 199

Figure 7.51 Schematic of conveyance infrastructure: pipes, elbows, fittings and other elements...................................................................................... 200

Figure 7.52 Pressure drop measurement setup for water flow in the heat exchanger............................................................................................. 205

Novel approaches to the design of domestic solar hot water systems xxvii

Figure 7.53 Experimental measurements for pressure drops vs. water flow rates in the heat exchanger and equation fits showing a linear response below 12 cc/s ....................................................................................... 206

Figure 7.54 Experimental measurements for the modified effectiveness vs. water flow rates in the heat exchanger and exponential equation fits to the data ...................................................................................................... 210

Figure 7.55 Experimental measurements for the modified effectiveness vs. ‘ Cm ⋅& ’ product quotient between water and air. An exponential equation fits the data well.................................................................... 210

Figure 7.56 Predicted values for modified effectiveness vs. water flow rate from the exponential expression of Equation 4.74 ...................................... 211

Figure 7.57 Variation of exchanger efficiency vs. water flow rate obtained from the experimental fit for modified effectivness .................................... 213

Figure 9.1 Original near-horizontal heat exchanger and proposed vertical arrangement for hot water stratification .............................................. 238

Figure B1 General optical system and the étendue invariant ............................... 255

Figure B2 The étendue for a general optical system (measure of angular displacement shown for y-coordinate) ................................................ 256

Figure B3 Two dimensional concentrator of acceptance angle 2θ and output angular range 2θ’................................................................................. 256

Figure C1 Construction of the CPC profile.......................................................... 258

Figure C2 Comparison of the fraction of radiation incident on the aperture of a CPC for different CPC scenarios (assuming perfect reflectivity) ....... 261

Figure C3 Compound parabolic profile for the horizontal absorber concentrator261

Figure C4 Truncated CPC .................................................................................... 264

Figure D1 Friction factors for vs. Reynolds number for various pipe roughness and diameter ratios and for laminar, transitional and turbulent flow .. 268

Figure G1 Plots of the linear fits for thermal diffusivity, kinematic viscosity and thermal conductivity of air vs. temperature.................................. 286

Figure G2 Plots of polynomial fits for specific heat and density of air vs. temperature.......................................................................................... 287

Novel approaches to the design of domestic solar hot water systems xxviii

Figure G3 Plots of the polynomial fits for selected physical properties of air vs. temperature .......................................................................................... 289

Figure H1 Picture-schematic of original heater core used as a heat exchanger.... 290

Figure H2 Picture-schematic of the fan/blower.................................................... 291

Figure I1 Speed profile for airflow in the pipes vs. transverse distance and polynomial fit ...................................................................................... 293

Figure I2 Correlation between anemometer readings and known air speed values showing a strong linear fit to the data. ..................................... 294

Novel approaches to the design of domestic solar hot water systems xxix

List of Tables

Table 1.1 Sizing recommendations for SHWS ....................................................... 8

Table 1.2 Energy and water volume targets for SHWS design............................... 9

Table 2.1 Quantities in Sun-Earth geometry ......................................................... 15

Table 6.1 Assumed efficiencies for basic system components ............................. 76

Table 6.2 Assumed energy and power requirements: Mode #1 ............................ 77

Table 6.3 Average irradiance and minimum collector area required: Mode #1.... 78

Table 6.4 Assumed energy and power requirements: Mode #2 ............................ 78

Table 6.5 Average irradiance and minimum panel area required: Mode #2 ......... 78

Table 6.6 Water conditions and required mass for boiling ................................... 79

Table 6.7 Real heat transfer modes in the system ................................................. 86

Table 6.8 Simplified heat exchange modes........................................................... 87

Table 6.9 Heat transfer model parameters for thermal network of Figure 6.7...... 89

Table 6.10 Numerical results for a panel with a single cover (no sheath) and for various absorber emittance values......................................................... 93

Table 6.11 Efficiency prediction for all prototypes .............................................. 125

Table 6.12 Collector efficiency parameters........................................................... 126

Table 6.13 Energy collection and heat losses for the water in the tank ................ 127

Table 6.14 Prediction of average system steam for truncation effects and different pipe losses from the plots of Figure 6.30 ............................. 129

Table 7.1 Assumed efficiencies for basic system components ........................... 135

Table 7.2 Assumed energy and power requirements for 6-hour operation ......... 136

Table 7.3 Average irradiance for minimum absorber area required during OPEN LOOP operation mode ............................................................. 138

Table 7.4 Average irradiance for minimum absorber area required during CLOSED LOOP operation mode ........................................................ 139

Table 7.5 Heat transfer model parameters for thermal network of Figure 7.7.... 147

Novel approaches to the design of domestic solar hot water systems xxx

Table 7.6 Numerical results for the complex double cover profile of Figure 7.22 for various airflow rates (Figure 7.6a absorber profile) ........................ 175

Table 7.7 Theoretical and experimental pipeline pressure drops.......................... 201

Table 7.8 Comparison of different values for the thermosiphon effective radius 207

Table 8.1 Projected costing for the first system developed.................................. 225

Table 8.2 Projected costing for the second system developed............................. 228

Table 8.3 Tentative sale prices for commercial versions of the SHWS............... 229

Table 9.1 Proposed materials for construction of the solar air heater panel: insulation, body structure and outer casing ......................................... 242

Table A1 Input/Output data for the solar geometry modelling program............. 254

Table E1 Modelling relationships ....................................................................... 270

Table G1 Thermal diffusivity and kinematic viscosity for air at atmospheric pressure................................................................................................ 285

Table G2 Thermal conductivity, specific heat and density for air at atmospheric pressure ........................................................................... 285

Table G3 Selected properties for water at atmospheric temperature .................. 288

Table H1 Specifications for the heat exchanger core.......................................... 290

Table H2 Specifications of the fan/blower motor ............................................... 291

Novel approaches to the design of domestic solar hot water systems xxxi

Statement of Original Authorship

The work contained in this thesis has not been previously submitted for a degree or

diploma at any other higher education institution. To the best of my knowledge and

belief, the thesis contains no material previously published or written by another

person except where due reference is made.

Signed:

Date:

Novel approaches to the design of domestic solar hot water systems xxxii

Novel approaches to the design of domestic solar hot water systems xxxiii

Acknowledgments

It is interesting how one can have different, or opposing, opinions on similar subjects

at different times of one’s life. Sometimes these might seem so contradictory that one

is left questioning how could it have ever been possible to think/act/talk/feel the way

we did before. What can be very good or pleasant at some point could become the

opposite at a later stage and vice-versa.

I had a very different view when I started this project: what I expected and wanted

and –most importantly– the reasons why I thought it was valuable. Most of it has

changed for the better.

The project has had much more value than what I anticipated and for reasons I had

not considered back then. I have greatly benefited from the interactions with other

people, which besides from the acquisition and use of academic knowledge for the

development of this venture, have allowed me to see, consider and honour other

probably even more significant aspects of humanness. The constant struggle for

“happiness” and the life we craft trying to achieve this has made me feel that it

ultimately all means a state of being/mind/existence, which apparently little has to do

with externalities but more with how we interact, bond and connect with other fellow

beings. For me, this PhD has been another milestone in the constant search for this

state and I acknowledge it as such, with its pleasant and not so pleasant events, and

am grateful to the Universe for having been able to live it.

There are many that have been part of this conjunct journey. The following is by no

means a comprehensive list and I apologise beforehand if anyone who reads this

feels left out. I do not want to be unfair to anyone, but I will address a few people

that clearly stand out:

First and foremost I wish to express my deep appreciation to my principal supervisor,

Ian Edmonds, whom from the start continuously and steadily supported me offering

his unconditional assistance in all matters related to this project. He provided the

testing facilities and on site tools that enabled the practical aspects of the project to

be carried forward from the start up to its completion. What most impressed me,

Novel approaches to the design of domestic solar hot water systems xxxiv

however, is Ian’s total focus on the creation and promotion of benevolent aspects of

technology in society and how he devotes himself wholeheartedly to such pursuits,

helping in the process those that come near him in a equally embracing way. This is

admirable. Maria, Ian’s wife, was always very dear to me, and supportive in any way

she could during the extensive periods I spent at their place. She treated me like a

member of her family and this is something for which I will remain always grateful.

My associate supervisor, Greg Michael, also provided very useful and timely

support, complementing the supervisory role shared by him and Ian. It was actually

thanks to Greg back in 2000 that I first knew about the possibility of doing this PhD

and it was after we spoke about it that everything was set in motion. Greg provided

his own, refreshing, view in tackling different problems, suggesting alternate

solutions drawn from his unique experience as a scientist and lecturer. At times he

was also a good devil’s advocate engaging the team in a pseudo-Socratic method of

discovery in the search for the solution to obstacles. Dear supervisors, I would

certainly enjoy the opportunity to continue working with you both in any related

projects and research that may become available in the future.

Special thanks go to our industry partner, Peter Sachs Industries Pty Ltd, for their

input and assistance during the first stage of the project in relation to the vapour

downward heat transport system. The interaction with them provided very useful

insight, particularly into the commercial and manufacturing areas of this technology,

so necessary in the comprehensive assessment of the feasibility of the solar hot water

units developed as domestic hot water alternatives.

Although I spent most of my time outside university premises during this research, I

recognise and am grateful for the help provided by academic and administrative staff

working “behind the scenes” so that everything ran smoothly for me. I am sure there

are many I am not even aware of. To all of you, a big THANK YOU for helping me

out. I particularly wish to thank Elizabeth Stein for her ongoing support in this regard

with her quick and sharp on-the-spot answers and solutions to every question I had

and situations in which I were involved. A/P Brian J Thomas was always there,

providing support and counsel when it was most sought with the distinct kindness

and care for the student that characterise him. The School of Physical Sciences aided

Novel approaches to the design of domestic solar hot water systems xxxv

me financially in the attendance of a paper presentation at the 2001 International

Solar Energy Society congress held in Adelaide. This was a great opportunity that

exposed me for the first time to the broader academic and current developments of

technologies in this field. I am most appreciative for this assistance.

There are those who have helped me indirectly in this process and their input and

support at earlier stages of my life has made it possible for me to be where I am now.

My mother and father are top on this list, together with my ‘other’ mom (my nanny).

They have not only given me all the emotional and physical support from very early

in life but have also supported me during the PhD to the best of their ability (despite

living on the other side of the world). My sisters are included here as well, with their

best wishes and unflinching faith in me.

My family-friends in the faith are next. They all cheered my decision of going ahead

with this research and remained excited and positive throughout, reminding me of the

greater good in all actions we engage ourselves in when done selflessly. Particular

thanks go to Venkat and Tim for their direct input during the final editing process.

Venkat, you are THE rock for all the youth and for everyone who crosses your path.

A special thanks to my dear friend, Ross Thompson, who provided invaluable

support with his simple, yet empowering self-insight techniques and methods for the

uncovering and development of human potential. I enjoyed every moment I spent in

your company and consider myself fortunate for having had that chance.

My last words of appreciation go undoubtedly to my wife, Mila. She has certainly

been there throughout these years of continuous ups and downs, taking the role of

nurturing wife and best friend with the utmost love for me. Thank you, my dear, for

your effort and care ☺.

Brisbane, 17 December 2004

Chapter 1 - Introduction

1.1 Solar energy and domestic solar hot water production

Most forms of energy available on Earth are a direct or indirect expression of solar

energy. It either manifests as kinetic or thermal energy, or is stored as chemical

energy in plants (photosynthesis). The direct expression of solar radiation as heat is

the most palpable form of solar energy we can experience. Past and present

implementation of solar energy applications1 (eg. solar clocks, passive solar

architecture) have demonstrated its usefulness.

Domestic hot water has been a common need in society. In the past, the heating of

water was only achievable by using energy extracted from the burning of renewable

(mainly wood) and non-renewable (gas, coal, oil) resources. With the advent of

electricity, electric domestic hot water systems have become mainstream, together

with the more refined gas water heaters that rely on the non-renewable fuel.

Depending on the nature of electricity production, it can have a high impact on the

environment by increasing greenhouse gases due to the burning of coal, oil and gas

in electricity power plants. In Economics, this is evidenced in the so-called

“externality costs”2, which is the ongoing financial burden borne by society as a

whole and not reflected in market transactions.

In any case it has an associated high cost to produce and –very importantly– has an

invasive effect on our biosphere. Solar energy on the other hand is environmentally

safe and totally free. Solar energy is "clean" energy.

Domestic solar hot water systems (DSHWS) have been developed in Australia with a

commercial aim since the 1960s. They date back to 1964 involving the Department

of Mechanical Engineering-CSIRO3, Australia. Patents had been sought for solar air

heating systems (SAHS) to heat water even before4 this. Since then, full commercial

development of the now well-known thermosiphon solar hot water system has led to

many modifications, refinements and improvements over the original designs.

Novel approaches to the design of domestic solar hot water systems


2

Currently, there are two mainstream types of SHWS: the passive thermosiphon

close-coupled system and the pump-driven remotely-coupled system. The description

and operation of commercial SHWS is widely available in the literature (for

additional information, refer to bibliography). However, a brief explanation of the

operation and benefits of the two basic systems is given next.

1.2 Conventional SHWS

Most solar hot water systems (SHWS) consist of three basic parts:

• Collector panels with heat absorbing media

• Circulation system for hot fluid

• Water storage tank

Solar radiation reaching the collectors is converted into heat and a proportion of the

heat is transferred to the tank by the circulation system. This allows the supply and

temporary storage of hot water for a house or building. These systems are used for

domestic and commercial solar hot water heating. The systems are usually mounted

on rooftops and, as mentioned above, are classed as close-coupled or remotely-

coupled, depending on the location of the storage tank in relation to the panels.

The basic configuration of a thermosiphon (close-coupled) hot water system and

system components is depicted in Figure 1.1:

Figure 1.1 A conventional close-coupled thermosiphonic solar hot water system



3

Purpose of each of the components

Collectors: Their function is to efficiently convert solar radiation to heat and

transfer the heat to the liquid, which flows through the circulation system. In the

simplest of systems, the liquid is the water to be heated and there is no exchange

compartment in the tank. There are two types of collectors:

i) Plate and tube: An absorber plate made of copper or aluminium to which

copper pipes are bonded.

ii) Flooded plate: An absorber plate which is made by bonding together

moulded sheets of metal (usually of mild steel) containing channels

through which liquid may flow.

Storage tank: This is the reservoir for the heated water, which has been

transferred by the circulation system. There are two types of storage tanks; low

pressure copper and high pressure steel. Mains pressure tanks are usually vitreous

enamel lined to protect the steel from harsh water conditions and are fitted with a

sacrificial anode in electrical contact with the steel that will corrode first if cracks

in the enamel appear. The anode has to be replaced every 5 years.

Circulation system: In a close-coupled configuration, the circulation system is

usually a natural thermosiphon process. As the liquid heats it becomes less dense

and rises towards the tank. It enters the top of the tank while the cooler liquid

leaves the bottom and flows into the collectors.

Control and protection system: This is a combination of valves designed to

maintain pressure and temperature levels in the tank below specified levels.

Auxiliary heater: This is the backup system for heating water when solar energy

is insufficient. It is usually electrically or gas operated.

Heat dump: This is a protruding attachment from the tank to the exterior for

dumping heat to the surroundings when the hot water approaches boiling point.



4

Conduction, convection and radiation losses are minimised by the use of bulk

insulation of the collectors and storage tank. Convection is reduced by the use of

transparent covers (usually glass) over the absorber plate. Radiation from the

absorbers is also reduced by the use of selective surface materials with high

absorptance for solar radiation and low emittance in the thermal spectrum.

All forms of domestic solar water heating used extensively today are variations of the

original thermosiphon hot water system.

Collector improvements have been mainly achieved in better automated and

expedited production processes as well as in the use of better solar selective surfaces

for panel absorbers. Water storage tanks have been modified to include heat

exchanger compartments with heating fluids, other than water, used in the circulation

system. This is especially useful for regions where freezing conditions can occur.

Tank construction and internal wall linings, sacrificial anodes, insulation, etc, have

also been subject of better engineering and manufacturing standards.

The market has also seen the introduction of some SHWS using concentrating

collectors and evacuated tube collectors instead of flat collector plates with the

promise of added advantages. To date, solar hot water systems of this and other kinds

are being produced in China, Portugal, Spain, Israel, Turkey, Australia and the USA.

In Australia, Federal and State governments are actively encouraging the use of

alternative, environmentally friendly, energy sources as a replacement for fossil fuel

dependence by means of industry and community awareness programs in the form of

legislation, subsidies and grants. The Queensland Government is currently offering

rebates5 of up to $750 per household for the installation of new SHWS. The rebate

scheme is intended to last until the end of 2005. The Federal Government has a

Renewable Energy Certificates scheme6 through which further savings, up to $1500,

can be made on the purchase price. Each eligible solar water heater has a deemed

amount of these certificates associated with it, and they can be either assigned or

traded (sold) to receive a financial benefit. Additionally, some manufacturers offer

additional discounts on their product range that combined with the rebate and

certificates can add up to substantial savings for the end-user. Considering that a



5

typical SHWS costs between $2000 and $3000, the savings may offset the original

price bringing the net cost close to that of a conventional electric hot water system

($700-$1100). Despite this and due to the lack of community awareness on the

subject, general perception is that SHWS are an expensive option and so, penetration

of SHWS in Queensland and Australia, generally, is still low.

1.3 Problems and disadvantages with existing systems

There are two main characteristics of conventional SHWS that can be considered

problematic or non-advantageous. In thermosiphon systems, requiring the tank to be

placed above the panels can be a source of inconvenience for various reasons:

installation difficulty, stress placed on rooftops, servicing and repairing difficulties,

non-integration with architectural concepts (aesthetics), decommissioning difficulty.

The disadvantage of remotely-coupled systems is the added complexity of a pump

and associated control system and the additional running and maintenance costs.

As part of this project, two new SHWS were developed together with a simulation

model that predicted the performance of these

1.4 Aims and objectives

The study set out to explore and design DSHWS without the inconveniences

mentioned above. The objectives were:

- Development of a collector-boiler steam generation passive downward heat

transfer prototype for solar water heating

- Development of an air-to-water heat transfer prototype for solar water heating

- Assembly of a full scale domestic SHWS with the above devices

- Usage of low cost, “off-the-shelf” and environmentally friendly materials

- Field-testing and comparison of experimental results with prediction models

- Economic analysis and feasibility as an alternative to current SHWS



6

1.5 Brief outline of approach to new designs

In the first system7 (Figure 1.2), from water stored in a small roof level reservoir,

energy concentrating panels produce steam that travels downwards to a ground level

water tank.

Figure 1.2 Schematic for the vapour phase downward heat transport SHWS

Through a heat-exchanging copper loop inside the tank, steam gives up heat to the

water, condenses in the process and flows into a collection tank. After daily

operation, when the system cools down the unit recharges itself by drawing the

condensate formed during the day back up to the reservoir tank due to the partial

vacuum formed in the panels. This is a self-pumped system requiring no control

mechanisms or the aid of active (e.g. pump) or passive (e.g. valve) components to

operate.

The second system (Figure 1.3) is based on an air-heating solar panel. A fan-blower

delivers the hot air into a radiator type heat exchanger, which is connected to a hot

water tank. Despite requiring the use of active components, it was less expensive to

manufacture and install thatn the steam based system

Condensate tank

Steam heat exchanger

(optional: heat exchanger coil for indirect hot water draw-off)

Hot water tank

Footer pipe

Header

Water heater & boiler panel

Down-coming Steam

Water reservoir



7

Figure 1.3 Schematic for the air-to-water heat exchanger-tank coupled SHWS

The design of these two systems went hand-in-hand with the study and development

of theoretical models that could predict their performance with reasonable accuracy.

Chapters 2 through 5 give the basic theory of solar geometry, concentrating optics,

heat transfer, fluid mechanics and hydraulics used to simulate performance. Chapter

6 deals with the steam generator system and chapter 7 deals with the air heater

system. Chapter 8 gives a brief economic appraisal for each system. General

conclusions, discussions and speculation for future work are given in chapter 9

1.6 Rationale behind the selection, construction and operation of

the designs developed

The Australian Greenhouse Office (AGO) has suggested that the average use of hot

water in a domestic situation is about 50 L per person per day. This has been used by

state government institutions in advisory fact sheets and technical notes8-9

10 as a

guideline in the selection of household SHWS. For a family of four, this equates to

Hot water tank

Fan/blower

Air Heater Panel

(optional: return pipe forclosed-loop operation)

Hot air

Heat exchanger



8

200 L daily usage. Also, it is necessary to be able to store additional amounts of hot

water for times when the weather does not provide sufficient insolation. Suggested

figures for SHWS sizing9 are given in Table 1.1:

Table 1.1 Sizing recommendations for SHWS

No. of persons served

Hot water delivery (L/day)

Approximate tank size (L)

1-2 120 180

3-4 200 300

5-6 300 440

It is possible to obtain near boiling point temperatures with conventional domestic

hot water systems. However, it is sufficient to have temperatures between 60°-70°C

for all domestic activities. A storage temperature of around 60°C is the maximum

advisable10F

11 for pressurised water storage tanks that work with direct draw-off (water

displacement tanks). For non-pressurised tanks, heat is drawn-off indirectly by mains

water passing through an immersed heat exchanger coil in the hot water (see optional

attachment in Figure 1.2). In this case the water storage temperature must be higher,

about 70°C, in order to provide enough heat transfer from water-to-coil to obtain a

hot water output comparable to that of pressurised tanks. The two SHWS of the

project were designed for use with non-pressurised tanks. The reasons for this are

listed below:

- The non-pressurised hot water tank with electrical heating element is the least

expensive tank option available. These tanks do not require strengthening to

withstand high pressures (0.5 mm sheet copper tank is adequate) and do not

have the associated maintenance inconveniences of mains pressure tanks,

where valves and sacrificial anodes must be replaced.

- The tanks have been used in Queensland for over 50 years and perform very

well when properly sized for domestic requirements.

- The tanks allow the possibility of retrofitting a solar hot water option of the

type described in this work via an extra pair of inlet and outlet ports.



9

Both systems were designed to have the storage tanks at ground level. Reasons for

this are:

- The tank is located where it can be serviced easily

- There is the possibility of better shelter from the elements (less wear, less heat

losses)

- Reduction of installation costs (no lifting of tanks or accommodation on roofs)

- Reductions of other collateral costs like roof reinforcing for heavy water tanks

- Better integration with pre-existing architecture (less invasive, better

aesthetics)

The following energy target was then chosen for the design of both SHWS:

Table 1.2 Energy and water volume targets for SHWS design

Daily heating requirement: 200 L of water by 30 °C – 35 °C

Energy required: 25 – 30 MJ

The target figure of 30 MJ/day corresponds to the recommended peak daily thermal

load for large SHWS sizing for low-latitude regions of Australia11F

12 (e.g., most of

Queensland).

The reader may wish to turn directly to chapters 6 and 7, which describe the

development of the two novel SHWS and where reference is made to the basic

theory (chapters 2, 3, 4 and 5) as required.

Chapter 2 - Solar radiation and solar geometry 2.1 Introduction

Prediction of SHWS performance over time requires the knowledge of, and the

capacity to model, solar irradiation patterns and trends for objects of arbitrary shapes

under different conditions and locations worldwide.

2.2 Solar energy and solar radiation

The amount of energy per unit time per unit area received from the sun outside the

earth’s atmosphere at the mean earth-sun distance is termed the solar constant, GSC.

A value of (1367 ± 23) W/m2 is used by many references 12F

13. The extraterrestrial

radiation, however, will vary due to the earth’s elliptical orbit around the sun with

the consequential variation in the earth-sun distance. An approximate expression for

extraterrestrial radiation as a function of the day of the year13F

14 is given in Equation

2.1.

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅⋅+⋅=

36536003301 ncos.GG SCo (2.1)

n is the day number starting from the beginning of a calendar year, i.e., 1 < n <365

The amount of incoming radiation that is not reflected back into space is attenuated

by the earth’s atmosphere due to absorption and scattering. Direct or beam radiation

reaches the surface with very little directional change. Radiation from the rest of the

sky hemisphere that has been scattered and eventually reaches the surface is termed

diffuse radiation. The combination of both direct and diffuse radiation is termed

global radiation.

The measurements of solar radiation in this study are all measurements of global

radiation.


Chapter 2 - Solar radiation and solar geometry

11

2.3 Air mass atmospheric transmittance model

Direct radiation on its way to the surface will traverse a certain atmospheric distance,

which will depend on the solar altitude angle, α (Figure 2.1). It is this distance that

accounts for attenuation of all sorts. It is minimum when the sun is directly above the

point of consideration (zenith point or maximum altitude angle, α = 90°).

Figure 2.1 Solar radiation travel distance through the atmosphere

Attenuation in the atmosphere can be quantified from Bouger’s Law for attenuation

of monochromatic light in a gas:

∫⋅=

⋅−D

dxk

, eI)l(I 00

λ

λλ (2.2)

Where kλ is the position- and wavelength-dependent (monochromatic) attenuation

coefficient and D is the distance travelled in the gas.

Solar radiation is not only not monochromatic, but the attenuation coefficients are

strongly dependent on the position of travel. To determine the attenuated irradiance

an approximation can be made by assuming a single, overall, attenuation factor, ‘K’

which varies with distance:

ldK

)l(cb

l

eGG∫

⋅=⋅−

00 (2.3)

The integral of Equation 2.3 is also known as the optical depth of the medium, τod(l).

For normal solar incidence (α = 90°), l = l0, and if τod(lo) = τo, the expression for direct

normal solar radiation is:

α

O

S Z

Earth’s surface

Atmosphere limit

Sun Zenith

l0 l



12

oeGGcbNτ−⋅= 0 (2.4)

GcbN represents the irradiance value on the surface of the earth for perpendicular

incidence arising from direct radiation.

For different solar altitude angles (from Figure 2.1):

αsinm

ll 1

0

≈= (2.5)

The quantity m, known as air mass ratio, is the ratio of an oblique path through the

atmosphere to the path when the sun is directly overhead. The approximation to the

right of Equation 2.5 may be used for solar altitude angles above 20° at sea level.

From this it is possible to formulate a general relationship for irradiance on the

surface for any solar altitude angle: m

cb eGG ⋅−⋅= 00

τ (2.6)

There are several approximations and empirical relationships offering closed forms

and ease of calculation for Gcb and the air mass ratio.

In this study the following expressions for global irradiation and air mass ratio have

been used14F

15:

( ) 584342 6146141229 .h

esinsinm −⋅⎥⎦

⎤⎢⎣⎡ ⋅−⋅+= αα (2.7)

2

0950650

0

m.m.cb ee

GG ⋅−⋅− +

= (2.8)

The air mass ratio is corrected for altitude15F

16, h. The relation 0GGcb is also called the

atmospheric transmission factor, or just atmospheric transmittance, τatm.

Irradiation on a flat surface, Gcb, is:

incatmcb cosGG θτ ⋅⋅= 0 (2.9)

where θinc is the angle between the surface and the solar beam.



13

2.4 Sun-earth geometry

Solar energy input on collector panels is dependent on the following factors:

- Date & Time

- Latitude

- Climatic conditions

- Collector panel orientation

- Geometric properties of the solar collector

The earth’s axis is tilted at an angle of 23.45° relative to the orbital plane. This tilt is

the main cause of the seasonal variations as the earth orbits the sun. It is convenient

to assume an apparent daily motion of the sun across the sky for all solar geometrical

calculations. This motion varies cyclically throughout the year and is defined by the

angle of declination, δ (Table 2.1). This angle varies ±23.45°, affecting the angle of

incidence of solar radiation on the surface of the earth and causing seasonal

variations in the length of the day.

For an observer on earth, the position of the sun can be completely specified by the

solar altitude angle, α, and the solar azimuth angle, ϕS. (Figure 2.2). These

quantities define the solar vector, VS.

(a) (b)

Figure 2.2 Sun path diagrams for seasonal times for a temperate austral latitude

N

Noon

8 am

6 am mid-winter

mid-summer Equinoxes

23.45°

23.45°

-40° Lat.

N

S α

ϕS

Summer

Winter

Equinox

W

Noon

8 am

6 am

VS



14

The time used in solar charts, diagrams and calculations is the solar time, ST, which

is often different from local standard time, LST, as this can apply over several

degrees of longitude (and 1° of longitude is equal to 4 minutes of standard time).

( ) ETminllLSTST localST ⋅⋅−+=o

4 (2.10)

lST and llocal are the standard time meridian and the local longitude, respectively. ET

is the equation of time, which is a correction factor that accounts for irregularities in

the earth’s speed around the sun.

Another fundamental quantity is the hour angle, hs, based on the 24 hours required

for the sun to “move” 360° around the earth.

omin

noonsolarlocalfromutesminhs

4= (2.11)

The determination and profiling of solar irradiance on panels of arbitrary orientation

is expressed in terms of panel azimuth, tilt, angle of incidence and solar altitude

angle, which, in turn, are related to the more fundamental quantities of hour angle,

latitude and declination. These quantities are summarised in Table 2.1

Solar geometry and sun-earth geometric relationships are well known and

documented in several sources16F

17,17F

18. Methods for determining solar radiation falling

on arbitrary tilted and tracking flat surfaces are also readily available18F

1919F20F

-21F

22.

The method is much more complex for a system of limited collection times, like

many types of concentrating collectors, and in particular the geometry of the

compound parabolic collectors (CPC) used in this project and explained in detail in

chapter 3. CPC collection times depend on their design, layout and orientation. While

a flat plate collector lying horizontally on the ground will collect sunrays for the

whole day, a concentrating device or CPC will collect for a limited time, due to a

restricted collection angle, θa < 90° (Figure 2.3)



15

Table 2.1 Quantities in Sun-Earth geometry

Quantities Description

Solar altitude angle, α The angle between the horizontal and the line to the sun.

Solar zenith angle, θz The angle between the vertical and the line to the sun.

Solar azimuth angle, ϕS The angle between a due north line0F

∗ and the projection of beam radiation on the horizontal plane.

Latitude, φ The angular location north or south of the equator.

Declination, δ The angular position of the sun at solar noon (i.e., when the sun is on the local meridian) with respect to the plane of the equator.

Hour angle, hs The angular displacement of the sun east or west of the local meridian due to rotation of the earth on its axis.

Angle of incidence, θinc The angle between the beam radiation on a panel and the normal to that panel.

Panel tilt angle, θ The angle between the surface of the panel and the horizontal plane.

Panel azimuth angle, ϕ The angle between the projection of the line-axis of the panel normal to the horizontal plane and due north line.

Atmospheric transmittance, τatm

Determined by natural and induced climatic conditions and geographical location.

Figure 2.3 Collection angle comparison between a flat plate and a concentrator

The general process for determining radiation collected by a solar panel over a day

involves:

1. Specifying the orientation of the panel

2. Determining the position of the sun in the sky over the day

3. Determining radiation intercepted over the day (for how long and in what way

the absorber elements of the panel “see” the sun)

∗ This definition holds for locations in the southern hemisphere. The converse is true (due south line) for the northern hemisphere.

Concentrating collector

θa

Flat plate collector

θa = 90°



16

For flat plates it is enough to specify azimuth and tilt angles to define the collectors'

layout because of symmetrical properties. For any orientation, (i.e. any combination

of azimuth and tilt angles) a collector of this type can be rotated by any angle, ρ,

about it’s normal and still have the same available incoming solar radiation. This is

not the case for a CPC panel, where additional angles are required to properly

determine energy collection times. The irradiance falling on the input plane of a CPC

panel will be the same as for a flat plate panel, but the actual collection times which

are dependent on the geometrical construction of the CPC, will vary with its position.

Existing mathematical relationships for calculation of general orientational aspects of

arbitrarily orientated fixed CPCs 22F

23-23F24F25F26F

27 are not straightforward as for flat plate

collectors. Derivations of such relationships focus on the determination of solar

energy input and collection times, but in doing so do not follow a standard approach.

One method of determining energy collection by fixed CPCs, which may be simpler

and more intuitive, is via a two-step process (section 2.5, next):

- Making use of algorithms and mathematical relationships for solar geometry and

terrestrial radiation calculations for arbitrary tilted surfaces.

- Considering additional relationships for the non-symmetrical characteristics of

arbitrary CPC panel layouts that, together with the solar vector, allow for proper

determination of collected solar energy.

2.5 Solar geometry and panel layout/orientation

1. Specifying the orientation of the panel

The location and layout for solar collector panels may be specified by a combination

of the following rotation angles in a 3D Cartesian system (Figure 2.4):

For a flat plate collector

· Azimuth angle, ϕ, about the normal to the plane (z-axis) (Figure 2.5)

· Tilt angle, θ, about the transverse axis of the plane (Figure 2.6)



17

For a CPC

· Azimuth and tilt angles as for the flat plate (θ and ϕ)

· Twist angle, ω, about the longitudinal axis of the plane (Figure 2.7)

· Rotation angle, ρ, about the normal to the plane in its final orientation1F

*

The CPC plane is identified by the unit vector normal to its surface, VN. Successive

operations of azimuth, tilt and twist result in a new positioning of this vector which

then indicates the position and orientation of the CPC plane. Changes in the actual

CPC layout can be tracked by following changes to another unit vector, VP, normal

to both VN and the line-axis of the collector (Figures 2.5 through 2.7). The final panel

position is then given by a {θ,ω,ϕ} combination and the final CPC position by

{θ,ω,ϕ,ρ}. With this in mind, the orientation of the panel can be redefined from what

is termed effective azimuth, ϕeff, and effective tilt, θeff. These are the angles that, if

applied to the plane of the CPC at starting point, give an equivalent location of the

panel as what the {θ,ω,ϕ} triad gives: {θeff, ϕeff}orientation ≡{θ,ω,ϕ}orientation

These effective angles can then used to determine the available radiation falling on

the aperture plane of the CPC depending on the position of the sun in the sky. A

general outline of how the process may be implemented is given next.

Specifying the orientation of the panel: step-by-step approach

Step 0 (starting conditions): A convenient starting position for the CPC panel is

lying flat (horizontally) with a North-South line-axis alignment as shown in

Figure 2.4.

Figure 2.4 Cartesian coordinate system for collector panel

* This extra degree of rotation has been referred to as “skewness” in the literature26 and presented as a useful parameter that could allow the optimisation of year-round energy collection for CPC devices.

N

S

E

W

y

z

x



18

For simplicity and illustration, only one CPC is shown on the panel. All rotations

refer to this panel.

Step 1: An azimuth angle, ϕ, is then given (rotation about the normal to the surface).

Figure 2.5 Plane of a CPC before and after azimuth rotation

Step 2*: A tilt angle, θ, is also given (rotation about the transverse axis of the panel).

Figure 2.6 Tilt angle for the plane of the CPC

At this point, the orientation of a flat plate collector relative to the starting position is

uniquely determined by these two angles.

Step 3 2F

∗: A twist, ω, angle follows (rotation about the longitudinal axis of the panel).

This angle allows for an extra degree of movement and is required for a CPC

collector.

∗ The panel may be first tilted and then twisted or vice-versa. It is noted that these operations are not commutative, i.e, tilting_and_then_twisting ≠ twisting_and_then_tilting.

θ

VN

VP VN

ϕ

VP

VN



19

Figure 2.7 Tilt and twist angles for the plane of a CPC

Step 4: Another rotation angle, ρ, about the normal to the surface is allowed.

Once the azimuth, tilt and twist angles are applied, it is possible to further rotate the

panel about the normal to its surface, in the same way the azimuth angle is given in

the beginning. This could be useful for investigating changes in radiation collection

times for a given {ϕ,θ,ω,ρ} panel position. The orientation remains the same but the

CPC position changes, therefore collection times also change (Figure 2.5).

Step 5: Redefining panel orientation based on effective azimuth and tilt angles

The final orientation of the CPC panel is defined by the coordinates of the unit vector

normal to its surface, VN’. This vector is expressed in polar coordinates by the tilt

and azimuth angles of its position resulting from all the rotations previously applied

(effective angles). As stated before, these angles produce the same orientation result

if applied to the plane of the CPC at starting point, but without requiring a twist

about the longitudinal axis (Figure 2.8). This is convenient since it enables

straightforward calculation of the angle of incidence, θinc, on the CPC plane from the

solar vector determination and from conventional relationships for flat surfaces,

which only require the tilt and azimuth of the surface. From the angle of incidence

the solar irradiance can be found. The calculation takes into account other quantities

as given by Table 2.1.

ωθ

VP

VN



20

Figure 2.8 Effective azimuth and tilt angles for the plane of a CPC and angle of incidence for

direct solar radiation

2. Determining the position of the sun in the sky during the day

The position of the sun is given by the solar unit vector, VS = {1,α,ϕS}, based on the

solar azimuth and altitude angles as defined in Figure 2.2. It was mentioned earlier

that these quantities are derived from the (more fundamental) hour angle, declination

and latitude angle and it was shown above that these three are sufficient for

determining irradiance falling on the CPC plane as far as solar position is concerned.

However, for the actual CPC collection times, it is necessary to determine the actual

azimuth and altitude of the sun and its relative position to the line-axis of the CPC.

For horizontal surfaces, the angle of incidence from direct solar radiation is the

zenith angle of the sun, which is the complementary angle to the solar altitude angle,

i.e., θz = 90-α. Calculation for solar altitude can, therefore, make use of the

relationships for irradiance on flat surfaces with no tilt.

The solar azimuth angle, ϕS, may (theoretically) vary between 0° and 360°, with the

angle convention as given previously and will depend on the declination, δ, the

latitude, φ, and the number of hours per day, n (refer to appendix A).

y x ϕ

θ ω

VN’

z

y

z

x

θeff

ϕeff VN’

θinc



21

3. Determining radiation intercepted by the CPC over the day, i.e.,

determining radiation collection times

The collection characteristic of the CPC is basically given by what is termed the

acceptance half-angle, θa (Figure 2.3). For collection to occur, this is the minimum

angle-value required between the projection of the solar vector on the transverse

plane perpendicular to the collector’s surface and the normal to the surface. From the

previous discussion, collection times for the CPC can then be determined as follows:

a) The collection angle, θc, between the projected solar vector on the transverse

plane, VST, and the normal to the collector’s surface, VN’, can be found for all

solar positions over the day. This is done by (Figure 2.9):

- Calculating the angles between the solar vector, VS, and VP’ and VN’, which

will give θSP’ and θSN’, respectively.

- Determining the projection of the solar vector on the axes of VP’ and VN’,

giving VSP’ and VSN’, and noting that tan(θc) = VSP’/VSN’ (Appendix A).

b) This angle can then be compared with the acceptance half-angle, θa, and if it is

smaller, collection is acknowledged.

Geometrical and analytical relationships that may be used for implementing the

process discussed so far are given in Appendix A. The computational process has

been detailed 3F

∗, based on the operations that would be required to produce the results

desired.

∗ Appendix A actually serves as a guide for implementing such process



22

Figure 2.9 Radiation collection and acceptance angles for an arbitrary CPC layout

y

z

x

VP’

VS

VN’

θa

VSP’

VSN’

VST

θSN

θSP

θc

Chapter 3 - Concentrating devices 3.1 Introduction

The maximum value for solar irradiance falling on the Earth’s surface cannot exceed

the value for the solar constant (1367 W/m2 - Chapter 2). The actual value received at

its peak, and for specific locations and times of the year, is more like 1100 W/m2. A

value of 1000 W/m2 (1 peak sun) has been chosen in solar research and engineering

for standardisation purposes as a figure for maximum irradiation attainable.

The Stefan-Boltzmann equation for blackbody radiation indicates the total emissive

power, Γ, in W/m2 radiated by a black body (perfect radiator) at a certain absolute

temperature. It enables calculation of an upper limit to the temperature of an object,

were it to completely absorb (and re-irradiate) this power:

Γ=⋅ 4Tσ (3.1)

where 42810675 Km/W. ⋅×= −σ , the Stefan-Boltzmann constant. At 90 °C a black

body radiates about 1000 W/m2.

Since there are other heat loss mechanisms (eg. convection, conduction) it is

uncommon for an object to reach temperatures close to the boiling point of water

under normal exposure to the sun (1000 W/m2). Clearly, for high temperature

processes (like steam production) flat plate collectors are unsuitable. The solution to

this situation is to increase the power density reaching the element of interest by

using concentrating devices.

3.2 Concentration

The development of most ideas and concepts in this section and supporting

appendices follows closely the treatise on non-imaging optics and concentration

given by Welford and Winston (see bibliography).


Chapter 3 - Concentrating devices

24

A concentrator is an optical system that receives a certain power density and delivers

a higher power density to the element to be heated. The ratio of these two quantities

is the concentration factor, which depends on geometrical and optical system design.

The concentration ratio is defined as the ratio between the input and output aperture

areas of the optical system.

'

'

AAC =

ΓΓ

= (3.2)

For a two-dimensional system: 'wwC = w = aperture width (3.3)

For a three-dimensional system: 2

2

'aaC = a = aperture radius (3.4)

And for a black body it follows that the temperature can be increased from

T to T’, where: TCT' ⋅=4 (3.5)

Concentrators can be reflectors or refractors, can be image forming (e.g. lens arrays,

parabolic dishes) or non-imaging. They can have two- and three-dimensional axes of

symmetry (such as cylindrical surfaces) and can be continuous or segmented.

An example of an image forming concentrator is a magnifying glass (Figure 3.1). If

sunlight is perpendicular to the plane of the lens and an object is near the focal

distance, the concentration can be high enough to elevate the temperature at the focal

point above 300°C. For instance, for a lens diameter of 50 mm that produces a focal

“spot” of 6 mm diameter, the concentration factor (Equation 3.4) is about 8.3. For

this case Equation 3.5 yields an upper temperature limit, T’, of about 340°C.

Figure 3.1 Magnifying glass

50 mm 6 mm

f



25

An example of a simple (but inefficient) non-imaging concentrator is a truncated

cone formed from reflective material (Figure 3.2). Radiation entering from the larger

aperture of the cone will tend to be “squeezed” on its way down the other end,

resulting in a concentrated output.

Figure 3.2 Cone concentrator (longitudinal profile)

3.2.1 Upper limit for concentration

The concentration ratio defined as the ratio of the output to input aperture dimensions

of the system (Equations 3.3 and 3.4) is termed the geometrical concentration ratio.

However, for every optical system there is a particular physical quantity that depends

on the spatial and angular displacement of input and output rays which remains

invariant throughout that system. This is the étendue invariant and it allows for the

determination of an optical expression for concentration ratio as well as the

maximum theoretical value obtainable. Derivation of the optical concentration from

the étendue is given in Appendix B and the expressions for maximum concentration

for 2D and 3D systems are:

θsinC D

max12 = (3.6)

θ23 1

sinC D

max = (3.7)

Where θ is the acceptance half-angle of the concentrator system.

Refractive imaging devices, like the magnifier, suffer aberrations and coma and fall

short from attaining the maximum concentration ratio, by a minimum factor of 2 for

2D systems and 4 for 3D systems27F

28. Image forming mirror systems (like parabolic

Collected ray

Ray sent



26

troughs) that focus rays parallel to their axis on a focal point, have no spherical or

chromatic aberrations. However, off-axis beams can be highly aberrated (Figure 3.3).

Figure 3.3 Off-axis aberrations (coma) for a parabolic trough mirror

For higher concentrations coma effects will be stronger and off-axis incoming rays

will be reflected farther away from the focal point. The output aperture area

(absorber area) must be increased in order to capture these rays and the increase will

depend on how much deviation from the normal is tolerable. However, an increase in

collection area means a decrease in concentration. Mirror concentrators must

therefore be constantly directed towards the sun with high precision and accuracy in

order to minimise these effects.

There is a family of non-imaging devices known as the compound parabolic

collectors (CPC) which do not suffer from these problems and can deliver high

concentration ratios attaining the theoretical limit without sun tracking.

3.3 The Compound Parabolic Collector (CPC)

The CPC concept was proposed and developed in the 1960's 28F

29,29F

30 and shortly after

found considerable use in solar energy applications30F

31,31F

32 and continues to do so32F

33-33F34F

35.

The term "compound parabolic" is derived from the fact that it is formed from two

parabolic segments joined by one or more arc segments. Different CPC

configurations are obtained for different absorber-recievers (Figure 3.4).

a) Normal incidence b) Oblique incidence (θ < 90°)

Axis of symmetry

θ

Axis of symmetry



27

(a) (b) (c)

Figure 3.4 CPC configurations for different absorber types.

The CPC comes very near in achieving the maximum theoretical concentration

possible, being limited basically by construction and material imperfections and

other practical problems35F

36.

Energy collection will occur when the angles between the projection of the incoming

rays on the transverse plane perpendicular to the collector’s surface and the normal to

the surface are less than, or equal to, θa (θc ≤ θa). If θc = θa the incoming rays are

extreme rays (Figure 3.5).

For the CPC configurations of Figure 3.4, the profile of the reflector consists of:

- an involute of the absorber (arc of a circle) inside the area defined by the rays

tangent to the absorbers at ±θ (dotted lines) and…

- a curve outside, such that a ray parallel to the extreme rays, falling on this curve

(wall of the CPC) and being reflected by it, touches the absorber tangentially (at

one of its extremes in the case of flat receivers).

For example, for the vertical fin this corresponds to:

- a circular arc segment (with centre at the top of the absorber and radius a/2)

beneath and inside the dashed lines and…

- two tilted parabolic sections outside the lines, where any extreme rays falling on

these will be reflected such that they are just tangent to the absorber (they just

touch the absorber top).



28

Figure 3.5 Projection of incoming solar ray on transverse CPC plane, normal to the surface

3.3.1 Conceptualisation of the CPC and the “edge-ray” principle

The CPC must be an optical system such that rays entering the input aperture within

a certain angular acceptance range are all admitted at the output aperture. The task is

then to produce reflector shapes that accomplish this. For ideal concentrators,

extreme input rays become extreme output rays. This is known as the edge-ray

principle. Although it is not sufficient (cannot be proven) to guarantee ideal

concentration in non-imaging optical concentrator systems, in practice it is found that

designs based on this principle have very high concentration ratios, and so it is a

valuable heuristic tool for concentrator design.

An example of a simple collecting 2D CPC is given in Figures 3.6 and 3.7. It is

designed to concentrate the light from an input aperture w down to a smaller aperture

w’ where a collector/absorber is placed (eg. flat plate, photovoltaic panel, etc). The

acceptance half-angle is θ and so the concentrator will have an angular acceptance

range of ±θ about its axis. In Figure 3.6, the blue rays are extreme rays that get

reflected from the upper section of the concentrator to point P’. Likewise, extreme

rays being reflected from the lower section will end up at point P (red ray). Rays

entering the system at a larger angle of incidence (green ray) will be turned back. All

other rays will be collected at some point over the extension of the exit aperture.

θcθa



29

Figure 3.6 Edge-ray principle for 2D CPC

The parabolic reflector shape has the property that any ray parallel to the axis of the

parabola will be reflected to the focal point. In the design of Figure 3.6, it is required

for all extreme rays incident on the upper reflector wall to be reflected to point P’.

The reflector shape is therefore obtained as a section of a parabola with focus at P’

and axis parallel to the direction of the extreme rays. The lower reflector wall is

obtained in an analogous way. Figure 3.7 shows the parabolas, their axes and focal

points for both CPC segments.

Figure 3.7 The CPC profile as compounded parabolic segments

2θ

θ

P'

P

w'

w

Parabola axis (for upper reflector section)

o

Blue and red rays are extreme rays (θ) that are collected at the rim of the aperture exit. The green ray has a direction greater than θ and is reflected back

P’ P

2θ



30

Concentrating devices constructed in this way will have profiles made up of

compounded parabolic segments, hence the name for these concentrators4F

*.

Formalisation of the CPC profile derivation based on the geometrical relationships of

the parabolic segments and their mathematical formulation is given in Appendix C

together with the derivation and construction of the horizontal absorber profile.

3.4 Exploring CPC orientations and collection times

Being able to fully determine CPC shapes, layouts and orientations, daily irradiance

profiles and collection times for a CPC configuration were explored for various

positions/orientations and for different times of the year. Figures 3.8-3.20 plot these

for a few select orientations. The latitude used in these examples was the latitude for

Brisbane, Queensland – Australia: φ = -27.5°. The day was counted from the

beginning of the calendar year and for most of the plots it corresponded to the

autumn equinox, March 21st- 22nd (day = 81) when the declination is zero.

The irradiance profiles show the amount of energy intercepted over the day by a CPC

with a 30° acceptance half-angle (concentration ratio of 2). The collection versus

time plots show the variation of the collection angle, θc, over the day and whether or

not its values fall within the admittance range of ±30°. The CPC icon on the top-right

corner of the irradiance plots represents the layout for the collector plane after all

rotations have been applied. The line-axis of the collector is represented by the

position of this icon, indicating the azimuth rotation. After this rotation, the panel can

be tilted or twisted or both. The red dot indicates a tilt in the given direction. The

yellow dot indicates a twist in the given direction. The effect of the optional

ρ-rotation is shown for the later plots as a potential useful parameter for year-round

orientation optimisation for energy collection.

*Not all non-imaging concentrators are made of compound parabolic segments as it depends on the nature of the exit aperture or energy collection absorber/receiver. An example of this is the circular absorber concentrator profile shown in fig. 3.4a, which has no parabolic sections.



31

(a)

(b)

Figure 3.8 Irradiation profile and collection times for east-west orientation and north

facing collector, i.e., twisted to the latitude angle

6 7 8 9 10 11 12 13 14 15 16 17 180

100

200

300

400

500

600

700

800

900

Irradiance variation over a day

Hour of the day

Irrad

ianc

e (W

/m²)

Latitude = -27.5° Day = 81 Original azimuth = 90° Original tilt = 0° Twist = 27.5° ρ-rotation = 0° Effective azimuth = 0° Effective tilt = 27.5° Concentration ratio = 2 Acceptance angle = 30°

N

E

S

W

6 7 8 9 10 11 12 13 14 15 16 17 18-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day

Solar energy collection times over a day

Angle collection limits

Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



32

(a)

(b)

Figure 3.9 Irradiation profile and collection times for north-south alignment and north

facing collector, i.e., tilted to the latitude angle

6 7 8 9 10 11 12 13 14 15 16 17 18 0

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)

Latitude = -27.5° Day = 81 Original azimuth = 0° Original tilt = 27.5° Twist = 0° ρ-rotation = 0° Effective azimuth = 0° Effective tilt = 27.5° Concentration ratio = 2Acceptance angle = 30°

N

EW

S

6 7 8 9 10 11 12 13 14 15 16 17 18 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day



Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



33

(a)

(b)

Figure 3.10 Irradiation profile and collection times for northeast-southwest aligned

collector, tilted to the latitude angle

6 7 8 9 10 11 12 13 14 15 16 17 180

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)

Acceptance angle = 30°Concentration ratio = 2

Effective tilt = 27.5° Effective azimuth = 45°

ρ-otation = 0° Twist = 0° Original tilt = 27.5° Original azimuth = 45°

Day = 81 Latitude = -27.5°

N

E

S

W

6 7 8 9 10 11 12 13 14 15 16 17 18-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day

Solar energy collection times over a day Angle collection limits

Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



34

(a)

(b)

Figure 3.11 Irradiation profile and collection times for northwest-southeast aligned

collector, twisted to the latitude angle

6 7 8 9 10 11 12 13 14 15 16 17 18 0

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)

Latitude = -27.5° Day = 81 Original azimuth = 315° Original tilt = 0° Twist = -27.5° ρ-otation = 0° Effective azimuth = 45° Effective tilt = 27.5° Concentration ratio = 2 Acceptance angle = 30°

N

E

S

W

6 7 8 9 10 11 12 13 14 15 16 17 18 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day


Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



35

(a)

(b)

Figure 3.12 Irradiation profile and collection times for east-west aligned collector, twisted

to the latitude angle and tilted east

6 7 8 9 10 11 12 13 14 15 16 17 180

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)

Latitude = -27.5° Day = 81 Original azimuth = 90°Original tilt = 30° Twist = 27.5° ρ-rotation = 0° Effective azimuth = 51.35° Effective tilt = 39.81°

Concentration ratio = 2Acceptance angle = 30°

N

E

S

W

Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e

6 7 8 9 10 11 12 13 14 15 16 17 18-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day




36

(a)

(b)


to the latitude angle, tilted east & rotated 5° about its normal

6 7 8 9 10 11 12 13 14 15 16 17 18 0

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)

Latitude = -27.5° Day = 81 Original azimuth = 90° Original tilt = 30° Twist = 27.5° ρ-rotation = 5°

Effective azimuth = 51.35° Effective tilt = 39.81° Concentration ratio = 2 Acceptance angle = 30°

N

E

S

W

6 7 8 9 10 11 12 13 14 15 16 17 18 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day



Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



37

(a)

(b)



6 7 8 9 10 11 12 13 14 15 16 17 180

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)


Effective azimuth = 51.35° Effective tilt = 39.81°


N

E

S

W

Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e

6 7 8 9 10 11 12 13 14 15 16 17 18-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day





38

(a)

(b)



6 7 8 9 10 11 12 13 14 15 16 17 18 0

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)



N

E

S

W

6 7 8 9 10 11 12 13 14 15 16 17 18 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day



Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



39

(a)

(b)



6 7 8 9 10 11 12 13 14 15 16 17 180

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)




N

E

S

W

6 7 8 9 10 11 12 13 14 15 16 17 18-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day



Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



40

(a)

(b)

Figure 3.17 Irradiation profile and collection times for east-west aligned collector, with a

30° twist angle and a 20° tilt – summer solstice

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0

100

200

300

400

500

600

700

800

900 Irradiance variation over a day

Hour of the day

Irrad

ianc

e (W

/m²) Latitude = -27.5°

Day = 356

Original azimuth = 90° Original tilt = 20° Twist = 30° ρ-rotation = 0°


N

E

S

W

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day



Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



41

(a)

(b)

Figure 3.18 Irradiation profile and collection times for east-west aligned collector, with a

30° twist angle and a 20° tilt – winter solstice

6 7 8 9 10 11 12 13 14 15 16 17 180

100

200

300

400

500

600

700


Hour of the day

Irrad

ianc

e (W

/m²) Latitude = -27.5°

Day = 171 Original azimuth = 90° Original tilt = 20° Twist = 30° ρ-rotation = 0°



N

E

S

W

6 7 8 9 10 11 12 13 14 15 16 17 18-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

Hour of the day



Ang

le ( θ

c ) bet

wee

n th

e no

rmal

to th

e su

rfac

e an

d th

e so

lar v

ecto

r pr

ojec

tion

on th

e tr

ansv

erse

pla

ne p

erpe

ndic

ular

to th

e su

rfac

e



42

(a)

(b)

Figure 3.19 Irradiation profile for a northwest facing collector with a 20° tilt, before and

after a +25° ρ-rotation – summer solstice

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)

Latitude = -27.5° Day = 356 Original azimuth = 315° Original tilt = 20° Twist = 0° ρ-rotation = 0°

Effective azimuth = 315° Effective tilt = 20° Concentration ratio = 2 Acceptance angle = 30°

S

W E

N

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0

100

200

300

400

500

600

700

800

900


Hour of the day

Irrad

ianc

e (W

/m²)


Effective azimuth = 315° Effective tilt = 20° Concentration ratio = 2 Acceptance angle = 30°

S

W E

N



43

(a)

(b)

Figure 3.20 Irradiation profile for a northwest facing collector with a 20° tilt, before and

after a +25° ρ-rotation – winter solstice

6 7 8 9 10 11 12 13 14 15 16 17 180

100

200

300

400

500

600


Hour of the day

Irrad

ianc

e (W

/m²)


Effective azimuth = 315° Effective tilt = 20° Concentration ratio = 2Acceptance angle = 30°

S

W E

N

6 7 8 9 10 11 12 13 14 15 16 17 180

100

200

300

400

500

600


Hour of the day

Irrad

ianc

e (W

/m²)


Effective azimuth = 315° Effective tilt = 20° Concentration ratio = 2Acceptance angle = 30°

S

W E

N



44

At solar noon, the incidence angle θinc on the plane of the collector is equal to the

absolute value of the difference between the latitude and the declination.

δφθ −=noon_inc (3.13)

During equinox, θinc_noon = φ (since δ = 0) and the results from Figure 3.8 show that

an east-west aligned collector, facing north, with a twist angle equal to the latitude

angle, maximises energy collection. Any other orientation (e.g., Figures 3.9-3.11)

will result in less collection times and also reduced available energy. However, in

order for the collector to work properly, a tilt angle must be present so that the water

is gravity-fed into the boilers and steam can be produced and delivered adequately.

Figure 3.12 shows an orientation for this case where a tilt angle is used, and the

collector faces northeast. Collection is biased towards the morning hours, due to the

tilt, and ends earlier in the afternoon.

Figure 3.9 shows the usual orientation for flat panel collectors, facing due north and

tilted to the latitude angle. Since the CPC under consideration has an acceptance

half-angle of 30°, in this orientation, the collection period is limited to 2 hours before

and after solar noon time (i.e., 4 hours total).

Figures 3.10 and 3.11 have essentially the same panel (not CPC) orientation, facing

due northeast, with the collector tilted and twisted as indicated. The available energy

falling on the panel is the same in both cases but collection times are different due to

the CPC layout, which is substantially different for each.

Figures 3.13-3.16 have the same panel orientation as Figure 3.12 but include the

effect of applying the ρ-rotation. Note how the effect in this case is only a restriction

in CPC collection (as in the example above). The available energy falling on the

plane of the CPC is the same, but collection times are reduced.

Optimisation of CPC energy collection for any date of the year is not a

straightforward exercise (except perhaps for the equinoxes). Different dates will

require different orientations. There is no single optimal orientation. Satisfying a



45

maximisation criterion on a regular basis (monthly, or even quarterly) is far from

practical since it would require constant adjustment of the collector, defeating the

purpose of having a stationary concentrator in the first place. A compromise must be

reached by selecting an orientation that will satisfy winter and summer requirements

as best as possible. A first approximation for this year-round single orientation is the

one which maximises collection during equinox with early morning bias and a slight

winter bias: an east-west aligned collector, with a twist angle greater than the latitude

angle and a shallow tilt angle for operational purposes (this makes for a northeast

facing collector). Results for the summer and winter solstices with this CPC

orientation for Brisbane are given by Figures 3.17 and 3.18, respectively. In this

situation collection is sacrificed during summer for the benefit of an increased energy

collection during winter. It is standard practice to incorporate a winter bias design, or

setup, in SHWS in order to maximise collection during this season since less

radiation is available and the load on the system is higher.

In reality, most SHWS are mounted on roofs that constrain their orientation leaving

little flexibility in the selection of azimuth and tilt angles (not to mention twist

angles) precluding optimal collection. In most cases, panels rest on roof surfaces

relying on roof pitch angle with its attendant shortcomings.

An annual optimal collector configuration requires a study of the varying conditions

from seasonal changes and collection restrictions imposed by the site.

It has been suggested that once CPC panels are located on a roof, optimisation may

follow by conveniently “skewing” the collector25, which is similar to giving the panel

a ρ-rotation as mentioned in this study. An example of how this can be done and the

effect it may have is given by Figures 3.19 and 3.20 which show the difference in

energy collection for a SHWS located flush on a northwest facing roof, with a 20°

pitch, before and after a ρ-rotation of 25°, and for summer and winter solstices. The

rotation angle was selected ad-hoc. For the winter solstice, the application of this

rotation biases the energy collection earlier in the day. Collection starts and finishes

about 45 and 85 minutes earlier, respectively. Although the overall collection time

decreases, the early available irradiance is much higher than what is available in the

last 85 minutes of operation. The total energy collected for the rotated configuration



46

is higher than for the original orientation. This rotation, therefore, enhances steam

production for the day, making better use of the available energy falling on the plane

of the collector.

On the other hand, for the summer solstice it is evident from Figure 3.19 that there is

a total decrease in collection times and energy collection. The first 55 minutes of

collection are eliminated with this rotation rendering this configuration seemingly

inefficient. However, the irradiance available in the first 50 minutes is the lowest of

the entire collection time. This means that the fraction of energy collected during this

period is smaller that at any other comparable period during the day and is close to

about 15% of the total collectable energy. The application of this rotation may be

justified on the grounds that little inconvenience may be experienced by this energy

decrease in summer (due to less demand and overall lower heat losses) offsetting

appreciable winter gains (higher load on the system).

The above brief examination points to the need for a more detailed inspection

covering additional dates and actual steam production. It is possible that in the

example above, actual optimisation involves an even stronger winter bias (i.e., ρ >

25°). What this shows is that the application of a ρ-rotation can improve year-round

collection for a particular SHWS orientation. An optimisation of this nature could be

built into the solar geometry and panel orientation programming code and would

certainly be an avenue for improvement in the future.

Chapter 4 - Heat transfer 4.1 Introduction

The energy exchanged between bodies of different temperatures is called heat

transfer. It occurs via three different mechanisms (or modes of transfer):

• Conduction

• Convection

• Radiation

An example of these transfer modes is sketched in Figure 4.1 for a cooling hot plate.

Figure 4.1 Convection, conduction and radiation heat transfer (qc, qk, qr, respectively) for a hot

plate exposed to a cool environment, Tp > Tair

In solar thermal processes, a way of assessing heat transfer amongst the elements of

the systems (eg., SHWS) is required for system design and performance prediction.

4.1.1 Conduction heat transfer

This transfer mode occurs in a body when a temperature gradient exists, where heat

travels to the region of lower temperature. The heat transfer rate in this case is

proportional to the temperature gradient times the area through which heat transfer

occurs (Figure 4.1):

x qk

qr

Tair

A

TP

qc


Chapter 4 - Heat transfer

48

xTAkqk ∂

∂⋅⋅−= (4.1)

Equation 4.1 is also known as Fourier’s Law of heat conduction. The proportionality

constant, k, is the thermal conductivity of the material. The negative sign indicates

that heat flows to the region of low temperature, as required by the 2nd law of

thermodynamics.

4.1.2 Convection heat transfer

This transfer mode occurs when fluids come in contact with solid objects. Heat

transfer in this case is proportional to the temperature difference between the fluid

and object’s surface and the surface area in contact by the fluid (Figure 4.1):

( )fscc TTAhq −⋅⋅= (4.2)

This is also known as Newton’s Law of cooling. Parameter hc is the convection heat

transfer coefficient and is temperature-dependent. It can be calculated analytically for

some (rather simple) systems and must be found experimentally, or inferred by using

computational fluid dynamics (CFD), in more complex scenarios.

There are two kinds of convection modes:

a) Free convection

When natural buoyant forces occur as a consequence of density differences in a fluid

that has come in contact with the surface of an object at a different temperature. An

example of this is the heat loss on the top (hot) cover of a flat plate solar collector

when no wind is blowing over it.

b) Forced convection

When a fluid is forced past the surface of an object at a different temperature. Due to

the higher fluid velocity, more heat can be transferred between fluid and object. An

example would be the same collector plate as before under windy conditions.



49

4.1.3 Radiation heat transfer

This transfer mode occurs via electromagnetic radiation emission and absorption

between bodies of different temperatures and is termed thermal radiation. It requires

no solid medium to propagate. The most obvious example of this is solar radiation

collected on the Earth’s surface. In Chapter 3, it was mentioned that the total

emissive power of a blackbody, or perfect emitter of thermal radiation, was

proportional to the fourth power of its temperature, as given by the Stefan-Boltzmann

equation (Equation 3.1). This can be re-written for energy rate emission, or power,

as:

4TAqr ⋅⋅= σ (4.3)

Since there are no perfect radiators, Equation 4.3 represents an upper limit for

radiation emission of real bodies. To account for this, a quantity known as emissivity,

ε, and defined as the ratio between the emissive power of a body to the emissive

power of a blackbody at the same temperature, is introduced in the previous

equation. Furthermore, during radiation heat exchange between finite surfaces, not

all the radiation emitted by one surface will reach the other, since some will be lost to

the surroundings. This is influenced by physical and geometrical properties of the

surfaces and is quantified by the parameter known as the view, or shape, factor, F12.

For radiation exchange between two surfaces, the net thermal energy transfer from

surface-1 to surface-2 can be approximated by:

( )

22

2

12111

1

42

411221

111AFAA

TTqq rr

⋅−

+⋅

+⋅

−−⋅

=−= ↔↔

εε

εε

σ (4.4)

The emissivity of “real” surfaces is dependent on wavelength, temperature and the

physical and geometrical properties of the surface. In order to use a constant value

for emissivity (and enable an otherwise nearly impossible analytical calculation), the

following assumptions are made:

- Radiation properties are independent of wavelength

- Surfaces are diffuse (radiation emitted equally in all directions)



50

- Surface temperatures are uniform

- Incident energy over the surfaces is uniform

When radiation interacts with matter, part of it is reflected, part is absorbed and for

translucent materials, part is transmitted. The following equation is obtained from the

1st law of thermodynamics and establishes a relationship between the fraction of

radiation reflected, ρ, the fraction absorbed, α, and the fraction transmitted, τ:

1=++ ταρ (4.5)

For bodies that are opaque to thermal radiation, τ = 0. The absorptivity of a body for

a given wavelength is equal to the emissivity of that body, i.e., α = ε. This is called

Kirchhoff’s identity.

In the following sections, heat transfer equations pertaining to the elements of the

SHWS developed are detailed and discussed.

4.2 Selected heat transfer equations and other relationships

Heat flow by convection, radiation and conduction between two arbitrary surfaces

may be expressed in a general form by the following equation:

)TT(hAQ T 211 −⋅⋅= (4.6)

Where: Q = heat or flow of thermal energy (W)

A1 = area of the surface (m2)

hT = heat transfer coefficient (W/m2 ·°C)

T1 -T2 = ΔT = the difference in temperatures between the elements (°C)

Equation 4.6 was the relation used in all heat transfer mode calculations in this study.

For additional information of the different parameters and quantities used hereafter,

refer to Appendix D.



51

4.2.1 Convection in SHWS

The general expression for the convection heat transfer coefficient involving flat

plates, hT, is:

LkNuhT ⋅= (4.7)

Nu is the Nusselt number, k is the thermal conductivity of the fluid (W/m ·°C) and L

is the characteristic length (m).

Convection problems usually rely on finding the Nusselt number in order to obtain

the heat transfer coefficient and finally the heat transferred, via Equation 4.6. The

characteristic length, L, depends on the actual convection situation, relating on most

occasions to the main dimension of the heated surface.

4.2.1.1 Free convection between a flat plate and the surroundings

Different empirical expressions for Nusselt number calculations have been used in

the simulation of the two SHWS developed. The reasons owe to operational

differences between them and the availability of additional resources during

development of the second system.

For the vapour phase downward heat transport SHWS

For isothermal plates, the following relationships were employed36F

37:

⎪⎩

⎪⎨⎧

≤<⋅⋅

⋅≤≤⋅⋅=

11631

6441

10108150

108102540

ff

fff

RaforRa.

RaforRa.Nu

( )( )b.

a.8484

Raf is called the Rayleigh number, which is the product of two other quantities, the

Grashof, Gr, and Prandtl, Pr, numbers (Appendix D).



52

For the air-to-water heat exchange SHWS

The heat transfer coefficient for an isothermal plate of arbitrary tilt angle was

calculated from the following relationships37F

38:

a) Horizontal plate (from Appendix D)

( ) 10110

lH10tHH NuNuNu += (4.9)

4.2.1.2 Forced convection between a flat plate and the surroundings

For an isothermal flat plate the following relationship was used38F

39:

21

31

x3320Nu RePr. ⋅⋅= (4.10)

The quantity Rex is called the Reynolds number. It is an indicator of the nature of the

flow; whether it is laminar, transitional or turbulent. Fluid flow over a surface is

influenced by its proximity to the surface, which will cause it to develop a particular

velocity flow profile. The flow is laminar when the fluid behaves as if it could be

characterised by a series of juxtaposed layers, moving uniformly, where the path of

individual fluid particles do not cross each other. In this case, adjacent fluid layers

move at nearly the same velocity. The flow becomes turbulent when paths of

individual fluid particles are erratic and cross each other, as if in the presence of a

random churning action. The flow is transitional during the process when it departs

from being laminar and advances towards turbulence.

For this case, x = l, since the entire length of the collector was considered. The heat

transfer coefficient for forced convection was averaged over this length and the result

was twice the value obtained from Equation 4.7:

forcedforced hchc ⋅= 2 (4.11)

And the final result for the convection heat transfer coefficient, hc, between a flat

plate and the surroundings was:



53

[ ]maxccc forcedfree

h,hh = (4.12)

For the air-to-water SHWS developed in the later stages of this project (Chapter 7), it

was necessary to determine the heat losses from large circular pipes carrying hot air.

Calculation of convection heat transfer over cylinders enabled this. The most

conservative approach in this case was to take the maximum value between free and

forced convection over horizontal and vertical pipes.

4.2.1.3 Free convection from horizontal cylinders

The air-heating system was designed as a split system, with the heating panel located

on the roof and the tank at ground level. The heating/exchange fluid was hot air and

it was transported downward via vertical plastic pipes. In a general case, however, a

system like this could also require horizontal pipes, or be mainly composed of them,

like when it is all set at the same level (e.g., tank and panel at ground level).

A conservative expression was used for the Nusselt number over a wide range of

Rayleigh numbers39:

( )

26

1

916

169

559013870600

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎥⎦⎤

⎢⎣⎡ +

⋅+=

Pr.

Ra..Nu freeH (4.13)

Where:

4.2.1.4 Free convection from vertical cylinders

In this case, vertical cylinders were treated as vertical flat plates by using the

following expression38:



54

( )9

4

169

41

49201

670680

⎥⎦⎤

⎢⎣⎡ +

⋅+=

Pr.

Ra..Nu freeV (4.14)

Where: 92 1010 << Ra

4.2.1.5 Forced convection from horizontal or vertical cylinders

A comprehensive relationship for the Nusselt number in such case is given next:

( )

54

85

41

32

31

21

2820001

401

62030⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅

⎥⎦⎤

⎢⎣⎡ +

⋅⋅+=

Re

Pr.

PrRe..Nu forced (4.15)

Where: 72 1010 << Re

In all cases of convection over pipes, the characteristic length was equal to the

diameter of the pipe, Dp.

The final (conservative) result for the convection heat transfer coefficient over

cylinders, hc_cyl, was:

[ ] maxforcedVHcyl_c h,h,hh = (4.16)

4.2.1.6 Free convection between flat plates

In this case, the Nusselt number was the ratio of pure conduction resistance to a

convection resistance and it can be seen that if Nu =1, substituting Equation 4.7 into

4.6 reduces to Equation 4.1, meaning that conduction would become the heat transfer

mode. The characteristic length for this situation was the interplate spacing distance.

Two relationships were used here39F

40:

- One for the parallel plate convection



55

- A second one for evaluation of convection suppression if slats are present

between the plates (as is the case for the top cover of the second system

developed)

For parallel plates with tilt angles, θ, from 0° to 75°, the Nusselt number was found

from the following expression:

(4.17)

The ‘+’ superscript means that only positive, or zero, values were to be taken.

In the case of slats between the plates, the following relationship defining a ratio for

Nu with and without slats was used to asses the magnitude of convection suppression

(Figure 4.2):

[ ][ ] 1

1130

111

580280

28021

≥⋅⋅

⋅⋅⋅= slats_no

max..

max.

slats_no

slats Nuif,ZRa.

,RaCC.

NuNu

(4.18)

(4.19)

Where C1 and C2 are derived from experimental correlations for different slat aspect

ratios, Ws/Hs, and C2 for different tilt angles as well; 40° ≤ θ ≤ 90°. If 0° ≤ θ ≤ 45°,

C2 ≅ 1. Note that Hs is the plate spacing.

Figure 4.2 Parallel flat plates with slats for convection suppression

( )45−= θcosZ

( )+

+

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ ⋅+⎥

⎦

⎤⎢⎣

⎡⋅

−⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅

−⋅+= 15830

17081811708144113

161 θθθ

θ cosRacosRacosRa

.sin.Nu.

H

W

θ



56

For tilt angles between 0° and 45° and Ws ≈ Hs (conditions appropriate for the

second system developed in this study):

C1 ≅ 0.145, C2 ≅ 1, 0.82 ≤ Z ≤ 1

Given the above and rewriting Equation 4.18:

[ ][ ]

[ ][ ]

max.

max.

slats_no

slats

max.

max.

,Ra.

,Ra.

NuNu

,Ra.

,Ra.

11070

1160

1130

1160280

280

280

280

⋅

⋅≤≤

⋅

⋅ (4.20)

If Nu > 1, the ratio above is independent of the Rayleigh number and for this

particular case it would mean that the presence of slats actually increased convection

by about 23% to 50%, which would have been undesirable.

4.2.1.7 Free convection between concentric cylinders

The following relationship was used in this case38:

⎪⎩

⎪⎨⎧

≤<⋅⋅⋅≤≤⋅⋅

=116200

64290

10108400108102110

δδ

δδδ RaforRa.

RaforRa.Nu .

.

( )( )b.

a.214214

The expression for the heat transfer coefficient was different in this case due to the

geometry of the surfaces involved:

⎟⎠⎞⎜

⎝⎛⋅

⋅=

2

12 r

rlnr

Nukhcδ (4.22)

Where: r2|r1 = Outer|inner cylinder radius (m)

δ = r2 - r1

4.2.1.8 Forced convection in a corrugated triangular duct

A V-corrugated absorber was used in the air panel of the first prototype developed

for the second system (Figures 7.5 and 7.10). Heated air was forced over and under

this absorber. It was necessary to determine convection arising from this process.



57

Calculating the heat transfer for air flowing in a triangular duct could approximate

convection heat transfer in a V-shaped absorber. In particular, it was desirable to

explore convection for an apex angle of ϑ ≈ 90°, which was relevant for the system

under consideration. Experimental and theoretical studies have been performed for

turbulent flow in finned equilateral40F

41 and isosceles ducts41F

42 (besides other geometries)

and the results can be used for the situation at hand.

Fluid flow in ducts and tubes is subject to frictional resistance from the walls.

Experimental correlations between the friction factor and the Reynolds number have

been developed, since the Reynolds number represents the status of the flow

(laminar, transitional or turbulent) and depends on the dimensions of the resistive

surface and the properties of the fluid. The Moody diagram (Appendix D) shows this

dependency graphically, where the friction factor is plotted versus the Reynolds

number for a series of relative roughness values and for laminar, transitional and

turbulent flow.

An expression for the Nusselt number for smooth circular ducts used in this study is

provided below 42F

43:

( )1Pr87.1207.1

PrRe83

221

−⋅⎟⎠⎞⎜

⎝⎛⋅+

⋅⋅=

f

fNusmooth (4.23)

For: ⎪⎩

⎪⎨⎧

<<⋅<<

5501054000 6

Pr.Re

For turbulent flow in smooth isosceles triangular ducts of apex angle, ϑ, equal to 90°,

experimental evidence40 suggests that friction factors can be calculated using the

same correlations developed for friction in circular ducts. Therefore, it would seem

possible to hypothesise that a similar equivalence exists between roughened

triangular and circular ducts with ribs or fins.

2000 < Re < 4000 ← Laminar flow

Turbulent →flow

↑ ↑



58

Given the absence of specific results pertaining to this situation, if this assumption is

extended to heat transfer behaviour, it is possible to make use of correlations

developed for heat transfer of turbulent flow in circular ducts with internal triangular

fins43F

44 as an approximation to the behaviour of turbulent flow in a V-corrugated

absorber, also with triangular fins and apex angle, ϑ=90.

Substituting Equation 4.23 in 4.24 allowed calculation of the Nusselt number,

Nurough, for the V-corrugated absorber approximation for various corrugation

parameters (Figure 4.3). Using this result in Equation 4.7 provided the convection

heat transfer coefficient (where L = Dh).

71

70240

29021021200360

906421⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡⋅⎟

⎠⎞⎜

⎝⎛⋅⎟

⎠⎞⎜

⎝⎛⋅⎟

⎠⎞⎜

⎝⎛⋅⋅+= −

−.

.r

.

r

r.

r

r.

smooth

rough Prdp

deRe.

NuNu α (4.24)

Figure 4.3 Corrugation parameters for circular ducts

4.2.2 Radiation in SHWS

From Equations 4.4 and 4.6:

( ) ( )211

12122

2

11

1

42

41

111TTAh

FAAA

TTq rr −⋅⋅=

⋅+

⋅−

+⋅

−−⋅

=

εε

εε

σ (4.25)

The general form for the radiation heat transfer coefficient between two surfaces is:

er = roughness height

dr = roughness pitch

αr= heliz angle of roughness

pr = rib spacing

dr

pr

er

αr



59

( ) ( )( )

22

12

121

1

212

22

1

111A

AF

TTTThh rT

⋅⋅−

++−

+⋅+⋅==

εε

εε

σ (4.26)

Where: σ = 5.6697 x 10-8 W/m2·K4 (Stefan-Boltzmann constant)

εi & Fij as defined in section 4.1.3

4.2.2.1 Radiation exchange between a convex object and a large enclosure

This situation applies when a convex object is completely enclosed by a very large

concave surface. In this case, 0AA 21 → and practically no radiation emitted from

the object is reflected back, so 112 →F . From Equation 4.4:

( )42

4111 TTAqr −⋅⋅⋅= εσ (4.27)

( ) ( )212

22

11 TTTThr +⋅+⋅⋅= εσ (4.28)

This expression is used in the case of a flat plate cover at temperature TC radiating to

the sky at temperature Tsky. It is convenient to rewrite Equation 4.28 with reference to

the ambient temperature, Tamb, for reasons that will become apparent in section 4.3:

( )( )ambC

skyCcCS TT

TThr

−

−⋅=

44

εσ (4.29)

Where: 2305520 ambsky T.T ⋅=

4.2.2.2 Radiation exchange between flat plates

An approximation is done in this case assuming that all the radiation is transferred

between the plates and none is lost, so 112 →F (strictly speaking, this is true for

infinite plates). Since A1 = A2 = A, from Equation 4.4:



60

( )111

21

42

41

−+

−⋅⋅=

εε

σ TTAqr (4.31)

( ) ( )

111

21

212

22

1

−+

+⋅+⋅=

εε

σ TTTThr (4.32)

4.2.2.3 Radiation exchange between two concentric cylindrical surfaces

The approximation of total radiation heat exchange was also used in this case with

112 →F and A1 ≠ A2 (Figure 4.4). The resulting relationship from Equation 4.4 was:

( )( )

2

1

2

2

1

42

411

11rr

TTrqr

⋅−

+

−⋅⋅=

εε

ε

σ (4.33)

( ) ( )( )

2

1

2

2

1

212

22

1

11rr

TTTThr

⋅−

+

+⋅+⋅=

εε

ε

σ (4.34)

Figure 4.4 Concentric cylinder arrangement for two radiating surfaces

For computational simplicity and conservative reasons (i.e., upper bound value), a

unity radiation shape factor, F12 = 1, was used in the calculations.

r1

r2

l



61

4.2.3 Conduction in SHWS

Conduction heat transfer in SHWS panels is a minor heat loss mechanism compared

to convection and radiation, which cover most of the heat exchange that occurs.

Efficient flat plate collectors and non-imaging concentrating collectors are contained

in well insulated housings, making these losses very small and so, they can be

neglected for simplicity and first order approximation calculations. For double

glazing covers, conduction between the covers may be the main heat transfer mode

and has been acknowledged accordingly (section 4.2.1.6). Conduction is important,

however, in the assessment of heat losses from hot water tanks.

4.2.3.1 Conduction between concentric cylinders

Heat flow via conduction between cylinders is useful to determine heat losses in hot

water tanks that are surrounded by an outer cylindrical casing with insulation

between them. A simple expression for the actual heat transfer in this case is 44F

45:

( )12

1

2

2 TT

rrln

Lkq cyl_k −⋅⎟⎠⎞

⎜⎝⎛

⋅⋅=

π (4.35)

Where: r2|r1 = Outer|inner cylinder radius (m)

4.3 Thermal network formulation and energy balance equations

Heat transfer processes may be represented by thermal resistance networks using an

analogy with Ohm's law. Solar energy systems may be modeled this way45F

46 and some

thermal analyses of flat plate and CPC collectors have incorporated this technique 46F

47.

ResistanceThermalDifferencePotentialThermal

FlowHeat = ( )T

T hA

TR

TQ⋅

Δ=

Δ=

1

1 (4.36)



62

The thermal network analogy is useful for obtaining the heat gains and losses

(Q values) by solving for combinations of parallel and series thermal resistances

which represent the modelled heat transfer modes.

Assuming that the example given in Figure 4.1 is a flat roof of a shed and that heat is

only lost via the roof, simplified heat transfer modes can be modelled as follows:

Figure 4.5 Thermal circuit schematics

for heat transfer through the roof of a shed

Since all the heat is lost through the roof, the energy balance relationships are:

Q = qc_shed = qk_roof = (qc_roof + qr_roof) (4.37)

Where:

(4.38)

(4.39)

(4.40a)

(4.40b)

(4.41)

Tir

Tor

qr_roof →

Tamb

Tshed

qk_roof →qc_shed →

Tsky

qc_roof → Rcs Rkr

Rcr

Rrr

cs

irshedshed_c R

TTqQ −==

kr

orirroof_k R

TTqQ −==

cr

amborroof_c R

TTq −=

⎪⎪

⎩

⎪⎪

⎨

⎧

−

−

=

∗rr

ambor

rr

skyor

roof_r

RTT

RTT

q

Tir Tor

qr_roof →

Tamb Tshed

qk_roof →qc_shed →

qc_roof → Rcs Rkr

Rcr

Rrr *

and also

qk_roof

qr_roof Tamb

Tshed

qc_roof

qc_shed

Tir

Tor



63

If Tshed, Tsky and Tamb are known, Q can be found as a function of these temperatures

and of the R-values by solving Equations 4.38 through 4.41. From this, the unknown

temperatures, Tir and Tor, can also be found and consequently, all heat transfer values

can be found.

Equation 4.40b corresponds to the second schematic where the radiation transfer

resistance has been referenced to Tamb (Rrr). This is done for convenience of

calculation, since it simplifies the solution of the network. In this case, the radiation

heat transfer coefficient is also referenced to the ambient temperature (hrr) as given

by Equation 4.29. By contrast, the radiation heat transfer coefficient when normally

referenced to Tsky (hrr) is given by Equation 4.28.

By combining Equations 4.38 and 4.39 it is easy to arrive at:

(4.42)

This is equivalent to considering both resistors in series and solving for Q at the

temperature nodes, Tshed and Tor.

From Equations 4.40, 4.41 and 4.42, Q is solved as a function of the three

temperatures and of the R-values:

r_eqkrcs

ambshed

RRRTT

Q++

−= (4.43)

(4.44)

BA

ambrrskycrshedB

RRTRTRTR

Q++

⋅−⋅−⋅=

1 (4.45)

(4.46)

(4.47)

The thermal resistances are the inverse of the heat transfer coefficients as defined in

4.51, which in turn are given by the relationships presented in the previous section.

krcs

orshed

RRTTQ

+−

=

rrcrB RRR +=

krcsA RRR +=

∗

∗

+⋅

=rrcr

rrcrr_eq RR

RRR

And also:

*

*



64

These values are temperature dependent, so the solution to the system is not purely

that of a standard linear equations system. The solution process requires an iterative

procedure, where the equations are simultaneously solved for all temperatures over

many cycles. For each cycle, new temperature values are found and fed back into the

system for the following cycle. The process continues in a converging manner until

the temperatures obtained remain virtually constant in subsequent iterations. Detailed

explanation for each of the systems developed is given in sections 6.4.1 and 7.2.2.

4.4 Energy and power in fluid flow and fluid storage

Thermal energy gained or lost by a body during a heat transfer process is expressed

in terms of the temperature change undergone by the body, the body mass and the

capacity to experience this change. This energy variation is expressed as:

( )fip TTCmQE −⋅⋅== (4.48)

Where: m = body mass (kg)

Cp = specific heat of the body at constant pressure (kJ/kg·°C)

In a similar way, thermal power transferred by a body of fluid is given as:

( )fip TTCmP −⋅⋅= & (4.49)

Where: m& = mass flow rate of fluid (kg/s)

The energy and power transferred during phase change of a fluid is given by:

Hphasephase LmQE ⋅== (4.50)

Hphase LmP ⋅= & (4.51)

Where: LH = Enthalpy of vapourisation (kJ/kg)

Equations 4.48 and 4.49, together with Equation 4.6 form the basis of heat flow

evaluation in all calculations performed in this work.



65

4.5 Heat exchanger effectiveness-NTU method

If input fluid temperatures in a heat exchanger are known and the effectiveness of the

exchanger in transferring a certain amount of heat can be determined, it is possible to

predict output fluid temperatures. The following development was used for the tank-

exchanger-coupled thermosiphon system (Chapter 7) as a means for determining the

temperature of the output hot water from the heat exchanger.

For illustration, consider the simple double-pipe heat exchanger of Figure 4.6, where

fluid B is the hot fluid. Fluid flow may be either parallel flow (fluids A & B flowing

in the same direction) or counterflow (fluids flow in the opposite direction). The

effectiveness is determined differently for each.

Figure 4.6 Double pipe heat exchanger

In parallel flow: 1221 AABB TTTT >>>

In counterflow:

211

221

AAB

ABB

TTT

TTT

>>

>> and it is possible for: 21 BA TT >

In counterflow, the output temperature of the cold fluid can lie between the input and

output temperatures for the hot fluid. This is the situation for the output hot water in

the tank-exchanger loop of the system incorporating the air heater panel. Given this

situation and even though the heat exchanger used is not physically like the one

pictured above, as a first approximation the exchanger was taken as a “black box”

input/output element with a behaviour similar to counterflow operation and so the

effectiveness was determined as for a counterflow system.

1 2

Fluid B

Fluid AParallel flow

Counterflow

TA2

TB2

TB1

TA1



66

The effectiveness-NTU method (NTU: number of transfer units) defines exchanger

effectiveness as the ratio of the actual to the maximum possible rate of heat

transfer47F

48:

max_x

act_x

PP

transferheatpossibleimummaxtransferheatactual

==ε (4.52)

Assuming no losses, the actual rate of heat transfer is given by the rate of energy loss

of the hot fluid or by the equal rate of energy gain of the cold fluid.

For parallel flow: ( ) ( )1221 cccchhhh||

act_x TTCmTTCmP −⋅⋅=−⋅⋅= && (4.53)

For counterflow: ( ) ( )2121 cccchhhhact_x TTCmTTCmP −⋅⋅=−⋅⋅=↔ && (4.54)

Where subscripts h and c refer to hot and cold fluid, respectively.

The maximum possible rate of heat transfer occurs when one of the fluids undergoes

the maximum temperature change available in the exchanger. This is the temperature

difference between the input hot air and input cold water temperatures to the

exchanger of the air heater prototype system. Only the fluid with the minimum value

of heat capacity rate ( )minCm ⋅& can undergo this maximum temperature change.

The maximum possible heat transfer is: ( ) ( )inletinlet chminmax_x TTCmP −⋅⋅= & (4.55)

For counterflow operation there are two possible relationships for effectiveness,

depending on which fluid has the minimum heat capacity rate:

Hot fluid → ( )( ) 21

21

21

21

ch

hh

chhh

hhhh

max_x

act_xh TT

TTTTCmTTCm

PP

−−

=−⋅⋅−⋅⋅

==&

&ε (4.56a)

Cold fluid → ( )( ) 21

21

21

21

ch

cc

chcc

cccc

max_x

act_xc TT

TTTTCmTTCm

PP

−−

=−⋅⋅−⋅⋅

==&

&ε (4.56b)

With increasing and decreasing fluid temperatures it is possible for both fluids to

share the role of having the minimum value of heat capacity at different times. The



67

“swap over” point occurs when ( ) ( )hc cmcm && = and the effectiveness is expressed

as 48F

49:

⎭⎬⎫

⎩⎨⎧

−−

−−

=21

21

21

21

ch

cc

ch

hh

TTTT

,TTTT

maxε (4.57)

It is noted that the same effectiveness value can be obtained for two different fluid

temperatures 49F

50 and two different flow rates. In the characterisation of heat

exchangers where the effectiveness is an input parameter in the model used to obtain

other parameters (as was the case with this study), the use of relationship 4.57 will

therefore not allow their unequivocal determination. For cases like these, a single

expression termed as “modified” effectiveness, ε’, has been proposed for empirical

prediction models50F

51:

( )( )21

21

21

21

chhh

cccc

ch

hh'

TTCmTTCm

TTTT

−⋅⋅−⋅⋅

=−−

=&

&ε (4.58)

This expression can be obtained by dividing Equation 4.54 by ( )21 chcc TTCm −⋅⋅& .

It was concluded from experimental measurements performed on the SHWS

incorporating the air heater panel that under steady-state conditions and the high

irradiance levels used, the water (which was also the cold fluid) was the fluid that

underwent the maximum energy change (see section 7.2.4 for details). The

effectiveness is then given by Equation 4.56b. This equation is useful in determining

the output temperature of the cold fluid, Tc1, if the other temperatures are known and

the effectiveness can be found.



68

Chapter 5 - Fluid mechanics and hydraulics 5.1 Introduction

In systems like those described in this work, the elements therein present a resistance

to fluid flow, causing pressure drops which modify the flow, influencing operation.

In the specific case of the SHWS with the air heating panel, where the airflow is

driven by a fan or blower, the energy expenditure of the motor used to circulate the

air must be considered in the final determination of a total, or effective, efficiency of

the system. The effective efficiency in this broader sense can be considered as51F

52:

AGPP

cb

net_moteff_watereff ⋅

−=η (5.1)

CPP motnet_mot = (5.2)

Pwater_eff is the effective power gained by water in the tank, Pmot_net is the net

pumping power required and Pmot is the pumping power of the motor. C is the

combined efficiencies of the fan, motor, transmission line and electricity generation

processes.

There are two types of friction losses in pipes: main, or head, losses and minor

losses. The first type deals with the resistance to flow offered by straight pipe

sections while the second one refers to bends, fittings, valves and other elements

present in a pipe system. Knowing the pressure losses in a piping system and the

pumping power required allows for sizing considerations of motors and pumps.

5.2 Pressure losses

This section shows the fundamentals of fluid mechanics necessary to understand and

determine pressure losses in pipeworks.


Chapter 5 - Fluid Mechanics and hydraulics

70

5.2.1 Pressure in fluids

If a force, F, is applied uniformly over a certain area, At, the pressure over that area,

p, is given as the ratio between these two quantities:

tt dAadm

dAdFp ⋅

== (5.3)

For fluid flow in pipes, At is the cross-sectional area of the pipe.

The volume occupied by a fluid is related to its mass via the mass density:

dVdm

=ρ (5.4)

ldAdV t ⋅= (5.5)

dmldAt =⋅⋅ρ (5.6)

Combining Equations 5.3 and 5.6:

lap ⋅⋅= ρ (5.7)

In dealing with many situations involving pressures in fluids, often the forces causing

the pressures are the weight of the fluids, or fluid elements (such as the pressure at

the bottom of a hot water tank). In this case:

hp ⋅= γ (5.8)

g⋅= ργ (specific weight) (5.9)

5.2.2 Energy and “head”

It is necessary to understand the concept of a “head” related to the energy that a

flowing fluid carries.

Consider a pipe section and fluid element as in Figure 5.1



71

Figure 5.1 Fluid element in a pipe section at height ‘h’ above reference level

There are three forms of energy that the fluid carries in its movement: potential,

kinetic and pressure energy.

Potential Energy is related to the weight of the fluid and its height above a reference

point:

hWhgmZ E ⋅=⋅⋅= (5.10)

Kinetic Energy is related to the mass and velocity of fluid flow:

gvWvmK E ⋅

⋅=

⋅=

22

22

(5.11)

Pressure Energy related to the work required to force the fluid over a certain distance

against the pressure:

lFPE ⋅= (5.12)

From Equations 5.3, 5.6 and 5.12:

ρmpPE

⋅= (5.13)

Total energy is the sum of Equations 5.10, 5.11 and 5.13:

ρmpvmhgmE ⋅

+⋅

+⋅⋅=2

2

(5.14)

From Equations 5.9 and 5.14 and rearranging, the expression for total energy as a

“head”, H, is defined:

v

lh



72

γp

gvhH

gmE

+⋅

+==⋅ 2

2

5F

* (5.15)

pressure head

velocity head

elevation head

Pressure drops will be a consequence of the friction exerted by the pipes and

elements affecting fluid flow. To determine these drops it is necessary to know the

behaviour of the fluids in closed circuits. Particularly, it is necessary to know if fluid

flow is laminar or turbulent and what the friction factors are for each section of the

pipe under study (section 4.2.1.8). By calculating Reynolds numbers, friction factors

and other parameters, the friction losses can be found.

5.2.3 Head (pressure) losses

The losses from friction flow in channels and ducts are given by the well-known

D’Arcy-Weisbach formula:

gv

Dlfhf

h2

2⋅⋅= (5.16)

t

v

AareationalseccrossrateflowVolumetric

vΦ

=−

= (5.17)

Dh, l, v and f are the hydraulic diameter, the length of the pipe the fluid velocity and

the friction factor, respectively.

Substituting 5.17 for the mean velocity in D.11 and noticing that x = Dh:

t

vh

AD

Re⋅

Φ⋅=

ν (5.18)

Substituting 5.18 for the Reynolds number in D.14:

* Note that this equation has length units



73

2

7781750

−

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅Φ⋅

⋅=t

v

AD

ln.fν

(5.19)

Finally, substituting 5.17 and 5.19 in 5.16, the head loss for each pipe section is:

g

A

Dl

AD

ln.hf i

i

t

iv

i

i

t

ivii 27

781750

2

2⎟⎟⎠

⎞⎜⎜⎝

⎛Φ

⋅⋅⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⋅⋅Φ⋅

⋅=

−

ν (5.20)

Total head loss from all straight pipe sections is then: ∑=i

ifTOT hfh _

5.2.4 Minor losses

Calculation of minor losses will be dependent on the number of fittings, valves and

other obstacles that affect the flow in any way. Therefore, in order to find these

losses it is necessary to know exactly how many attachments of this nature are part of

the piping system.

Minor losses are usually expressed by specifying a “loss coefficient”, K, as a ratio of

the head loss through the element to the velocity head of the fluid in the system.

The resultant expression is: ( )g

vhK m

22= (5.21)

Therefore, minor head losses are given by:

gA

Kg

vKhv

m 22

2

2 ⎟⎠⎞⎜

⎝⎛Φ

⋅=⋅= (5.22)

Loss coefficients can be determined from experimental data and in most cases are

function of the geometry of the element only. Tabulated values for fittings, bends,

tees and valves are available in the literature52F

53.



74

For sudden expansions and contractions, where turbulent fluid suddenly encounters

an increased or reduced space, plots of K-values versus input/output diameter ratios

(for a pipe system) and empirical relationships are used:

Sudden expansion of cross section: 2

2

1exp 1 ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

AA

K (5.23)

Sudden contraction of cross section: 2

1

21420 ⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅≈

AA

.Kcon (5.24)

Where A1 and A2 are the cross sectional upstream (first) and downstream (second)

conduits areas, respectively.

Friction coefficients for other elements, such as heat exchangers and collector panels,

are much more complicated to determine and are usually case-specific to the

particular situation under study.

The total minor head losses are given by: ∑=i

iimTOT g

vKh2

2

_ (5.25)

Therefore, total head loss by adding Equations 5.20 and 5.25 is:

∑∑ +

⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧⎟⎠

⎞⎜⎝

⎛Φ

⋅⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅⋅

Φ⋅⋅=

−

i

ii

j

tj

jv

j

j

tj

jvjTOT g

vK

A

DL

AD

ln.H227

7817502

2

2

ν (5.26)

By knowing the total pressure losses, the required pumping power and the effective

efficiency for the system can be found.

vFtlF

tE

P net_motnet_motnet_mot

net_mot ⋅=⋅== (5.27)

( )tt

net_motnet_mot Av

AF

P ⋅⋅= (5.28)

pΔ vΦ



75

From Equations 5.8, 5.9 and 5.28:

TOTvTOTvvnet_mot HgHpP ⋅⋅⋅Φ=⋅⋅Φ=Δ⋅Φ= ργ (5.29)

5.3 Thermohydraulics

5.3.1 Poisseuille’s Law for laminar flow

It has been shown for laminar flow that the volume of a liquid flowing through a tube

is directly proportional to the pressure difference driving the liquid, p, and

proportional to the fourth power of the tube radius, r.

Poiseuille's law accurately describes the flow of liquids through pipes as long as

laminar flow exists:

lpr

v ⋅⋅Δ⋅⋅

=Φη

π8

4

(5.30)

Where: r = radius of pipe

η = viscosity of water

Δp = pressure difference

l = length of pipe

This relationship is of particular interest in the case of natural thermosiphon flow as

occurring in the air-to-water heat exchanger of the second system developed in this

study and referred to in chapter 7. In this case, Δp =ρ·g·h, where the pressure is given

by the density differences of hot and cold water columns of length ‘h’ in the

thermosiphon system (Figure 7.9).

Chapter 6 - Solar hot water system with passive

downward vapour phase heat transport 6.1 Introduction

This solar water heater was composed of six sections:

• Heat collection elements: concentrating collector panels and absorber-boiler tube

arrays where water is converted into steam.

• Roof reservoir (20 L) that supplies cold water to the collector

• Conveyance infrastructure: header and footer tubes and and insulated copper pipe

that transport steam to the water storage tank.

• Storage tank: an insulated 200 L tank.

• Heat exchanger: a short copper loop located inside the tank where steam

condenses and gives off heat to the storage water.

• Condensate receptacle: a container under the water tank for condensate collection.

The concentrating collectors generate steam, which flows down the transfer line into

the exchanger coil in the tank, heats the water, condenses and ends up as condensate

in the receptacle. A partial vacuum forms in the collector after cooling, pulling the

condensate back up to recharge the collector chambers and reservoir tank. Even

though high temperatures and steam production have been achieved by using flat

plate collectors53F

54, such temperatures are easier to obtain with concentrating optics.

The main developments were:

1. The design and implementation of the concentrating collectors

2. Roof reservoir water supply

3. Separation of the steam and water

4. The downward steam transfer system

5. Steam to water heat exchange mechanism

6. The night time recharge process


Chapter 6 - Solar hot water system with passive downward vapour phase heat transport

77

6.1.1 Basic design considerations

To meet the proposed daily target of 30 MJ (Table 1.2), the following efficiencies

were assumed as a starting point for system design (Figure 6.1):

Table 6.1 Assumed efficiencies for basic system components

Elements required Efficiencies Steam to water heat exchange 80% or higher

Collector panel 40% or higher TOTAL SYSTEM ~32% or higher

Figure 6.1 Sketch for the downward vapour heat transport SHWS

The steam-to-water heat exchange efficiency of Table 6.1 included the efficiency of

the transfer line, the efficiency of the exchange coil and the efficiency of the tank for

heat retention. The combined efficiency was assumed to be about 80%, provided the

transfer pipeline and water tank were well insulated. Operation of the system was

assumed to occur in the following way:

As the tank water temperature increased the efficiency of the steam/water heat

exchanger would decrease. The efficiency of the tank would also decrease, although

to a lesser extent. For the steam, zero efficiency would be expected as the tank water

approached 100°C. A stagnation temperature below 100°C would set in when heat

gains from the steam and heat losses from the tank were in equilibrium. In this

situation most steam would flow to the receptacle, which would then serve as a heat

dumping mechanism.

Water tank

Heat exchanger

Receptacle

Reservoir tank(optional: hot water draw-off coil)

Collector panel



78

A copper pipe loop would be used as the steam/water heat exchanger and placed near

the bottom of the tank. Since the cold condensate would return to the roof reservoir

at the end of the day it would be desirable for it to not come in contact with the

stored hot water. However, its placement at the bottom of the tank would result in

mixing of hot and cold water inside the tank with little stratification expected. Even

so, the bottom of the tank would always have the coldest water.

The system would operate only on clear days, when irradiance values were high

enough to enable steam production. In many places in Australia and particularly in

Queensland, cloudless and clear skies are the norm throughout the dry period

extending from April to November. Most SHWS in use in Australia do not give

significant output during overcast days. During winter, when the load on SHWS is

the highest and ambient temperatures are low, a system can produce a considerable

amount of hot water since irradiance values close to 1000 W/m2 can still be obtained

(section 6.6.2.3).

As concentrating collectors have limited collection angles, orientation of the panels

greatly affects performance. Two different panel orientations were considered

hypothetically for comparison and evaluation of potential performance:

Mode #1

For a north-facing panel with a 30° collection half-angle and optimum tilt, the system

would be expected to operate for 4 hours on clear days with an average irradiance of

about 880 W/m2 (Figure 3.9). Tables 6.2 and 6.3 summarise the required

performance based on these conditions and the assumptions of table 6.1.

Table 6.2 Assumed energy and power requirements: Mode #1

Required daily energy in the water (from Table 1.2): 25 – 30 MJ Required average power into water (4 hours): 1740 – 2100 W Required average power output from panel: 2175 – 2600 W Required average power into system: 5400 – 6500 W



79

Table 6.3 Average irradiance and minimum collector area required: Mode #1

Average irradiance over 4 hours: 880 W/m2 Absorber aperture area required: 7.4 m2

The absorber area was determined from the required average power into the system.

Mode #2

For an east-facing 30° tilted panel with optimum twist angle and same half-angle, the

system would be expected to collect energy for most of the day. However, it would

be expected to operate with an average panel efficiency of 0.4 for about 5 hours

(between 8:00 am and 1:15 pm) when the irradiance values falling on the aperture

area were over 600 W/m2 (Figure 3.12). The average irradiance during this period

would be expected to be around 820 W/m2. Tables 6.4 and 6.5 indicate the required

performance of the system.

Table 6.4 Assumed energy and power requirements: Mode #2

Required daily energy in the water (from Table 1.2): 25 – 30 MJ Required average power into water (5.25 hours): 1320 – 1580 WRequired average power output from panel: 1650 – 1975 WRequired average power into system: 4125 – 4940 W

Table 6.5 Average irradiance and minimum panel area required: Mode #2

Average irradiance over 5.25 hours: 820 W/m2 Absorber aperture area required: 6.0 m2

If the efficiencies of the system and/or the average irradiance happened to be lower

than the assumed values of Tables 6.1, 6.3 and 6.5, the concentrator aperture would

have to be either increased to compensate for the lower power outputs or have a more

efficient design.

It also appeared from the above that the east facing panel would be a better

arrangement for optimum energy collection and minimal use of resources. Actual

performance of the units, however, was measured mainly for a north facing



80

configuration owing to testing location constraints (reduced solar window and the

unfeasibility of having an optimum twist angle).

The amount of water required for boiling was determined from the required daily

energy into the water and the cold water temperature. The total energy in the water

was given by:

- The phase-change energy from steam to 100°C condensate

- The sensible heat from 100°C to cold condensate

For a cold condensate at 20°C, the sensible heat is about 10% of the heat available

from condensation. Therefore, for simplicity and to be conservative, only the energy

from the heat of vaporisation of the condensing steam was used in design

calculations. From chapter 4:

LmEsteam ⋅= (4.65)

Table 6.6 Water conditions and required mass for boiling

Required daily energy in the water: 25 – 30 MJ Cold water temperature (Twater_cold ≅ Tamb): 20 °C Boiling water temperature (Tsteam): 100 °C Enthalpy of vapourisation for water (L): 2260 J/g Required mass of water for boiling: 11 – 13 kg

It was necessary to have significantly more than this amount of water in the roof

level reservoir so that the system would not boil dry. The roof reservoir was designed

for 20 L capacity.

The estimated total panel areas required was (6–7 m2). Actual panel dimensions were

constrained to a maximum of 2.4 m × 1.2 m = 2.9 m2, due to material availability so

the system was designed with a double-panel configuration (~5 m2).

The theoretical framework for concentrating devices was given in Chapter 3 with

emphasis on non-imaging concentrators and specifically compound parabolic

collectors, CPC, since these were the designs of choice for this system. Imaging and

non-imaging concentrators have been developed and used for solar applications for



81

over 30 years and there have been many collector designs studied, tested and

implemented54F

55. However, not much has been done in relation to their integration

with SHWS where flat plate collectors have dominated as the fluid heating elements.

6.2 Concentrating systems – a review

Concentrators have mainly been studied, proposed and used for non-domestic hot

water production, for example: detoxification of contaminated water55F

56,56F

57 and

improved steam generation57F

58; electricity production58F

59, cooking59F

60 and sterilisation

purposes60F

61 and also photovoltaic electricity applications 61F

62,62F

63.

Relatively inexpensive concentrators have been designed and proposed for SHWS to

improve collector performance and most of these63F

64 have involved the use of the non-

imaging CPC type. Asymmetric concentrators with simple absorber configurations

have been shown to be suitable for direct water heating64F

65,65F

66.

Many variations and modifications have been made to proposed CPC geometries,

some of which include: CPC truncation for cost reduction, easier manufacture and

building integration, double-trough arrangements for increased performance66F

67, two-

stage arrangements for increased concentration67F

68,68F

69 and compact design69F

70, “hybrid”

designs of imaging and non-imaging devices70F

71,71F

72 introduction of baffles in collector

cavities to reduce heat losses72F

73, etc.

Integrated collector storage (ICS) SHWS for domestic use incorporating both

symmetric and asymmetric concentrators have demonstrated their capability in

achieving moderate temperatures with lower thermal losses than conventional flat

plates73F

74. They also offer comparable performance, or better, if high reflectance

materials are used74F

75, are configurable so that the entire integrated system requires

less auxiliary boosting75F

76 and represent a reduction in material costs71,76F

77. Better

aesthetic building integration is also alleged for ICS systems.

A conventional CPC with novel absorber geometry77F

78, convection suppression

mechanisms and lowered optical losses has also shown an improved performance



82

over flat plates and evacuated tube collectors up to 100°C with comparable, or

potentially lower, costs.

These studies demonstrate that concentrating collectors can replace flat plate

collectors by offering equal or better performance for similar costs.

In many cases, however, the design of the collectors can still represent an added

complication. The introduction of asymmetric geometries, for example, may imply

reflector dimensions that could be bulky and difficult to integrate, and even maintain,

with conventional building structure, especially in the case of ICS systems.

Realistically, “pleasant aesthetic integration” is a matter of subjectivity and lifestyle,

and does not benefit from large or awkwardly shaped structures on domestic roofs.

Additionally, the generation and use of steam as the heat transfer medium has not

received much attention. As such, concentrators proposed as alternatives for hot

water production are not necessarily geared towards high performance at higher

temperatures, although they might be capable of doing so.

The initial stages of this work aimed at producing a self-pumped domestic SHWS of:

- Completely passive operation and low maintenance.

- Remotely coupled components (panels on roof and water tank at ground level)

- Simple and inexpensive elements, where possible (steam as heat transfer fluid)

Examples of self-pumped systems, capable of domestic use, have been proposed78F

79,79F

80,

modelled80F

81 and operated81F

82,82F

83. They have considered low boiling point fluids, other

than water, which have not required concentration techniques and have therefore

used conventional flat plate collectors. They share common advantages with the

system proposed in this project (e.g., passive operation and remotely coupled).

However, they suffer from a few disadvantages such as lower heat of vapourisation

for phase-change energy transfer, technical difficulties in their elaboration and the

use of certain passive control mechanisms, requiring a maintenance routine.

A passive downward heat transport system, using water, was proposed in 1988 and

considered the use of an adjustable concentrating collector with evacuated tubes83F

84. A



83

subsequent simulation84F

85 devised a full scale model that operated successfully over a

height of one storey to advance the model.

Non-imaging asymmetric concentrators, also with evacuated tubular absorbers, have

been developed and tested85F

86 for solar cooking with a similar passive downward

transfer principle. This and the previous system were sealed requiring high-pressure

protection valves. The solar cooker had a somewhat bulky collector-absorber unit

due to the high-load seasonal winter bias incorporated into reflector design.

The present work has taken into account these advantages and disadvantages.

Non-maging concentrators for steam generation were considered prudent. In the

interest of marketability, the dimensions of the collector would necessarily have to be

comparable to those of conventional flat plates. The use of readily available, “off the

shelf” if possible, materials and devices would improve the chances of a

cost-effective system.

It was clear that the CPC was the element of choice for the following reasons:

- Stationary

- Flexible and highly configurable for different absorber geometries.

- Relatively simple manufacturing compared to other concentrating devices

- Proven efficacy for steam generation

- Relative construction simplicity and set-up of a symmetric vs. asymmetric CPC

In this study, CPC vertical and horizontal fin profiles (Figure 3.4) were tested as a

modular array of concentrators and were put together in what became the first

prototype constructed. For subsequent prototypes, the horizontal fin profile was

chosen exclusively for two main reasons:

- The upper face of the horizontal fin receives radiation directly entering the

aperture area of the collector, while the lower face receives radiation via the

reflector. The vertical fin profile is totally dependent on the reflector, therefore

more affected by optical losses introduced in the reflection process. The

horizontal fin profile also allows for using lower cost materials that somewhat

compromise on optical efficiency.



84

- Convection heat losses are expected to be lower for the horizontal fin, since hot

air under the plate at the involute section is partially trapped.

Modelling of sun-earth geometrical relationships and heat transfer dynamics in the

collector-boiler assemblies was done to predict the behaviour of the system.

6.3 Solar Geometry and panel layout/orientation

Determination of energy collection for the CPC geometry was obtained as an

extension to the methods applicable to flat surfaces, where it was possible to

manipulate position and orientation of a CPC to suit any situation. The mathematical

treatment proposed for this was given in Chapter 2 and detailed in Appendix A.

Starting with a horizontal CPC panel and a north-south line-axis alignment, it was

possible to rotate the panel in 4 different ways (Figure 6.2) in order of importance

(tilt and twist are user preferred).

1. An azimuth rotation, ϕ, about the normal to the plane

2. A tilt,θ, or rotation about the transverse axis Main rotations

3. A twist, ω, or rotation about the longitudinal axis

4. A rotation, ρ, normal to the plane after reaching its final orientation (optional)

Figure 6.2 CPC main plane rotations

Azimuth angle

y

z

x ϕ

Tilt angle

y

z

x

θ

Twist angle

y

z

xω

θ

⎭⎬⎫



85

By knowing the relative positions between the sun, the CPC and the plane orientation

(Figure 6.3), it was possible to determine the irradiance and collection times over a

day.

Figure 6.3 CPC collection and acceptance angles

The recirculation in the collector requires a tilted configuration. The simplest

arrangement that satisfies this is orientation mode #1 (section 6.1.1): a north-facing

panel tilted to the latitude angle. Other possible configurations were also explored in

Chapter 3, such as orientation mode #2, which is the tilted east-facing panel with a

twist angle and which appears to be the most efficient for energy collection.

The first prototype was orientated according to mode #2 while the second and third

prototypes as by mode #1, with the third (and last) prototype the only one for which

long term measurements were taken and with collection times of approximately 4

hours per day (Figure 3.9a).

VS

θc

θa

VN’

VST



86

6.4 Heat transfer

The next part in performance prediction of the CPC configuration was the study of

heat transfer modes in the CPC absorber-boiler arrays.

A cross section of the CPC profile and element description is given below:

The system comprises:

• Top cover

• CPC reflector

• Absorber-boiler

• Insulation

Figure 6.4 CPC cross-section

The simulation of heat transfer and thermodynamic processes in multicomponent

systems is complex. Analytical solutions that account for all interactions between all

constituents and the surroundings are difficult to obtain.

Simulation models and different approaches proposed for solar water heating designs

can be divided in two main types:

- Models which rely on algebraic manipulation of well-established analytical

relationships for heat transfer modes.

- Models which rely on numerical approximations. Time-dependent equations for

temperatures, pressures, and fluid motion within the systems are solved in this

manner.

Models of the first type77,86F

87-87F88F

89 produce results in a relatively shorter time and offer a

more direct analysis and understanding of the heat transfer intricacies of the systems

under study but require much more simplification. Numerical solutions obtainable

from modular simulation programs89F

90,90F

91 provide the most complete and accurate



87

results, but require relatively long user experience and appreciable expertise to

exploit full model capabilities. They also require higher capital investments.

The analytical model approach was employed in the present work. Table 6.7 lists the

heat transfer interactions of the steam production system:

Table 6.7 Real heat transfer modes in the system

Heat exchange in this system occurs between

Cover and environment Absorber and cover Reflector and absorber Reflector and cover Reflector and insulation Insulation and environment

Heat transfer modes between enclosures of arbitrary shapes and sizes and their

surroundings are very difficult to determine analytically. Even empirical equations

are scarcely available. This is especially the case for convection heat transfer. To

date, there appear to be no general relationships applicable to a wide range of cases

involving arbitrary enclosures91F

92. Most of them relate to rectangular and box-type

(parallelepiped) arrangements. In the heat transfer analysis undertaken, several

assumptions were made and simplifications introduced to be able to tackle the

modelling process in a simple, yet accurate way, so to produce acceptable results:

1. Temperatures are constant and uniform for absorber-boilers

2. Heat capacity effects of all elements are negligible

3. Temperature drop across the cover is negligible

4. Conduction losses through insulation are insignificant

5. Radiation exchange between grey bodies with form factors equal to 1

6. Optical properties only vary discretely for solar and thermal spectral differences

7. The system is equal to a concentric cylinder arrangement for convective transfer

8. Heat generated from reflector absorptance ends up on the top cover

The simplified heat transfer model used was based on the following interactions:



88

Table 6.8 Simplified heat exchange modes

Heat exchange in the system is described by modelling convection and radiation transfer modes between:

Cover and environment Absorber and cover

Reflector and absorber Reflector and cover*

*single, combined, transfer mechanism for both modes.

The simulation also considered a system with a

cover on top of the CPC structure and a second

cover in the form of a semi-cylindrical sheath

around each absorber.

The energy balance equations for heat exchanged due to convection and radiation are

described in the following section (refer to nomenclature page for description of

variables and subscripts):

6.4.1 Collector panel energy balance equations and relationships for heat

transfer modes

For top cover (C)

( ) ( ) ( ) ( ) ( )ambCCCFCACFFFCFCCCCCC TTAhrhcTTAhrhcrAIAI −⋅⋅+=−⋅⋅++−⋅⋅⋅+⋅⋅ 1τα (6.1)

For sheath (F)

( ) ( ) ( ) ( )CFFFCFCFAAAFAF TTAhrhcTTAhrhc −⋅⋅+=−⋅⋅+ (6.2)

For absorber (A)

( ) ( ) ( )FAAAFAFCCACAC TTAhrhcrAAIAI −⋅⋅+=⋅⋅−⋅+⋅⋅ ττ (6.3)

It is assumed that the sheath does not absorb radiation.

Figure 6.6 Double cover model

4444 34444 21

0η⋅= IS

Figure 6.5 Heat transfer modes



89

To solve these equations to find the temperatures of each element and ultimately the

heat losses the thermal resistance network formulation explained in Chapter 4 was

employed. The thermal network corresponding to this model is shown in Figure 6.7

and an explanation of the parameters used is given in Table 6.9:

(a)

(b)

Figure 6.7 Thermal network resistance for the CPC heat transfer model

The model did not explicitly consider transfer modes associated with the reflector

surface. During operation, depending on the reflectivity of the material used on the

walls of the collector, more or less incoming radiation was reflected onto the

absorbers. Even though high reflectance values were possible, there was always a

certain amount of energy absorbed in the walls and subsequently exchanged in the

system, in the form of radiation and convection. The reflector walls, therefore,

radiated energy to the absorber and cover. A convection flow within the CPC cavity

(in addition to that arising by heat losses from the absorber) was also established.

For simplicity it was assumed that, because the absorber was relatively small (about

31 the area of the reflectors), the energy absorbed by the reflector walls eventually

ended up on the top cover of the CPC. This is the reason why the thermal network

shows a constant heat source, QK, at the TC node. QK includes the combination of

convection and radiation modes for the reflector, which is equal to the energy it

absorbs (QR) and this is why it is considered as a single constant. The other

component, QC, refers to absorption of solar radiation by the cover. The QK input on

the cover raises its temperature and has the effect of contributing to higher overall

system efficiencies.



90

Table 6.9 Heat transfer model parameters for thermal network of Figure 6.7

Parameters Description

Temperatures: TA Absorber-boiler (TA = 100°C) TF 2nd cover (sheath) TA > TF > TC TC Top cover

Tamb Ambient temperature Thermal resistors

(RT = 1/A·hT):

RRAF Radiation mode RCAF Convection mode

Absorber → Sheath

RRFC Radiation mode RCFC Convection mode

Sheath → Cover

RRCS Radiation mode Cover → Sky

RCCS Convection mode Cover → Environment Equivalent resistors

(Req= {Σ RT-1}-1):

Radiation-convection thermal factors combined

RA Absorber → Sheath RF Sheath → Cover RC Cover → Environment

Input factors: S Attenuated solar energy reaching absorbers

QO Heat losses from the absorber boiler QK= QR + QC Input heat term arising from:

-Transfer modes linked to CPC walls (QR) -Radiation absorbed by top cover (QC)

Another important point to notice is that, whilst convection resistance from the cover

to the surroundings, RCCS, was naturally referenced to the ambient temperature, the

radiation resistance from the cover to the sky, RRCS, was also referenced to this

temperature when it should rather be the sky temperature. The reasons behind this

are explained in section 4.3 and it is mainly for simplicity in the solution of the

thermal network. The expressions and calculations for the heat transfer coefficients

were taken from various sources as referred to in Chapter 4 and are given in

Appendix E. Examples of typical numerical results for these losses are given in

Table 6.10.



91

Qualitative explanation of model simulation and heat flow in the system:

1) Heat input

a) Radiation admitted by the CPC traverses the top cover where most of it is

transmitted (~90%), a fraction is reflected and a fraction is absorbed.

b) Transmitted radiation reaches the CPC walls, where most is reflected (~95%)

onto the absorber-boilers and a small portion is absorbed within the walls.

c) Radiation reaching the boilers is mostly absorbed (90-95%)).

d) The energy absorbed by the boilers is equal to the energy falling on the CPC

plane modified and attenuated by the optical efficiency of the system. This

optical efficiency incorporates the transmittance, reflectance and absorptance

values of the components involved.

e) The ‘S’ parameter shown in the thermal resistance network is this final

energy reaching the absorber-boiler.

2) Heat losses

a) Part of the energy absorbed is used in the production of steam by heating and

boiling water. The rest is lost by convection and radiation.

b) The model was analysed in steady-state mode of steam production. Under

these conditions, the model considered a constant temperature for the

absorber-boiler fixed at boiling point (TA = 100°C) 6F

*.

c) Thermal resistors RRAF and RCAF represent the energy losses from the absorber

to the second cover (sheath) due to radiation and convection, respectively.

d) Thermal resistors RRFC and RCFC represent the energy losses from the sheath

to top cover.

* In reality, temperatures will vary and will be higher at the edges of the fins, but will be close to boiling point in the tubules where water is vapourised



92

e) Finally, thermal resistors RRCS and RCCS represent the energy losses from the

top cover to the ambient.

The problem lay in solving this network in order to find all temperature values, T,

and ultimately heat values, Q.

In principle, heat flow can be calculated from the thermal resistance network

formulation by finding R and T values as explained in chapter 4. However, the

thermal resistance values are not fixed, but are dynamic quantities that depend on the

temperatures and the temperatures depend on the R-values and on the heat flow.

The network was reduced to equivalent thermal resistors as shown in Figure 6.7. It

was further reduced by adding RA and RF, since the heat flow from absorber to sheath

and from sheath to cover is the same (QO). This eliminated parameter TF and

simplified the calculations.

From the network, it can readily be seen that:

AOAF RQTT ⋅−= (6.4)

FOFC RQTT ⋅−= (6.5)

By algebraic manipulation, it is possible to show that:

CFA

CKSAO RRR

RQTTQ

++⋅−−

= (6.6)

If RF is set to zero, the second cover is not considered and the problem reduces to

that of a single cover CPC/absorber-boiler.

Solution process

The solution for finding the temperatures and the heat loss of the panel was based on

the iterative approach for thermal networks (chapter 4). The following flow chart

illustrates the different steps through which the solutions algorithm was applied.



93

Figure 6.8 Solutions algorithm flow chart for simulation of heat transfer in the system

and calculation of relevant parameters

By solving the balancing equations, the iteration process looped until previous and

new temperatures differed by 0.01 °C. Once this point was reached the process ended

and the desired temperatures and heat flow values were found, allowing

determination of the efficiency of the system.

Convective and radiative heat transfer coefficients are calculated (hconv, hrad)

Equivalent thermal resistance values (RA, RF, RC) are calculated

QO is determined (eq. 6.22)

If |TFnew - TF| > tol or |TCnew - TC| > tol

Else

New TF is found (eq. 6.20): TFnew

New TC is found (eq. 6.21): TCnew

Previous values replaced by new ones:

TF = TFnew TC = TCnew

END

Temperature input

TA & TS: known values



94

Table 6.10 Numerical results for a panel with a single cover (no sheath) and for various absorber emittance values

Emittance of the absorber (ε) Calculated and given parameters 0.1 0.3 0.6 0.9

Absorber length 2.25 m Fin width 0.05 m

Fin surface width 0.10 m CPC Aperture (truncated) 0.16 m

Optical efficiency 0.8 Average irradiance 900 W/m2

Temperatures: ° C Tamb 20 TA 100 TC 42.3 45.5 49.6 53.2

Heat transfer coefficients: W/m2·°C HRAC 0.93 2.83 5.76 8.76 HCAC 2.36 2.32 2.26 2.20 HRCS

6.39 6.49 6.63 6.75 HCCS 8.08 8.39 8.76 9.05

Equivalent resistors: °C/W RA

* 1.35 0.86 0.56 0.41 RC 0.19 0.19 0.18 0.18

Total heat loss: [A· (RA + RC

)]-1 W/m2·°C

U 1.8 2.6 3.8 4.8 * Absorber-cover heat transfer resistance values are calculated based on the absorber area

Cover-ambient heat transfer resistance values and total heat loss from the CPC are calculated based on the cover (CPC aperture) area

Table 6.10 shows that the heat losses are under 5 W/m2·°C for a worst-case scenario

of high absorber emittance. Less is expected if a selective surface is used for the

absorbers (as was the case in this study). The main contributors to changes in overall

heat loss are the convection and radiation losses from the absorber to the cover. The

losses from the cover to the ambient have very little impact, and in fact do not

change significantly.



95

6.4.2 Conveyance infrastructure / transfer line

Steam produced in the absorber-boiler section traveled down the transfer line into the

exchanger loop inside the water tank. The heat lost in this trajectory had to be

minimised and adequately predicted for overall performance evaluation.

These losses were calculated and assessed experimentally by setting up at 10 m long

equivalent pipeline, transferring steam from one end to the other and measuring

condensate formed in the transfer line and steam collected at the output (Figure 6.9).

Figure 6.9 Assessment of heat losses for an experimental transfer line

The pipeline was insulated with 25 mm thick fabric-protected polyester tubes, slit in

the middle. Five of these tubes were used and joined together with masking tape. The

set-up included a condensate trap and a graduated cylinder for accurate measurement

of total condensate volume (Figure 6.9).

The volume of the water collected in the trap arising from condensation in the pipe

gave an indication of the losses. From equations 4.49 and 4.51:

( )TCpLVQ Hcondpipeloss Δ⋅+⋅⋅= &ρ (6.7)

Where condV& is the volume flow rate, ρ is the density of the condensate formed in the

pipe, ΔT is the temperature difference between condensate and ambient values and

LH is the enthalpy of vapourisation.



96

Experimental measurements took about 20 minutes with a condensate volume of

(73 ± 1) cc and condensate temperatures of 93 °C at pipe exit. From equation 6.7

about 150 W are required to produce this amount of steam condensate.

The calculated value for pipe heat loss (from equation 4.35) was about 170 W,

where, T1 = Tamb = 25° C ± 2 °C, κtube= 0.058 W/m2·°C (at 25°C), r2 = 31.4 mm,

r1 = 6.4 mm.

Power losses from the pipe depend on the ambient temperature and are not constant.

However, for simplicity and since ambient temperatures did not vary much during

system operation, a fixed figure, initially of 150 W, was used in the overall

performance calculation of the SHWS, where the experimental measurements were

considered more reliable that the calculated value. This figure was later reduced to

100 W since a different material (Armaflex™) with 33% lower thermal conductivity

was used as thermal insulation for the transfer line (section 6.2.2).

Solution process

Power going into the water due to steam condensation was determined as:

Vcond_ktanpipe_lossout_panelin_steam LVPPP ⋅⋅=−= &ρ (6.8)

Vcond_tot LV ⋅⋅ &ρ

150 W (as mentioned above)

Where cond_totV& is the total condensate volume rate, which was due to pipe losses and

heat exchange in the tank. cond_ktanV& is the condensate volume rate from heat

exchange in the copper loop inside the tank. The difference between the two is the

volume rate of condensation that occurred in the transfer line.



97

6.4.3 Hot water tank and exchanger

A commercial tank was used and modified to include the heat exchanger. Energy

gained from steam condensation occurred essentially via: 1) the phase change from

steam to water, and 2) the sensible heat transfer from hot water condensate as it

travelled through the exchanger

While heat transfer remained relatively constant during initial stages of operation, it

decreased as the temperature of the water in the tank rose. A stagnation water

temperature, Tstag, was reached, where the effective energy gained by hot water was

equal to the tank losses. The system gained much more heat from steam phase

change than from the hot condensate resulting from this change.

In a situation like this, the highest contribution that sensible heat could have to the

overall energy gain of the water in the tank, and for water at 20 °C, is about 15% that

of steam. In reality it would be less, since the water in the tank would desirably never

be allowed to go below 35°-30° since it would not be useful for domestic tasks. For a

tank water temperature of 50°C, the contribution would be less than 10%. For 70°C,

it would only be about 5%.

Therefore, power delivered to the water was conservatively estimated by assuming it

was equal to 105% (5% extra) of the amount contributed by steam phase change

during operation of the system. Effective power was then this amount moderated by

a temperature-dependent steam energy transfer efficiency, ηS, less tank losses:

( ) ktan_lossin_steamseff_water PP.P −⋅⋅≅ 051η (6.9)

An approximation to tank losses was made by assuming only conduction losses

occurring via the insulation to the surroundings and in a radial direction. This

enabled the use of equation 4.35 for multilayered cylindrical structures.

[ ]⎪⎪⎩

⎪⎪⎨

⎧

≡

<=

=

etemperaturoffunctionT

ionapproximat

ionapproximat

ss

ndeff_ss

sts

ηη

ηη

η

21

11



98

( ) ( )ambiw

T

T_insT

Tktan_loss TT

DtDln

lP −⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛ +

⋅⋅=

2

2 κπ (6.10)

DT is the diameter of the water tank proper, tins_T is the thickness of the insulation and

lT is the height of the tank. The assumption was that the temperature of the internal

tank wall was equal to the water temperature: Tiw = Twater_tank. Since the water was

heated from the bottom, Twater_tank was taken as the maximum recorded temperature

of the water.

A second approximation, which was more accurate with the experimental results,

included the top and bottom areas of the tank as well. The value of lT was augmented

to reflect the augmented area. In this case equation 6.10 becomes:

( )( ) ( )ambktan_water

T

T_insT

TTktan_loss TT

DtDln

DlP −⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛ +

+⋅⋅=

2

22 κπ (6.11)

Alternatively, the tank may be modelled as a cylinder of area Atank and the losses

found by the experimental determination of an overall heat loss coefficient, Utank,

using the following equation:

( )ambktan_waterktanktanktan_loss TTAUP −⋅⋅= (6.12)

The disadvantage of this method is that it is specific to the tank used, while the

previous method, in principle, can be adapted to any cylindrical tank.

Solution process

The net heat gained by the water was predicted from equations 6.8, 6.9 and 6.11:

( ) ( )( ) ( )ambktan_water

T

T_insT

TTpipe_lossVcond_totseff_water TT

DtDln

DlPLV.P −⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛ +

+⋅⋅−−⋅⋅⋅⋅≅

2

22051

κπρη & (6.13)



99

6.4.4 Summary of solution process for the entire system

Solving for the collector meant

determining output power as steam

production. Solution for the collector

included Sun-Earth geometry, energy

collection and heat transfer dynamics.

Solving for the transfer line meant

calculating the effective steam power

coming into the storage tank heat

exchanger as useful steam after transfer

losses. An experimental (conservative)

value of 150 W was used.

Solving for the storage tank meant

obtaining effective power transferred

and retained in the water by useful

steam. Solution included sensible heat

contributions and approximation to

losses from an augmented cylinder.

Collector simulation results are given in section 6.6.1. The efficiency was assessed

versus concentrator reflectance and absorber emittance (Figures 6.39 and 6.40).

Steam production was assessed versus concentration ratios and an optimal figure was

found for different absorber emittance values (Figure 6.43).

Results for the storage tank in section 6.6.4 show the increase in losses with

increasing water temperatures, with a maximum power loss estimated at

(100 ± 11) W. The higher accuracy in tank loss calculation for the modified

relationship of equation 6.11 was acknowledged.

Collector

Inputs:

Outputs:

Solution’s algorithm

for CPC panel

(figure 6.24)

Transfer line

Inputs: Psteam_coll

Outputs: Psteam_intank

Water storage tank

Inputs: Psteam_intank

Outputs: Pwater_eff



100

6.5 Experimental work: prototype and system construction

The system designed was composed of the following elements:

• Solar collector panels for steam production with top cover

• Roof reservoir tank providing the water for steam conversion

• Conveyance system (tubes and pipes)

• Storage tank

• Heat exchanger

• Condensate receptacle

All three prototypes constructed were based on the same design principles. The

difference lay in materials chosen for construction of boilers and reflectors and

variations in the number of CPC structures per collector. The reservoir tank, the top

cover, the conveyance system, the hot water tank and the heat exchanger were

practically identical in all three.

6.5.1 System components

The CPC reflector

The criteria for construction of the CPC shape was based on the following:

- Collection times of 4 hours, meaning an acceptance half-angle of 30°

- Theoretical maximum concentration factor of 2

- Truncation to obtain a low height profile, comparable to flat plate collectors

- Vertical and horizontal fin profiles

The shapes of the reflectors were obtained from the parametric equations for the CPC

as given in chapter 3 and Appendix C. The absorber fins considered were 5 cm wide,

giving a surface of 10 cm2 per cm length. The aperture of the collector, therefore,

would be 20 cm wide in order to obtain the maximum concentration of 2 for these

circumstances. However, truncation was done at approximately a third of the total

height (8 cm), leaving the CPC structure with an aperture of 16 cm. An example of



101

the actual horizontal fin profile used is given in Figure 6.10. The concentration factor

was reduced to 1.6 by this change with a slight increase in collection times.

Figure 6.10 Truncated CPC profile used (scale 1:3)

Absorber-boilers

The absorber boilers were a combination of copper fins, 50 mm wide, 1.8 m - 2.25 m

long and 0.07 mm thick, with copper tubes of 4.5 mm ID soldered on top (Figure

6.11).

Figure 6.11 Schematic of the fin and tube copper absorber

Soft soldering with a lead-tin alloy was used to attach tubes to fins in all but one of

the modules constructed (the exception being a brazed array for the second

prototype). The fin & tube arrangement was soldered or brazed to header and footer

pipes making up absorber-boiler modules (Figure 6.12). Each module had return

pipes at each side for convenient return of hot water bubbled-up into the header pipe

by the boiling process. If this water was not removed from the header pipe it would

interfere with and hinder steam delivery down the transfer line. The footer pipe was

connected to the bottom of the reservoir tank, which held the water that was gravity

fed to the boilers. All prototypes were blackened. The first and second prototype

2θa

Soft SolderTube

Fin



102

modules were spray-painted black. For increased efficiency, a spectral selective paint

(Solkote™) was used for the second prototype and a spectral selective self-adhesive

material (Maxorb™) was used for the third prototype.

Figure 6.12 Absorber-boiler array of 7 fins & tubes connected to header/footer tubes and

return water pipes prior to blackening (2nd prototype)

An upper limit measure of fin efficiency was estimated based on standard heat

transfer relationships for flat plate collectors92F

93, owing to the similarity between the

straight rectangular fin-and-tube profile of flat plates and the CPC absorber profile:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅

⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅

⋅=

2

2

tubefin

fin

tubefin

fin

fin Dwt

U

Dwt

Utanh

κ

κη

(6.14)

Where: U = total heat loss coefficient from the panel in W/m2·°C

κ = 385 W/m·°C, the thermal conductivity of copper

tfin = 0.07 mm, thickness of the copper fins

wfin = 50 mm, width of copper fins

Dtube = 4.5 mm, diameter of absorber tubules



103

For conservative purposes, a U-value of 8 W/m2·°C for the CPC panel was used,

which is above typical values for single cover flat plates93F

94. For these conditions, the

fin efficiency from equation 6.14 is above 94%, and so little thermal penalty was

expected by this design.

The small diameter for the boiler tubes was chosen on the need for expedite steam

creation. A small volume of water would be readily converted into steam, since it

was desirable to reduce as much as possible operation downtime arising from a

reduced solar input on days of partial cloudiness and other transient effects. For an

input of 820 W (from Table 6.5) on the array of Figure 6.12, each absorber-boiler

section will receive about 295 W. For a panel optical efficiency of 70%, about 205 W

of heat will be delivered to the water in each tubule. Assuming 90% of this heat is

converted into steam (185 W) the time taken to heat up all the water in the tubules

(about 30 cc) up to 100 °C and then vaporise it, is between 6 to 7 minutes, with a

mass flow rate of about sg

121 . This will depend on whether the panel has been

operating in steady-state mode or not. This also means that a steam flow rate around

scm3140 and a steam velocity of about 8.5 s

m could be expected. Under the most

favourable conditions and best prototype design, a steam flow rate close to 0.75 sL

(± 10%) was observed.

Roof reservoir tank

The reservoir tank was constructed of rolled and brazed galvanised iron sheeting. At

2 m long and 0.12 m in diameter, this reservoir was able to hold more than 20 L of

water (Figure 6.13). It was housed in a rectangular enclosure, made of the same sheet

metal, insulated with polyurethane foam and fibreglass wool. Copper pipes were

attached at each end of the tank. The bottom was connected to the footer pipes,

feeding the boiler array directly with cold water. The top was connected to the

transfer line for pressure equalisation throughout the system allowing the water to

flow freely into the boilers.



104

Figure 6.13 Reservoir tank (from final prototype)

The connection to the transfer line was done with a smaller diameter pipe in order to

reduce as much as possible any steam condensation in the tank. As steam was

produced throughout the day, water levels in the absorber-boiler array and water tank

decreased. The fact that the tubes acted as “bubblers” enhanced the flow and mixture

of hot and cold water and kept recirculation happening with reduced water levels. As

long as the self-pumping mechanism worked well and the system was properly

primed from the beginning, a water level of 30% the total capacity of the tank was

not considered problematic in terms of the likelihood of having hot spots and high

stagnation temperatures. This was evidenced in preliminary rig tests of early

absorber-boiler modules.

Hot water tank with heat exchanger coil

The water tank used was a Saxon Copperflow™ 200 L domestic hot water tank

manufactured by Peter Sachs Ind. The tank itself is made of copper sheeting which

has been rolled and brazed together into a cylinder, then sealed top and bottom with

copper covers. It is contained in a BHP Colorbond steel case into which polyurethane

is injected to provide insulation (except for the top and bottom covers that use

polystyrene). The tank is factory fitted with a lengthy heat exchange copper coil and

an electric heating element. The coil is connected to the cold water inlet and to the

hot water outlet.



105

The tank used in this system had the heating element removed and replaced by a

single copper pipe loop of 12.5 mm ID for heat exchanger from condensing steam.

The upper end of the heat exchanger was connected to the downward steam pipe.

The bottom end was connected to the condensate receptacle (Figure 6.14). As heat

transfer to the water in the tank from the phase change of steam was very efficient,

the length of the looped tube required was about 1 m. In order to recover as much

heat as possible from the hot water condensate a near horizontal loop was used.

Figure 6.14 Hot water tank

The final setup consisted of a 7 m long copper

transfer line running from the roof of a two

storey house to the ground level

Figure 6.15 Insulated vapour transfer line

(trajectory indicated by red arrows)

(a) Exchanger coil used (red) (b) Input and output ports for steam and condensate.

(c) Properly insulated and protected tank



106

6.5.2 First prototype collector panel

The initial prototype (Figure 6.16) consisted of 4 modules, each module made up of

3 CPC absorber boiler structures with vertical fins. The boiler arrays were 1.8 m in

length. The reservoir tank was located to the left of the collector. A non-return loop

was placed at the bottom of this tank to prevent hot water in the footer tube from

thermosiphoning into the reservoir.

a) Single module on test rig b) 1st prototype

Figure 6.16 CPC modules and 1st prototype

The CPC profile was provided by mould forming of polyurethane foam. The mould

was made out of wood shaped to the vertical fin profile configuration of the CPC

(Figure 6.17). Two different materials were used for the reflectors. One was an

anodised and polished aluminium sheet of 0.5 mm which exhibited a mirror quality;

Anocoil™. This was used in three modules. For the remaining module, a 0.2 mm

thick polished aluminium roll sheet was used. Both were bent to shape and fixed onto

the mould before casting of the modules.

Figure 6.17 Vertical fin profile CPC mould before and after aluminium lining



107

The absorbers were spray-painted with flat black paint and the modules covered with

3 mm UV resistant polycarbonate sheeting of 0.9 transmisivity. Four modules were

paralleled together by joining header and footer tubes and connecting the assembly to

the transfer line.

For this prototype, a second header tube was used to connect all modules and

reservoir tank to the downward transfer line (Figure 6.18)

Figure 6.18 Header tube of the 1st prototype and transfer line connection

Insulation for all piping was provided by foamed elastomeric nitrile rubber sleeve

tubing, Armaflex™, of 25mm OD (thick), 12.7 mm ID and thermal conductivity of

0.039 W/m2·°C at 45°C.

The entire assembly was set on a purpose built wooden structure with a tilt angle of

30° ± 3° and faced east for its entire operation. East facing was chosen as this

maximised solar input at the trial site and for the duration of the testing (summer).

Performance of this prototype was predicted from the mathematical model based on

the heat transfer modes discussed in previous section. There was good agreement

between experimental and numerical results (as detailed in section 6.6.1).



108

6.5.3 Second prototype

To improve on the manufacturing process and cost-effectiveness of the collector, the

following changes were proposed and implemented in a second prototype:

• Increase module dimensions from 3-CPC to 7-CPC cavities.

• Replace relatively expensive reflector materials with low-cost reflector materials

• Replace vertical fin & tube configuration for a horizontal profile

• Layer the absorber boiler with a spectrally selective paint for increased efficiency

• Replace mould forming method by precision-cut polyurethane blocks.

• Increase aperture area of the entire collector system (2 modules)

• Encase modules in galvanised and robust metal enclosures

• Use brazing instead of soft-soldering

The end result was a double module collector arrangement of 5 m2 collection area

with a central reservoir tank (Figure 6.19).

Figure 6.19 Double-panel 2nd prototype with reservoir tank in the centre

Each module comprised seven absorbers (at 0.16 m spacing) 2.25 m long, assembled

in parallel and also attached to header and footer pipes, now included as an integral

part of the modules. Both modules had 2 copper return pipes. One of the modules

was brazed in an attempt to achieve better rigidity and have a system less prone to

leaks. Total effective area of each module was about 2.5 m2.



109

Both assemblies were spray-coated with a solar selective paint of 0.9 absorptance in

the solar spectral range and a minimum achievable emissivity of 0.22 in the thermal

range (SolkoteTM Hi/Sorb-II selective solar coating). The spray painting was carried

out by a spray painting company so it was not possible to closely monitor the surface

thickness of the coating, which was a crucial aspect in the proper selective

functioning of the surface. The fins and tubes were identical in dimensions and

construction to the previous prototype, except for their increased length (2.25 m as

opposed to 1.8 m)

The process of fabricating the modules in this case was quite different. The

insulation and support structure for the boiler assemblies was obtained from

polyurethane foam blocks precision-cut to the required profile; length, width and

thickness. This was done by computer guided machinery provided by an industrial

application’s company (ReMax Pty Ltd). The CPC profile that eventuated was of

good precision and reproducibility, although about 1 mm extra depth was carved

from the intended mathematical shape. The polyurethane CPC structures were

painted to improve surface stability and improve reflector material adhesion. The

reflective material used was an aluminium coated paper (SisalationTM), fixed to the

profiles using a two-part self-curing epoxy resin (Araldite®). The cusp of the profiles

was reduced by about 5 mm so that the absorbers would not be directly in contact

with the reflectors and minimise heat losses via conduction. The modules were

placed in a galvanised iron sheet metal enclosure (Figure 6.20) and the absorber-

boiler arrays placed in position on top and in line with the axis of the CPC reflectors.

Figure 6.20 7-CPC module structure with reflective lining in metal case



110

This was done for protection, stability and ease of use during transportation and

operation. Insulating and reflective polyurethane end pieces were placed at both ends

of the modules and polyurethane foam was mixed and poured into the side areas to

provide insulation for the return pipes and to secure the CPC profile in the container.

A cover of 3 mm clear polycarbonate with the edges bent up to provide a water

barrier was placed over the assembly and secured in place with galvanised sheet side

and end sections.

The modules were placed on a metal frame and oriented due north with a tilt angle of

approximately 30°. The transfer line was a 15 m long 12.7 mm OD copper tubing

with 19 mm foam rubber insulation. The system was located at the premises of the

industry partner, Peter Sachs Ind. Pty. Ltd.

6.5.4 Third prototype

The results from the second prototype revealed problems associated with the design

and operation of the unit. Even though lower costs were achieved in its fabrication,

the degraded performance clearly made it unsuitable for the objectives of this study.

Therefore, a third and last prototype was constructed, including the modifications for

improved performance from first prototype, correcting the issues of poor

performance for the second prototype, and adding the following changes:

• Use of spectrally selective nickel chrome surface on the absorber-boilers

• Use of highly reflective silver surface for the CPCs

• Replacement of rigid return pipes for flexible hoses

A module identical to the second prototype, was produced and tested (Figure 6.21).

Every copper fin and tube was layered with thin self-adhesive metal strips of

blackened nickel foil (Maxorb®) of very high absorptance in the solar spectrum

(α > 0.9) and low-emittance in the thermal spectrum (ε < 0.11) (Figure 6.22). All fins

were cover-protected after layering until the array panel was assembled.



111

Figure 6.21 Single-module 3rd prototype with reservoir tank to the right

The CPC reflectors used were 0.5 mm thick acrylic sheets with a highly reflective

metallised backing (Silverlux™, ρ > 0.9), bent to the profile shape and glued on with

fast setting epoxy adhesive (Araldite®) (Figure 6.21). The CPC polyurethane module

was painted beforehand for improved strength and material adhesion. Interestingly,

the thickness of the reflector laminates seemed to partially compensate for the extra

depth that was cut-off from the structure as mentioned before.

a) Fin & tube prior to assembly b) Back side of array and lining of last fin

Figure 6.22 Fin and tube copper array before and during maxorb layering

It was realised that for return pipes it would be better to have flexible high

temperature tubing instead of rigid copper tubes. This would avoid expansion stress

between return tubes and absorber tubules, which could create vacuum leak points

affecting system performance. The third prototype therefore used high-temperature

(automotive) rubber hoses for return pipes, eliminating this problem.



112

Figure 6.23 CPC structure with reflector material Silverlux™ (still covered with protective

foil) and maxorb-lined boiler array

The casing of the module, polycarbonate cover and water reservoir tank were

identical to the previous prototype and the entire module was placed in the same test

site as for the first prototype with a north-east orientation.

This prototype had the best performance, being almost twice as efficient as the first

prototype and was the concluding unit in the study of a SHWS incorporating passive

downward vapour phase transport. All numerical and experimental results are given

in the next section.

Figure 6.24 Steam production from 3rd prototype



113

Figure 6.25 Collection and orientation layout for 3rd prototype showing collector and

reservoir on the roof and the storage tank at ground level

Figure 6.24 shows the panel in operation producing abundant steam. Figure 6.25

shows the panel in its final location and orientation, connected to the water tank via

the insulated transfer line.



114

6.6 Results and discussion

6.6.1 Modelling results

The mathematical model was implemented using MATLAB™ and allowed for

performance prediction of CPC panels and the system as a whole. It assessed

radiation collection for any position, latitude, date and time as per Table 2.2 and

incorporated the algorithm for simulation of the heat transfer dynamics (Figure 6.8).

The modelling relationships were based on the simplified heat transfer modes of

Table 6.8 and Table E1. Temperatures and heat losses were obtained as well as

energy production and efficiency of the system for variations in input data

parameters (irradiance values, optical characteristics, etc.).

The design of the second prototype was made with the results obtained by this

process with further improvements carried on to the third prototype.

The efficiency plots of the following figures are the model predictions for the CPC

panel. Efficiencies were later estimated for each prototype by measuring the rate of

steam condensate produced during panel operation (section 6.6.2). The plots are

based on the well-known Hottel-Whillier-Bliss formulation for the derivation of solar

collector efficiencies94-94F95F

96 from which the efficiency equation for the CPC boiler can

be deduced:

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡ −⋅−⋅==

GTTU

'FG

A/Q ambAcpcLAu

0ηη (6.15)

Qu is the useful heat collected, η0 = τC·Rcpc·αA, is the optical efficiency of the CPC, in

this case the product of cover transmittance, concentrator reflectance and absorber-

boiler absorptance. cpcLU = UL/C the collector heat loss coefficient (to the

surroundings) modified by the geometrical concentration ratio, C, (equation 3.2). F’

is the collector efficiency factor, a measure of the effectiveness of heat transfer from

the absorber to the fluid (the other quantities have been defined in previous sections).



115

Since these collectors are intended for water boiling, they will not operate unless

TA ≥ 100°C. This means that the maximum efficiency obtainable will always be

below F’η0. In the plots, an upper limit for efficiency under near-extreme conditions

was chosen (e.g., Tamb ≅ 34°C, G ≅ 1100 W/m2):

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−⋅≈

503

0cpcLmax U'F ηη (6.16)

Figure 6.26 Performance plots for variations in CPC wall reflectance

An important change between the first and second prototypes was the change in

reflector material (Figure 6.26), which was assessed concurrently with the

construction of the latter. The efficiency and reflectance are directly proportional, as

expected, since more radiation reaching the absorber means more energy available to

produce steam. From the plots above it is seen that reflectance changes of +0.1

equate to changes between 14%-35% in CPC efficiencies. The differences are higher

for lower reflectance values, suggesting that small changes can have a significant

effect in efficiency and must be taken seriously (as it was seen for the second

prototype results – Figure 6.45).

0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.150

0.05 0.1

0.15 0.2

0.25 0.3

0.35

0.4 0.45 0.5

0.55 0.6

0.65 0.7

Efficiency curves for different CPC reflectance and irradiance values

(Ta - Tamb) / G [K·m²/W]

Effic

ienc

ies

Irradiance range = 600 - 1000 W/m²

Ta - Tamb (steady state) = 80 °C

Optical efficiency range = 0.47 - 0.81

Irradiance range = 600 - 1000 W/m²

Ta - Tamb (steady state) = 80 °C

Optical efficiency range = 0.47 - 0.81

Reflectance 0.55 0.65 0.75 0.85 0.95



116

Figure 6.27 Performance plots for single- and double-cover collector models

0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0

0.05 0.1

0.15 0.2

0.25

0.3 0.35 0.4

0.45 0.5

0.55 0.6

0.65 0.7

Efficiency curves for different absorber emmissivities and irradiance values


Effic

ienc

ies

Irradiance range = 600 - 1000 W/m² Ta - Tamb (steady state) = 80 °C Optical efficiency = 0.65 (External model from A Rabl - see text)

Irradiance range = 600 - 1000 W/m² Ta - Tamb (steady state) = 80 °C Optical efficiency = 0.65 (External model from A Rabl - see text)

SINGLE COVER SYSTEM

Emittance ( ε ) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Rabl, ε = 0.1 Rabl, ε = 0.9

0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0

0.05 0.1

0.15 0.2

0.25 0.3

0.35

0.4 0.45 0.5

0.55 0.6

0.65 0.7

Efficiency curves for different absorber emmissivities and irradiance values


Effic

ienc

ies

Irradiance range = 600 - 1000 W/m² Ta - Tamb (steady state) = 80 °C Optical efficiency = 0.65

DOUBLE COVER SYSTEM

Emittance ( ε ) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9



117

Initially, with the intended construction of the first prototype it was thought that a

single cover system would be ideal and suffice for the objectives of the project. The

use of a double cover was later investigated for efficiency evaluation by absorber

emittance comparison (Figure 6.27). Also, predicted efficiency of the system is

directly proportional to the emittance of the absorber. This is true for both single and

double cover systems and was expected, since less radiation emitted by the absorber

means lower losses.

The other important observation is that for absorber emittance values below

approximately 0.4, the double cover system with a sheath surrounding the absorber

appeared to be less efficient than the single cover one. This showed that a simpler

and possibly lower cost CPC system could be devised by appropriate engineering of

the absorber-boiler in this area. Double cover systems have been proposed77,96F

97 for

reduction of losses in solar heating, therefore, it was considered during construction

of the second and third prototypes. However, due to the expected low emittance

values of the absorbers for these prototypes (less than 0.4), no double-cover or sheath

was used.

Efficiency results in the previous figures were compared to the work done by Rabl35

for similar panel set-up and conditions employed in this study:

- CPC panels of 1.6 concentration ratio

- Wind speed of 4.5 m/s

- Selective (ε = 0.1) and non-selective (ε = 0.9) absorber surfaces

- Tamb = Tsky = 10°C

- Optical efficiency of 0.65

Despite the simplified approach of this study’s prediction model, the efficiencies for

the single cover system were in moderate agreement with Rabl’s results. The model

developed predicted higher efficiencies for lower irradiance values and vice-versa.

For high emittance (ε = 0.9) and irradiance values above 800 W/m2, the models

differed by less than 20%. For low emittance (ε = 0.1) and irradiances over

600 W/m2, the models differed by less than 15% (Figure 6.27).



118

An optical concentration ratio of 1.6 (without truncation) equates to an acceptance

half-angle of about 38.7°. This means that collection times would ideally take just

over 5 hours and for a north facing panel, collection would start roughly at 9:30 am

and finish close to 2:30 pm. The maximum irradiance values at start and finish times

with optimum tilt angle and clear sky conditions would rarely reach 800 W/m2 in

subtropical latitudes peaking around 1000 W/m2 around noon. For a truncated CPC

with a reduced geometrical concentration ratio from 2 to 1.6 (as was the case with all

prototypes) the situation is different. Truncation will reduce the available power

input compared to the full-size scenario (Figure 6.10) with a slight increase in

collection times that will result in low radiation gains (Figure C2).

For low radiation gains the system would not operate, so in reality, it was expected to

behave very similarly to a full-size CPC arrangement with a reduced power input due

to geometrical reduction of the aperture. This meant that collection times resulting in

effective system operation would be close to the collection times expected for a non-

truncated concentrator. The experimental work confirmed this.

Total effective volume of water converted to steam over an entire operation cycle

was predicted to be between 6 L to 12 L for a 4 m2 collection area and an average

irradiance value of 880 W/m2 (Figure 6.28). Again, production is higher for lower

emittance values, as expected. The pre-boil time seen as nil production of steam at

the beginning of operation does not account for heat capacity effects of the elements.

In reality this time would be longer as the system heats up completely and

approaches thermal equilibrium.

From these results and from equations 6.9 and 6.13 it was possible to estimate the

requirements for the design of CPC collector panels based on hot water needs. For

instance, to supply the energy target of 30 MJ to 200 L of water, the amount of steam

necessary to transfer this energy would have to be more than 13 L, after taking into

consideration heat losses and steam/water heat exchange efficiencies. There are

different ways of achieving this:

- Increasing the collection area

- Using a higher reflectance material for the CPC



119

- Using a lower emittance surface for the absorbers together with high absorptance

- A combination of the above-

In commercial design it is then a matter of optimising these, and other factors, to

produce the optimum ‘high-performance/cost-effective’ ratio.

Figure 6.28 Total steam production for a typical CPC panel over 5 hours

There is also an optimum concentration ratio for different absorber emittances and

the model allowed to determine which concentration ratio would yield maximum

steam power production (Figures 6.29 and 6.30)

The horizontal line in Figure 6.29 (pink) represents the average power for optimum

concentration, which would deliver the largest amount of energy to the water for the

parameters selected (latitude, tilt, etc). The optimum in this case was 1.7 and steam

production would last close to 5 hours: from about 9:36 am to 2:24 pm (cyan curve,

indicated with arrow). By integrating over time, total steam energy could be found

0 25 50 75 100 125 150 175 200 225 250 275 3000

2

4

6

8

10

12

14

Heating time of absorber (min)

Volu

me

of w

ater

vap

ouris

ed (L

)

Steam production vs. heating time of absorber

Irradiance (fixed) = 880 W/m² Concentration ratio = 1.6 Collection area = 4.032 m² Ambient/sky temperature = 20° C

EMITTANCE (ε) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9



120

for each concentration curve. The highest value obtained of about 1542 W·h or

5.55 MJ, was for this concentration. The values are strongly dependent on the

emissive and absorptive properties of the collection medium. The figures above were

obtained for high emittance and high absorptance.

Figure 6.29 Steam power produced for various CPC concentration ratios

The plots of Figure 6.30 are an extension of Figures 6.28 and 6.29 considering how

steam energy produced by the CPC panel varies with absorber emittance and

concentration. Steam output varies markedly with the emittance of the absorbing

surface. It is seen that for high emittance values (ε ≥ 0.7), concentration ratios

between 1.5 and 2 appear to yield very similar results with no more than 3%

difference. As the emittance of the surface is lower, the optimum concentration

decreases.

These results depend on the geographical location and date and positioning of the

collectors. The plots of Figures 6.28, 6.29 and 6.30 were obtained for latitude -27.5°,

autumn equinox (21st March) with the collector facing north and tilted to the latitude

angle (maximising energy collection).

6 7 8 9 10 11 12 13 14 15 16 17 18 0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

Solartime

Pow

er p

er u

nit a

rea

(W/m

²)

Steam power production over a day for different concentration ratios

Absorber emittance/absorptance = 0.9 / 0.95

OPTIMUM CONCENTRATION RATIO = 1.7

Steam production energy ~ 1542 W·h

Average Power ~ 321 W

Azimuth = 0°

Latitude = -27.5° Tilt = 27.5°

Tamb = 20°

Concentration (angle)

C = 1 (Ø = 90°) C = 1.4 (Ø = 45.6°) C = 1.6 (Ø = 38.7°) C = 1.7 (Ø = 36°) C = 1.8 (Ø = 33.7°) C = 2 (Ø = 30°) C = 2.5 (Ø = 23.6°) C = 3 (Ø = 19.5°) C = 5 (Ø = 11.5°) C = 11 (Ø = 5.22°) Average power Irradiance profile

OptimumOptimum



121

Figure 6.30 Daily steam energy produced for various CPC concentration and emittance values

The results of Figure 6.30 could be used as a design tool in the selection of optimal

characteristics for the SHWS given the requirements for domestic hot water. For

seasonal and panel orientation changes, several plots would be required for a more

comprehensive assessment.

The energy target of 30 MJ is about 8.4 kWh. Thus, referring to Figure 6.30 it would

appear that the minimum collector area required is 4.5 m2 for a solar selective

absorber ε = 0.4 with concentration in the range 1.3-1.8. In reality, it will be higher

than this since these are results for steam power output from the panel, without

considering transfer line losses, steam heat transfer efficiency (ηS) in the exchanger

and tank losses.

Additionally, Figure 6.30 does not consider truncation for the CPC. In this study the

collection aperture for 2× concentration was truncated to 80% the original value. An

80% power output was then used as an empirical lower limit to the real output.

1 1.5 1.7 2 2.5 3 3.5 4 4.5 5 5.5 60

500

1000

1500

2000

2500

Concentration ratio

Stea

m e

nerg

y pe

r uni

t are

a pe

r day

(W·h

/m2 ·d

ay)

Steam energy per unit area vs. concentration ratios

EMITTANCE (ε) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9



122

Therefore, as a design tool, these results would still require adjustment for:

- Truncation of the CPC

- Pipeline losses, which were taken as 150 W (section 6.4.2)

- ηs values (section 6.4.3)

- Tank losses (section 6.4.3)

6.6.2 Experimental results from prototypes

6.6.2.1 First Prototype (Figure 6.31)

Figure 6.31 Efficiency results for the 1st CPC prototype

For efficiencies above 20%, experimental data for this prototype and results from

Rabl’s numerical study were in very close agreement, with differences being smaller

than 3%. The differences between the model prediction from this study (blue curve)

for the same data and same efficiencies were under 13%.

0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0 0.025 0.05

0.075 0.1

0.125 0.15

0.175 0.2

0.225 0.25

0.275 0.3

0.325 0.35

0.375 0.4

(Ta - Tsky) / G [K·m²/W]

Effic

ienc

ies

Efficiency curves comparisons for 1st prototype

HIGH EMMITTANCE ( ε = 0.9) Model prediction Results from A Rabl* Results from 1 s t prototype

R > 0.99 P < 10-11

ΔF’η0 = 0.03

ΔF’UL = 0.3

(Eq. 6.30)GT..exp

Δ⋅−= 76880η

cpc



123

For irradiance values above 840 W/m2, the efficiencies of the collector were above

25%. To supply 30 MJ/day to the water in a 4-hour period, an average power of

delivery of about 2100 W is required (Table 6.2). The aperture area of this panel was

about 3.5 m2 (4 modules of 1.8 m × 0.49 m each). For an average irradiance of

880 W/m2 (Table 6.2) and considering associated heat losses in the system, to able to

deliver close to 2100 W to the water a SHWS incorporating the design of this first

prototype would require a minimum of 3 panels.

6.6.2.2 Second Prototype (Figure 6.32)

Figure 6.32 Efficiency results for the 2nd CPC prototype

The disappointing performance of this prototype was most probably due to the

overestimation of the true optical efficiency of the system:

- Use of lower average reflectance material for the CPC reflectors (Sisalation™)

- Overestimation of the actual reflector values since the reflectance of the material

was not well characterised after application

0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.140

0.025 0.05

0.075 0.1

0.125 0.15

0.175 0.2

0.225 0.25

0.275 0.3

0.325 0.35

0.375 0.4


Effic

ienc

ies

Efficiency curves comparisons for 2nd prototype HIGH EMMITTANCE (ε = 0.9) Model prediction Results from A Rabl* Results from 2 n d prototype

(Eq. 6.30)GT..exp

Δ⋅−= 64570η

R > 0.98 p < 0.003

ΔF’η0 = 0.04

ΔF’UL = 0.5cpc



124

- Underestimation of the emittance of the absorber-boilers since the Solkote™

solar selective surface was not well characterised after application

- Suspected steam leaks in the system

- Insufficient insulation used for transfer piping

The nominal value for solar reflectivity of the Sisalation product is about 0.82. It is

possible that the average reflectance of the CPC structure was well below this value

due to handling in the process of adhesion. It is noticeable from the photographs that

the CPC reflectors presented visible defects, such as crevices and bumps (Figures

6.19-6.21). Also, due to surface damage during soldering, brazing and inadequacies

of surface cleaning of the copper substrate, it is possible that the emissivity was

higher than the suggested range (0.28-0.49). The experimental determination of

system optical efficiency seems, therefore, necessary, and could be incorporated as

part of future prototype development. A suitable method is discussed in section 6.7.

Since top-up water was often required in the reservoir tank during operation, it is

probable that there was a leak in the system. Any escape of steam would have

lowered the measured collector efficiency.

6.6.2.3 Third Prototype (Figure 6.33)

The third prototype exhibited the best performance with over 50% efficiency for the

higher irradiance values (over 800 W/m2). The improved performance was attributed

mainly to the high attention to detail and improved fabrication process. In particular:

- Absorber-boiler array layout and soldering

- Application of a high quality selective surface

- Use of highly reflective material as CPC reflector

- Use of flexible return pipes as part of the boiler array

Results were close to model predictions for surface emittance below 0.3. Numerical

predictions from Rabl’s work were similar as well, although the experimental results

were higher, on average. Rabl’s model slightly underestimated the measured results

for low irradiance values while the model of this project produced an overestimation.



125

Figure 6.33 Efficiency results for the 3rd CPC prototype

Despite the improvements, the system presented inaccuracies and other defects:

- The alignment of tubes and fins in the centreline focus of the CPC

- The layering of the fins with the selective surface product

- The actual CPC profile (shape)

- The adhesion of the reflector material to the CPC walls.

Additionally, the system suffered mechanical and thermal stress prior to operation at

the designated test site. It was observed after several weeks of operation that the

self-pumped mechanism was progressively diminishing which inevitably required a

manual refilling of the reservoir from time to time.

Taking all this into account, and the fact that a simple simulation model was used,

the results obtained from the third prototype were in very good agreement with both

numerical models. It is concluded that this system had an excellent performance.

0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.180

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6


Effic

ienc

ies

Efficiency curves comparisons for 3rd prototype

LOW EMMITTANCE ( ε = 0.1) Model prediction ε = 0.1 Model prediction ε = 0.2 Model prediction ε = 0.3 Results from A Rabl* Results from 3rd prototype

R > 0.96 p < 10-5

ΔF’η0 = 0.03

ΔF’UL = 0.3

(Eq. 6.30)GT..exp

Δ⋅−= 54570η

cpc

GT.. exp

Δ ⋅ − = 92 77 0 η



126

6.6.3 Comparison of the 3 prototypes (Figure 6.34)

Figure 6.34 Prototypes performance comparison

The average efficiencies for temperature differences (Tabs - Tamb) = (80 ± 2)°C and

irradiance values of 800 and 1000 W/m2 are given in Table 6.11.

Table 6.11 Efficiency prediction for all prototypes

ESTIMATED EFFICIENCY % Prototype

(for 800 W/m2) (for 1000 W/m2) 1st 20 ± 5 34 ± 5 2nd 12 ± 2.5 21 ± 5 3rd 47 ± 10 54 ± 5

The last prototype clearly outperformed the other two, with much higher efficiencies

and in 3 out of 4 cases, more than double the values for the first and second ones.

Comparison of efficiency parameters (Table 6.12) also shows this superiority and the

fact that it compares very well next to other collector types77.

0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6


Effic

ienc

ies

Efficiency curves comparison between all prototypes Results from A Rabl, ε = 0.1 Results from A Rabl, ε = 0.9 Results from 1 s t prototype Results from 2 d d prototype Results from 3 r d prototype



127

Table 6.12 Collector efficiency parameters

Efficiency parameters Collector

F’η0 F’ULcpc

7F

* 1st Prototype 0.88 ± 0.03 6.7 ± 0.3 2nd Prototype 0.57 ± 0.04 4.5 ± 0.5 3rd Prototype 0.77 ± 0.03 2.9 ± 0.3

CPC with inverted ‘V’ receiver 0.74 4.0 Flat plate with non-selective surface 0.75 8.0

Flat plate with selective surface 0.75 5.0 Evacuated tube 0.6 1.2

6.6.4 Water tank

Assessment of water tank temperature variations was done over a continuous period

of 6 days and 5 nights for the calculation of heat losses from the tank water.

Figure 6.35 Water tank temperature for no-load conditions over 6 consecutive clear days

* Note that for a flat plate, where C =1, L

cpcL UU =

Water tank temperature vs. time for daily operation

0 5

10 15 20 25 30 35 40 45 50 55 60 65 70 75

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

Time (h)

Tem

pera

ture

(°C

)



128

Figure 6.35 shows a typical set of temperature results obtained from the SHWS using

the last prototype operating for about 4 hours each day (i.e., 1 panel system). The

average irradiance on the system was fairly similar for all 6 days. The daily energy

gain was similar in all cases and revealed what could be expected for hot water

production from a system of this type with a single panel (Table 6.13). The losses

were higher for higher tank temperatures (more pronounced negative slopes)

doubling by the third day. Even though there was a tendency for slightly higher

associated cooling times overnight as days went by, the differences were not

significant (less than 5%). The differences between daily temperature gain of the

water were within ±1° C, which for the amount of tank water, equated to about

±0.8 MJ of energy gain. Given the fact that overnight heat losses increased steadily

for consecutive days, it would appear that the average steam efficiency, ηs_eff, did not

vary significantly even at water temperatures of 68° C (albeit a slight decrease, see

section 6.4.3). Environmental conditions were basically the same for the duration of

this analysis on water tank energy gain and losses, which gave a good indication of

the performance of the tank in this regard.

Table 6.13 Energy collection and heat losses for the water in the tank

Period Energy_IN Power_IN Max. Temp.

Cooling time Q-loss U-loss

(MJ) (W/m2) (°C) (h) (W) (W/m2·°C) Day 1-2 12.61 ± 1.18 876 ± 104 30.9 ± 0.5 18.9 ± 0.1 37 ± 11 1.3 ± 0.4 Day 2-3 12.21 ± 1.17 848 ± 103 43.1 ± 0.5 19.1 ± 0.1 59 ± 11 1.1 ± 0.2 Day 3-4 12.53 ± 1.18 870 ± 103 53.8 ± 0.5 19.4 ± 0.1 77 ± 11 1.1 ± 0.2 Day 4-5 11.42 ± 1.17 793 ± 101 61.2 ± 0.5 19.3 ± 0.1 92 ± 11 1.1 ± 0.2 Day 5-6 12.13 ± 1.17 843 ± 103 68.5 ± 0.5 19.8 ± 0.1 100 ± 11 1.0 ± 0.1 Average 12.2 ± 1.2 846 ± 12% - - - -

The theoretical calculations for tank losses based on the initial approximation of

equation 6.10 underestimated the experimental results by 20% to 36% and it was

believed that the losses through the top and bottom sections of the tank were partly

responsible for this, given the fact that this simplification is only valid when

lT >> DT. This prompted the use of equation 6.11, which resulted in a more accurate

loss assessment with errors ranging from –14% to +8%.



129

It is important to note that there was very

little insulation on the bottom of the tank.

Better insulation is warranted, since losses of

about 100W over a 19-20 hour period

amount to high overall energy losses. Albeit

being under cover, the outdoor and relatively

exposed positioning of the tank (Figure 6.36)

most probably contributed to higher heat

losses than what could have been obtained if

it had been better sheltered and/or kept

indoors.

Figure 6.36 Hot water storage tank, transfer

pipe and condensate receptacle

6.7 Conclusions and discussion

6.7.1 Performance of the downward vapour heat transport SHWS

The development of a fully functional vapour downward heat transport solar hot

water system revealed that the self-pumped approach is a viable option in providing

domestic hot water. The system was operated separately with each of 3 different

concentrator-boiler collector panels designs. In the case of the last collector

prototype, it was seen that efficiencies over 40% were achievable, which makes it

possible to provide the entire hot water needs for a dwelling by proper sizing of the

system. Great attention to detail, better construction skills and better quality products

were the reasons for improved performance.

The system using the last prototype (2.5 m2 panel) was able to deliver an average of

12 MJ to the water in the tank, operating for about 4 hours each day (9:30 am –

1:30 pm) over a 6-day period during winter. Average power delivered to the water

store was 846 ± 100 W.



130

Simulation predictions

The results of Figure 6.33 for the last prototype revealed very high panel efficiencies.

For an average measured irradiance over the panel of about 850 W and ambient

temperatures between 15 °C to 20 °C, an efficiency of 49% would yield close to

1050 W output average steam power. Truncation effects were included in these

calculations.

From Figure 6.30, for emittance values, ε, between 0.1 and 0.3 and concentration

ratios between 1.7× and 2×, the simulation model predicted an average steam power

output from the CPC panel, PS_avg, of about 1300 W for daily operation.

The plots of Figure 6.30 were repeated including the effects of truncation and pipe

losses for a realistic comparison with experimental results (Table 6.13). For

emittance values between 0.3-0.1, and for pipe (transfer line) losses ranging from

zero to 150 W, the model now predicted the results shown in Table 6.14.

Table 6.14 Prediction of average system steam power for truncation effects and different pipe losses from the plots of Figure 6.30

Pipe losses (W) PS_avg (W) 0 1100 50 1040 100 1000 150 960

The slightly higher results (+50 W) compared to the predictions from the plots of

Figure 6.33 were attributed to a more accurate time-integration calculation over the

full operation cycle of the collector.

From the experimental results, the average power gained by the water in the tank,

water_effP , was close to 850 W. The model predicted average output steam power from

the panel, panel_outP , close to 1100 W for the same operating conditions. Assuming

low tank losses, loss_tankP , of 30 W during the day and average pipeline losses,



131

loss_pipeP , of 100 W, it was possible to determine an effective steam heat transfer

exchanger efficiency, ηs_eff, for daily operation and assess the capabilities of a

multipanel system.

Combining equations 6.8 and 6.9 and rearranging for efficiency:

( )[ ]pipe_lossout_panel

ktan_losseff_watereff_s PP.

PP

−⋅

+≅

051η (6.17)

Substituting the proposed values in equation 6.17 gave 840.eff_s ≅η

The remaining 16% steam power that apparently does not go into the water is

assumed to be a result of the experimental error in the measurements, the

assumptions and simplifications of sensible heat contribution (section 6.4.3) and the

characteristics of the condenser coil. Despite the fact that a near horizontal loop was

used to recover as much sensible heat as possible, this actual design and the diameter

of the pipe probably did not favour a speedy heat transfer from the flowing

downward steam as initially thought. Hence, a fraction of the steam power could

have ended in the condensate receptacle, with little sensible heat being collected.

This would warrant a proper design analysis of the heat exchanger tube, possibly

increasing pipe diameter and/or length. Another reason for the reduced steam transfer

efficiency could also be an overestimation of the average steam power given by the

numerical model. Additional temperature measurements close to the coil (and maybe

the use of heat flux sensors) and temperature determination of the condensate would

shed more light into any possible heat being unaccounted for.

Nevertheless, a second panel added to the system should be able to deliver an

additional 950 W of average power to the water. It could be thought of as if the first

panel were supplying close to 850 W (after allowing for pipe and tank losses) and the

second one were supplying close to its full effective steam output of around 1100 W,

reduced by the steam transfer efficiency. This is easily verifiable from equation 6.13

setting the pipeline and tank losses to zero.



132

Duplicating the panel arrangement in the system to a tytal of 5 m2 collection area

would increase daily energy delivery to over 25 MJ.

It is estimated that increasing the area of each panel by 20% to 3 m2 would surpass

the daily average requirement of 30 MJ for domestic hot water. For year-round

performance, it is possible the values would be higher, since these calculations are

based on winter measurements for a non-optimal panel orientation.

6.7.2 Elements construction and materials used

The construction process and materials used were very much improved in the

development of the last prototype. All panels, however, encountered a few problems

during and after fabrication.

CPC profile design and reflective material layout

Polyurethane foam appeared to be the best material for CPC insulation and structural

support, despite the disadvantages associated with brittleness and high cost. For the

different reflector materials used in each prototype, the best performance was

obtained from the highest reflectivity element (Silverlux™) for the third prototype.

All reflectors exhibited shifting, misalignment and deformations during construction

and to some degree during operation. The first prototype modules appeared to have

fewer problems in this regard since they were made by mould forming with the

reflectors already in place. In contrast, the second and third prototypes had their CPC

profile determined by the foam structure with the reflectors later glued on top.

Absorber-boiler copper array and roof reservoir

The copper array of fins, tubules and pipes was very successful in boiling water at a

fast rate and producing useful steam. It was, however, difficult to assemble and

manipulate and relatively expensive to produce. Its effectiveness was dependent on

the accuracy of the line-focus alignment of the boilers within the CPC cavities, the



133

reflectance of the CPC walls and the quality of the black coating used on the fins to

maximise absorption and minimise emission.

The best performance was obtained for the third prototype, which operated for two

years until it was dismantled. The reservoir tank was operated for the second year

with the use of a timed electric pump that took about four minutes each day to pump

up 20 L of water from the condensate receptacle and refill the reservoir.

The prototype arrays were found to be prone to leaks. The self-pumped mechanism

worked flawlessly only in the first prototype after leaks where identified and repaired

on some modules. For the second prototype, the soft-soldered panel was certainly a

suspect for leaks as well as the reservoir tank. For the third prototype, leaks occurred

after a month of operation. Both second and third prototypes experienced a decline in

operation of the self-pumped recharging mechanism over time.

The water reservoir tanks constructed showed signs of rusting with the water

progressively turning brown over months of operation of the units. Dismantling of

the first and second prototypes confirmed this.

From continued operation of the third prototype during clear sky conditions it was

found that the water tank, under no-load, reached a stagnation temperature of

(84 ± 2) °C (Figure 6.37).

At this water temperature, and for ambient temperatures between 15–30 °C, the

losses from the tank were around 110-130 W. At this point, the losses were equal to

the gains, so there was no effective power delivered to the water, i.e, 0Pwater_eff =

and abundant steam was seen flowing into the condensate receptacle.

As demonstrated by the results of Figure 6.37, the system had a self-regulating

mechanism for dumping excessive heat.



134

Figure 6.37 Water tank temperature for no-load conditions over 12 consecutive days showing stagnation water temperature

6.7.3 Model predictions compared with experimental results.

The results from the model allowed a satisfactory characterisation of the SHWS as a

whole. From the calculation of energy collection (for date, time and location),

together with a simplified analytical approach for heat transfer (for collector panels,

transfer pipe, exchanger and tank losses) the model was able to predict performance

to a reasonable accuracy, despite the relatively high experimental errors (±10% of

effective average power delivered to the water in the tank over a day). The model

was, therefore, useful as an indicator of how a SHWS incorporating downward

vapour phase transport would operate. It was also useful in predicting how different

parameters affect system performance, enabling optimisation with a lesser need for

continuous prototype construction and testing.

The simplifications would also explain the linearity of the model and overestimation

of efficiencies for low irradiance values, when compared to Rabl’s model for similar

CPC concentrations and when compared with experimental results.

Water tank temperature vs. time for daily operation

0 4 8

12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Time (h)

Tem

pera

ture

(°C

)



135

The experimental determination of panel optical efficiency would allow for a more

reliable verification of the thermal modelling and to better assess discrepancies such

as those encountered with the second prototype. To this end, a simple method that

could be applied to each prototype in future development is the following:

- Obtain the efficiency curve of the prototype by measuring water temperature rise

(not steam production) as water of known flow rates is pumped through. The

resulting curve will be similar to those of Figure 6.34

- Fit the data obtained to an expression of the form of equation 6.15

- The resulting maximum efficiency (y-axis intercept from this fit) occurs when

there is virtually no temperature increase in the water, therefore no heat losses. In

these conditions, the amount of heat absorbed by the water is purely determined

by the optical efficiency. Therefore, this value is an estimate of the optical

efficiency8F

*.

Economics

The excellent performance of the third prototype did, however, carry the

disadvantage of higher costs. Certainly, the use of a much better reflector (specular

silver), a high performance selective surface (Maxorb™) and the degree of attention

to detail in its fabrication came at an increased price. It was then determined that by

automating the design process in the construction of the absorber boiler and given the

current costs of the materials used, a unit of this type would be comparable in cost to

the higher end SHWS models currently available in the market. More on the

economics of this system is given in chapter 8, but it can be said that this particular

high-efficiency prototype requires additional work and re-engineering from a

fabrication and material usage perspective in order to make it a competitive product

with mainstream units.

* Actual determination of solar panel efficiency from standardised industrial tests is much more involved. See Australian Standard AS 2535.1(1999) for further reference.involved.

Chapter 7 - Air-to-water heat transfer solar hot water

system with heat exchanger-water tank

coupling 7.1 Introduction

The air heater SHWS is composed of five sections:

• Collector panel that heats air

• Pipes that transport the air to and from the panel

• Heat exchanger: where the air exchanges heat with the water in the storage tank

• An insulated, large capacity water tank, coupled to the heat exchanger

• A centrifugal fan blower to mobilise the air around the system

This system relies on the heating of air in flat collection panels. The hot air is

delivered to the heat exchanger for heat transfer to the water. Hot water in the

exchanger drives a thermosiphon between the exchanger and the water tank. The

output air from the exchanger is either discarded or recycled back into the panel

since the system can operate, and was evaluated, in open and closed loop modes.

7.1.1 Basic design for the construction and operation of the air-to-water heat

exchanger-coupled tank SHWS

To meet the proposed daily target of Table 1.2, the following assumptions and

considerations were made for system design (Table 7.1, Figure 7.1):

Table 7.1 Assumed efficiencies for basic system components

Elements required Efficiencies9F

* Air-to-water heat exchanger 50% or higher

Collector panel 60% or higher TOTAL SYSTEM ~30% or higher

* Efficiencies assumed for a minimum required airflow rate of 60 L/s at 50°C, or 0.065 kg/s


Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling

137

Assumed airflow rate for

efficiencies of table 7.1

Φv = 60 L/s or kg/s 0.065 =m&

Cair @ 50°C = 1007 J/kg·°C

Figure 7.1 Sketch for the air-to-water heat exchanger-coupled tank SHWS

Preliminary tests with the heat exchanger used showed that efficiencies above 50%

could be obtained at airflow rates of 60 L/s and water flow rates of about 10 cc/s.

For design purposes, since the panel had a 90° collection half-angle, the system

could be expected to operate for about 6 hours in winter and about 8 hours in

summer. For 6 hours of operation:

Table 7.2 Assumed energy and power requirements for 6-hour operation

Required daily energy in the water (from Table 1.2): 25 – 30 MJ Required average power into water: 1160 – 1400 WRequired average power input to the exchanger: 2320 – 2800 WRequired average power into system: 3900 – 4700 W

The airflow rate should be sufficiently high to draw enough power from the collector

and carry it into the exchanger. To satisfy power requirements the following scenario

was assumed for airflow rates of 60 L/s and water flow rates of 10 cc/s:

Given Parameters

Collector input

Initial air temperature, To = 30 °C

+

Using: TCmP air Δ⋅⋅= & Eq. 4.64

Collector panel

Water tank

Heat exchanger

(Optional: return pipe)

Fan/blower



138

For operation in closed-loop mode:

- the optional return pipe is used

- the exhaust air is fed back into the panel

- input air temperature will rise

Finally, the sizing of the collector panel would be dependent on the required average

power input to the system over a 6 hour period (3900 – 4700 W) and the average

irradiance during operation.

Required collector output

Power to be gained by air = 2320 – 2800 W

Expected air temperature = 65°C – 73°C

Required exchanger input

Power carried by air at entry point = 2100 – 2500 W

Expected air temperature = 61°C – 68°C

Hot tank water

Average power going in the water = 1050 – 1250 W

Energy gained over 6 hours = 22.7 – 27 MJ

Output air temperature

Tair_out ≈ 40 - 45°C

Collector input

Tair_in > To

Back to:

Less than 10% losses from air pipes

Exchanger efficiency 50%

Closed-loop operation



139

Table 7.3 Average irradiance for minimum absorber area required during OPEN LOOP operation mode

Average irradiance over 6 hours: 770 W/m2 Absorber area required: ~6.0 m2

For lower input air temperatures a larger absorber area would be required. For

example, if input air temperatures were 10 °C (winter), air would have to be heated

by about 60°C in order to obtain the required collector output air temperature (about

70°C). The required average power input to the exchanger, from Table 7.2, would

then become 3900 W and the required average power into the system 6500 W. For

the same average irradiance of Table 7.3, this would require an absorber area of

about 8.4 m2. This is, however, considering open loop operation, where ambient air

is drawn into the panel and warmer air is discarded at the exhaust of the exchanger.

For closed-loop operation the system cannot be simply characterised as for the

preceding situation. In this case, the input air temperature would rise as the air is

heated and recycled. If irradiance values were constant, this rise would halt when

equilibrium was reached and the heat gains and losses would be the same. Since

irradiance values are constantly changing, this dynamic cannot be so easily

estimated. In any case, this configuration would be expected to have a better

performance prospect and was the option of choice since:

- The closed system is not subject to foreign contamination/hindrance, therefore…

- Internal maintenance (panel heating element, pipes, exchanger) is reduced

- Higher temperatures are achievable and better use is made of the energy available

- Smaller panel collection area required

- A return pipeline is not a significant additional cost

- The disadvantages related to a longer pipeline are outweighed by the benefits

For the closed loop mode a rough estimate of panel area required could be made by

considering that the return pipe would also produce near to 10% power drop in the

recycled air. This means that most of the power lost from the exhaust air in open loop

mode (~50% of the total at exchanger input) would go back into the system.

Considering this, the panel area for closed loop operation could be much smaller

(Table 7.4).



140

Table 7.4 Average irradiance for minimum absorber area required during CLOSED LOOP operation mode

Average irradiance over 6 hours: 770 W/m2 Absorber area required: ~3.0 m2

It is possible that in closed loop mode, very high air temperatures (above 100°C)

would be obtainable, in which case a heat dumping mechanism would have to be

contemplated. The return pipe could be engineered for such purpose.

Also, in both open and closed loop modes with no air circulation, high stagnation

temperatures would set in the panel, requiring some stagnation control mechanism.

The actual large-scale collector prototype constructed was 3.6 m × 1.2 m, with an

effective absorber area of 3.25 m × 1.14 m, or 3.7 m2.

The novel developments in this system were related to the engineering of the

collector panels and the heat exchanger/exchanger-tank coupling.

7.2 Types of solar air heating panels

Flat plate collection systems are the means by which most domestic SHWS are

operated. Although extensive research has gone into the fabrication and improvement

of these panels for the transport of liquid fluid, not as much has been done when air

is the transport fluid. This is because solar air heating systems (SAHS) have mainly

been used for space heating97F

98-98F99F

100 and food dehydration and drying applications100F

101-101F102F103F

104.

Air type collectors have similar components as water type ones. They are composed

of: glazing, absorber, flow channels (manifolds, etc) and a container with insulation.

The crucial development in a collector of this type is the design of the absorber.

Different geometrical approaches for absorber-heaters have been tested and

documented. Examples are given next according to the absorber type used.



141

Group A: Air heating panels using flat absorbers

Figure 7.2 Longitudinal view for 3 different air-heating flat-plate solar panels

The collectors in this group (Figure 7.2) use the same type of absorber, but the fluid

flow is different in all of them and removes heat in a different way. Type A(a) is the

simplest arrangement where the heat absorber is in contact with the back insulating

material and the fluid flows over it. In type A(b) the absorber is placed at a certain

distance from the back and the fluid flows under it. This arrangement produces lower

convection losses to the top cover. In type A(c) the fluid flows over and under the

absorber and is capable of delivering more energy to the air under certain

circumstances. Type A(d) is similar to type A(b), where the absorber has protrusions;

fins or baffles that increase turbulence, increasing heat transfer to the fluid.

Group B: Air heating panels using corrugated & finned absorbers

Figure 7.3 Transverse view for 2 different air-heating solar panels with multi-channel

absorber plates

In type B(a) (above) the absorber has a series of channels through which the fluid

flows. Type B(b) is a triangular shaped absorber with fluid also flowing between the

channels. For the latter, fluid can flow below or above, or both below and above the

absorber. This configuration is designed to reduce the losses due to radiation and at

the same time increase turbulence and heat transfer.

For all the preceding collectors, the materials used as absorbers are commonly

aluminium and steel sheets, formed into the desired shapes.

Vf →

a) Conventional single channel panel

Vf1 →

Vf2 →

c) Double-channel panelb) & d) Single channel panel with modified top

Vf →

(Optional: protrusions/ribs)

a) Multi-channel absorber panel

Vf ⊗ ⊗ ⊗

b) Triangular shaped multi-channel absorber panel

Vf1

Vf2⊗ ⊗ ⊗



142

Group C: Air heating panels using alternative absorbing media

Type C(a) collector absorbers (Figure 7.4) are made of a series of overlapped glass

plates creating narrow channels over the entire depth of the flow chamber through

which fluid flows. A part of the plates have been blackened so that the fluid in its

entirety is heated while traversing these narrow passages.

Figure 7.4 Longitudinal view for 2 different air-heating flat-plate solar panels using

alternative absorber type

Type C(b) is the so-called metal matrix collector. As its name implies, this collector

has a matrix-like metal structure through which the fluid flows as if it were being

forced through a wire mesh. Other variations in collector design include the use of

double-glazing and various absorber corrugation shapes.

Of the air heating solar applications and studies available, a small proportion refer to

the generation of domestic hot water by making use of solar air heating panels.

A means for obtaining domestic hot water from the use of a totally passive SHWS

incorporating collectors with a similar construction to those of type C(a) above is

described in a US Patent dated to the early 1950s4. The system referred to employs

natural air convection in a closed loop circuit, where hot air is driven upward towards

the tank that contains the water to be heated. It is a close-coupled system. Another

patented system designed in the 1970s104F

105 describes a SAHS for domestic water

heating employing a collector panel, which is crossed by a forced airflow fed by an

electrical fan. Heat is exchanged with an internally located water container. Both

systems have the option of using the hot air for other purposes, not just for hot water

generation (eg. space heating). A third system, proposed in 1987 105F

106, describes

another passive SAHS for domestic water production. The heat collection method in

this case is by open convection air trapping in a purpose-built black box. By clever

engineering, hot air is carried to the water tank for production of hot water.

a) Overlapped glass plates absorber panel

Vf →

b) Metal-matrix absorber panel

Vf



143

Other theoretical and experimental developments have shown that SHWS using

air-heating collectors can be a viable, inexpensive, solution for domestic hot water

needs. For example, the study of a SAHS prototype based on air recirculation across

an air/water heat exchanger revealed that collector panel areas of 8 m2 were adequate

for this purpose106F

107. Another study of a system, adapted for Indian climates,

employing commercially available plastic air heating collectors and an air/water heat

exchanger, concluded that the use of plastic panels as a replacement for conventional

all-metal air heater panels in SHWS, is better suited for domestic hot water supply107F

108.

Other studies have provided simulation prediction models that describe collector

panel efficiencies and overall system performance108F

109,109F

110 and techno-economic

analyses for maximising hot water production and minimising costs110F

111.

Since solar hot air can be used for a variety of purposes, research has had strong

concentration on the development and engineering of collector panels themselves,

without necessarily creating an entire solar heating system for a specific purpose.

Some of these developments, which are of direct interest to this study, are explored

in the following section.

7.3 Heat transfer

Heat transfer assessment was done for all the elements of the system; the panels, the

piping, the heat exchanger, the fan-motor and the storage tank. Additionally, a

thermohydraulic assessment was done, since the overall performance was

conditioned by the fluid resistance posed by each of those elements.

The intended design for the SAH considered the following characteristics:

- Readily available building materials

- Inexpensive

- Easy to manufacture

- Easy to handle, install and maintain (if required)

- Durable

- Acceptable performance



144

7.3.1 Air heating collector panel

In this study, a flat panel was considered the most suitable collector device, owing to

its geometrical properties; ease of manufacture and ease of integration into building

architecture, as well as offering typical all-day solar energy collection times.

Of the three kinds of flat absorber collectors, type A(c) has been considered as

offering a better performance under most conditions111F

112-112F113F114F

115.

In solar engineering, collector types B have received a lot of attention, with many

different absorber shapes studied and tested. These have included corrugated,

roughened, finned and channeled absorbers. There are many studies of the design,

modelling and experimental and simulated performance for this kind of

absorber115F

116-116F117F118F119F120F121F122F123F124F125F

126. Amongst them, it is worth noting the development of the so-called

“Vee” corrugated or V-corrugated (V-type) absorber, where the plate has V-shaped

creases or folds, resembling triangular channels. Several studies105-109,113 have

suggested their superiority over conventional flat plates under a variety of conditions.

The use of channels, roughened plates, and fins and baffles has also been regarded as

a better substitution for flat plate types111,126F

127.

A study comparing five different collector designs127F

128 with single glazing suggested

no particular advantage in using a V-corrugated absorber in place of conventional

flat absorbers. The best performance was obtained by the use of an undulated duct as

a fluid flow channel.

Studies of the effect of collector aspect ratio (length/width) on different types of

collector panels have also suggested that thermal performance is improved by

modifying the geometrical characteristics of these panels104,128F

129-129F130F

131.

From the literature, it seems that non-flat plate absorbers outperform the

conventional ones in most cases. However, there is nothing conclusive other than

what pertains to very specific, localised and custom-tailored conditions of

experimentation and setup.



145

The first air collector prototype of this study was built with the V-corrugated

absorber profile (Figure 7.5). The heat transfer dynamics of such system is explained

in detail in the following pages. The construction process and materials used is given

in subsequent sections.

Figure 7.5 Transverse view of 1st prototype with a V-shaped absorber panel and triangular fins

Detailed explanation of the modelling development of the collector is necessary since

this represents the foundation over which any prediction of heat transfer dynamics

can be claimed. As such, the following pages examine and explain:

- The energy exchange between the elements within the collector and between the

collector and its surroundings

- The heat transfer modes associated with the above

- The relationships that lead to realistic modelling

- A mathematical formulation for convenient expression and manipulation of these

relationships (thermal networks)

- The evolution of the thermodynamic system and an algorithm for determining the

required parameters in performance prediction (temperatures and efficiencies)

The heat transfer modes for triangular and flat profile collectors with air flowing over

and under the absorbers are similar and are depicted in Figure 7.6

In the heat transfer analysis several assumptions were made:

1. The system is air tight (no leaks)

2. Heat capacity effects of cover, absorber and back plate are negligible

3. Temperature of the elements varies only in the direction of fluid flow

4. Each panel can be considered as made up of small transversal sections of the

whole that have been joined together. Temperatures of the elements of each

section can be considered uniform.



146

Figure 7.6 Heat transfer modes for a) double channel flat and b) V-shaped absorber

configurations

7.3.2 Collector panel energy balance equations and relationships for heat

transfer modes

The energy balance equations for heat exchanged due to convection, conduction and

radiation for the absorber panels of Figure 7.6 follow (refer to nomenclature page for

description of parameters and subscripts):

For upper side of top cover (C1)

( ) ( ) ( ) ( )skyCCSambCCACCC TThrTThcTThrhcI −⋅+−⋅=−⋅++⋅ 11122121α (7.1)

For lower side of top cover (C2)

( ) ( ) ( ) ( )122121212122 CCCfCfCabC

ababCC TThrhcTThcTT

AA

hrI −⋅+=−⋅+−⋅+⋅⋅ ατ (7.2)

For fluid flow above absorber (f1)

( ) ( ) ( ) ( ) ( )111212111 inoutpCfCCCffababababf TTCmTTdxwhcTTdxwhc −⋅+−⋅⋅⋅=−⋅⋅⋅ & (7.3)

a) Longitudinal view of a double-channel absorber panel

Qair1

Qair2

I

I·τ

I·τ 2

hcabf1

hcf2B

hcf1C2

hcabf2

hc21

hcCA

hrabC2

hrabB

hrCS

hr21

I

I·τ

I·τ 2

hcabf1

hcf2B

hcf1C2

hcabf2

hc21

hcCA

hrabC2

hrabB

hrCS

hr21

Qair2 ⊗

Qair2 ⊗ Qair1

⊗

b) Transverse view of a multi-channel triangular absorber panel

ϑ



147

where: dxab = dxC = dx = element surface length

wab = width of absorber

wC = width of collector

(7.4)

(7.5)

(7.6)

(7.7)

(7.8)

( ) ( ) ( ) ( ) ( )111212111 2 infpCfCCCffababababf TTCmTTdxwhcTTdxwhc −⋅+−⋅⋅⋅=−⋅⋅⋅ & (7.9)

( ) ( ) ( )dx·w

TTCmTThcTThcC

ifpCfCffababf12 111212111 ⋅−⋅+−⋅=−⋅Ω⋅ & (7.10)

For heat absorber (ab)

( ) ( ) ( ) ( )2211222

fabC

ababffab

C

ababfBab

C

ababBCab

C

ababCab TT

AAhcTT

AAhcTT

AAhrTT

AAhrI −⋅⋅+−⋅⋅+−⋅⋅+−⋅⋅=⋅⋅ ατ (7.11)

For fluid flow below absorber (f2)

( ) ( ) ( )dx·w

TTCmTThcTThcC

ifpBfBffababf12 2222222 ⋅−⋅+−⋅=−⋅Ω⋅ & (7.12)

For bottom back (B)

( ) ( ) ( )ambBBSBfBfBabc

ababB TThTThcTT

AAhr −⋅=−⋅+−⋅⋅ 22 (7.13)

(7.14)

(7.15)

( )

( )dx·w

TTCmQ

dx·wTTCmQ

Cifpair

Cifpair

12

12

2222

1111

⋅−⋅=

⋅−⋅=

&

&

Ω=

=⋅

2

2

1θ

θ

sin

wsinw Cab

( )

( ) ( )1111

111

111

2

2

2

infinout

infout

finout

TTTT

TTT

TTT

−=−

−=

=+



148

The energy equations for the flat plate collector of Figure 7.6a are derived as a

special case of the previous, by noting that Aab = AC and that if θ = 180° Ω = 1.

Table 7.5 Heat transfer modelling parameters for thermal network of Figure 7.7

Parameters Description

Temperatures: Tamb Ambient Tc1 Top cover – upper side Tc2 Top cover – lower side Tf1 Air in upper channel Tab Absorber Tf2 Air in lower channel TB Bottom of panel

Thermal resistors: (RT = 1/A·hT) RQ1sky RQ1A

RQ1 Radiation & Convection Cover → Ambient

RQ2 Radiation & Convection* Cover → Cover R1 Radiation Absorber → Cover

Rf1C2 Convection Upper channel → Cover

Rabf1 Convection Absorber → Upper channel

Rabf2 Convection Absorber → Lower channel

Rf2B Convection Lower channel → bottom R2 Radiation Absorber → bottom RB Conduction & Convection Back → Ambient

Heat flow: QC1 Heat absorbed by upper side of cover QC2 Heat absorbed by lower side of cover QL Total heat losses from absorber to cover QR1 Radiation losses from absorber to lower side of cover Qair1 Useful heat carried away by air flowing in upper channel Qf1 Heat lost from absorber to air flowing in upper channel Qab Attenuated solar energy reaching absorber Qf2 Heat lost from absorber to air flowing in lower channel

Qair2 Useful heat carried away by air flowing in lower channel QR2 Radiation losses from absorber to bottom of panel Ql Heat losses from bottom and sides of panel

* It is later seen that there is no convection, but rather conduction, inside cover space

}



149

To solve the energy equations and find the temperatures of each element and the

temperature of the air exiting the collector the thermal resistance network

formulation explained in chapter 4 and used in chapter 6 was used here as well. An

explanation of the parameters for the heat network for this model (Figure 7.7) is

given in Table 7.5:

Figure 7.7 Thermal resistance network for absorber panel configurations of Figure 7.6

The expressions and calculations of radiation and heat transfer coefficients were

taken from various sources as referred to in chapter 4 and are given in Appendix F.

Solution process

The iterative procedure mentioned in chapter 4 and used in the SHWS of chapter 6

was employed here as well. The solutions algorithm followed a very similar structure

with the difference that the air heater panel was divided into several transverse

sections (typically 20), where width >> length, and the iteration process was done for

each (refer to Figure 6.16 for a flowchart description):

For each section (j-th section):

1- Input air temperature10F

*, ambient and sky temperatures were known.

2- Temperatures were assumed for each of the elements (cover, airflow, etc)

3- Heat transfer coefficients and thermal resistances were found.

4- Energy balance equations were solved simultaneously.

5- New element temperatures, new_jiT , were found.

6- Old temperatures were replaced by new ones and steps 2-5 were repeated.

* For an open loop system, the input air temperature for the first section is always the ambient temperature. For a closed loop system it is the air temperature at the end of the return pipe.

QR1→

Tf2 Tb Tamb Tab

Tf1

TC2TC1 Tamb

Qab

QL + QC2 →

Ql ←

← QR2

Qair2 Qair1

QC2 QC1 R2

RB Rf2B Rabf2 Rabf1 Rf1C2

R1

RQ2

RQ1sky

RQ1A

← Qf2 Qf1→



150

7- Output air temperature, out_jairT , obtained when: o010.TT old_j

inew_j

i ≈− .

8- The process was repeated for the next section where: in_jair

out_jair TT 1+=

9- The temperature of the air exiting the collector was found from the last section.

The solution process was implemented using MATLAB™. Numerical results are

shown in Figures 7.22 through 7.37. Typical numerical values for a panel with the

absorber profile of Figure 7.6a are given in Table 7.6.

7.3.3 Conveyance system energy balance equations and relationships for heat

transfer modes (pipes and bends)

Heat was lost to the environment from the associated conveyance system. Heat

travelled from the hot air to the walls of the pipe, from there to the insulation and

then git was taken away by convection air currents that enveloped the pipe.

Convection from the outside of the insulated pipes was the main mechanism of heat

loss in this case. Radiation losses were not considered since the insulation was also a

highly reflective material, thus reducing radiation emission.

Energy balance equations were established again with the help of the corresponding

thermal resistance network of Figure 7.8. The calculations are given in Appendix F.

Figure 7.8 Pipe section / schematic for air pipe heat loses to the environment

The energy balance equations for the pipe are:

Tw out Tamb

Tw_in

T1 T0 Q0 →

↑ Q0_loss

Q1 →

Q0_eff

Vf →

Q0_eff

Twin Tf TambTwout≈ 0



151

( ) ( ) ( ) ( )ambpoutworat

ambop TTCmTTAln

LTTCm −⋅⋅=−⋅⋅⋅⋅

−−⋅⋅ − 12 κπ (7.16)

( ) ( ) ( )amboutw'

cvoutworat

TTAhTTAln

L−⋅⋅=−⋅

⋅⋅⋅−−

κπ2 (7.17)

From Equation 7.17, Tw-out was found, substituted in Equation 7.16 and T1 was also

found. This was the output temperature of the pipe section. With these two

parameters, power lost from the pipe and power conveyed by the pipe at its outlet

was determined. This way, the temperature drop in the circulation pipes for open and

closed loop modes were found.

The heat transfer coefficient, hcv, was dependent on the dominant convection modes

operating at any one time (free or forced convection) and further influenced by the

position of the pipe itself, ie. vertical, horizontal or a combination.

The maximum value for this coefficient (Equation 4.16) was (conservatively) taken

as: [ ] maxforced

cfree

cVfree

cHcv h,h,hh =

The heat transfer coefficients were determined by the use of relationships 4.1, 4.7

and 4.13-4.15, as given in chapter 4 (where the characteristic length, L, was equal to

the diameter of the pipe, Dp).

Solution process

The entire pipe was divided into many “slices”, or transverse sections, and the

balance equations were solved for each of them. The output temperature of one slice

was the input temperature for the next and so on.

Equation 7.16 can be solved deterministically, but not Equation 7.17. Since the

Nusselt number for the outer convective currents was dependent on the temperature

of the fluid, when Equation 7.17 was solved for Tw-out, the resultant equation was

implicit in form. This required Tw-out to be found via iteration. For each section of the

pipe, a series of iterations were done to determine Tw-out and from there T1. Eventually



152

all T1 temperatures were found for all slices, where the last slice gave the output air

temperature of the pipe.

For typical conditions and experimental setup (4.1 m pipe length of 90 mm diameter,

5 mm insulation thickness, 60 L/s airflow, 20°C ambient temperature, air

temperature of 70°C at pipe entrance) the predicted temperature drop was 5.5°C and

the power loss was 361 W, with an average heat loss coefficient over the length of

the pipe from insulation to the ambient of 5.8 W/m2°C

7.3.4 Heat exchanger energy considerations and power gain in the water

Due to the inherent complexities of the thermal behaviour of a compact heat

exchanger and to the dynamic nature of this situation, the losses and gains in this

particular case study were determined with the aid of experimental measurements.

There was one balance equation for this case:

xoutwaterinxoutxlosswaterinxin PPPPPP ______ +≈++= (7.18)

The exchanger was well insulated so the loss from the exchanger was considered

small enough to be neglected in the expression for the power going into the water. To

predict overall system performance it was necessary to determine power gained by

the water in the thermosiphon process and how much power was returned to the

system (air recycling) or discarded to the ambient via the air exiting the exchanger

(open loop mode). It was therefore necessary to be able to predict:

- water flow rates

- output water temperature from the exchanger

- output air temperature from the exchanger

Pin_x = Power carried by the air at exchanger input

Pout_x = Power carried by the air at exchanger output

Pin_water = Power gained by the water in the exchanger

Ploss_x = Power losses from the exchanger



153

Water flow dynamics of the heat exchanger-water tank thermosiphon circuit is quite

complex and is determined by many factors: input/output temperatures of air and

water entering and exiting the exchanger, water column density in the tank, hydraulic

resistance of connection pipes and exchanger itself. There is no direct,

straightforward, approach to be used in this case. In fact, it is very dependent on the

specifics of the elements used to create the thermosiphon effect, making it very

difficult to develop a general solutions method. However, experimentally it was

found that water flow rates were no larger than 10.5 cc/sec with temperatures

peaking at 62°C. For a pipe diameter of 12.7 mm, these conditions would produce

Reynolds numbers below the transition value of 2000. Assuming then that the flow

was laminar, flow rate was calculated by using Poisseuille’s equation for laminar

flow in straight pipes. The method used is loosely based on the original formulation

developed for thermosiphon assessment in a SHWS 131F

132 and further exploration and

developments of other studies132F

133,133F

134 on the topic.

The thermosiphon was driven by the

density differences between hot and cold

water columns. From Equation 5.30 and

noting that Δp =ρ·g·h (see Figure 7.9):

(7.19)

Figure 7.9 Thermosiphon and hot water stratification for the SHWS heat exchanger and tank

Water density is a function of temperature and for the operational temperature range

of the thermosiphon system (0°C-70°C) it can be approximated to a quadratic

equation with very good accuracy (< 0.2%). Water viscosity is also dependent on

temperature and can be approximated reasonably well to a 3rd order polynomial

(< 5.5%). See appendix G for details on these approximations.

As hot water entered the top of the tank, the cold column height progressively

diminished. Due to the physical setup of the thermosiphon loop (Figure 7.9) about 31

of the total water of the tank lay above the hot water entry point. If there had been no

( )l

)hh(g)(r nv ⋅⋅

−⋅⋅−⋅⋅=Φ

ηρρπ

810

4

Thot

Tcold

Hot air

Cold air

lh=h hn

ρ1

ρ0



154

water mixing and little conduction, the height and temperature for the cold water

column would have remained relatively unchanged at the initial stages. For (upper

value) water flow rates of 11 cc/s in a tank containing 190 L, this would have lasted

approximately 1½ hours.

Therefore, as an approximation to the water flow equation, hn ≈ 0. Since h = lh

(length of the thermosiphon pipe):

ηπ

ηρρπ

⋅⋅−⋅⋅⋅

=⋅

⋅−⋅⋅≈=Φ

88

21

20

410

4 g)TT(Crg)(rmwflow & (7.20)

ηπ

⋅

⋅−⋅⋅⋅≈

8

224 g)TT(Crm water_outwater_in

w& (7.21)

Where C = -0.004 is a quadratic constant in the density formula approximation and

η≡η[T], as given by Equations G5 and G4, respectively (Appendix G). Tin_water and

Tout_water represent the exchanger input and output water temperatures, respectively.

Power delivered to the water was (from Equation 4.49):

( )water_inwater_outwwwater_in TTCmP −⋅⋅= & (7.22)

Substituting for water flow from Equation 7.21:

( ) ( )η

π⋅

−⋅−⋅⋅⋅⋅⋅=

8

224water_outwater_inwater_inwater_outw

water_in

TTTTCgCrP (7.23)

All parameters in Equation 7.23 were known or easily determined, with the

exception of Tout_water. An expression for Tout_water as a function of other known

parameters was found from the exchanger effectiveness, which was determined

following the effectiveness-NTU method described in chapter 4.

Temperature measurements of the exchanger showed water output temperatures lay

between the air input and air output temperatures, so for simplicity and as a first

approximation it was assumed that the exchanger was operating as if in counterflow



155

mode (as explained in chapter 4). The output water flow from the exchanger was

experimentally inferred to be no more than 11 c/s and the temperature no higher than

62 °C. The airflow was fixed at a semi-constant 60 L/s (0.065 kg/s) with air input

temperatures close to 75 °C for irradiance levels over 900 W/m2. Given these

conditions, the fluid with minimum value of heat capacity was the water:

( ) CW

watcm o& 46< , whereas ( ) CW

aircm o& 60> .

The relationship for effectiveness (Equation 4.56b) under these considerations was:

water_inx_in

water_inwater_out

TTTT

−

−=ε (7.24)

Tout_water was then determined since Tin_x, Tin_water and ε were known:

( ) water_inx_inwater_out TTT ⋅−+⋅= εε 1 (7.25)

Since the effectiveness was determined experimentally ( 730.≅ε & 0.69 for open and

closed loop modes, respectively - section 7.6.2), the following expressions for output

water temperatures were used:

Open loop operation → water_inx_inwater_out T.T.T ⋅+⋅= 270730 (7.26a)

Closed loop operation → water_inx_inwater_out T.T.T ⋅+⋅= 310690 (7.26b)

By substituting these equations into Equation 7.23, power delivered to the water was

found. Since the air power going into the exchanger, x_inP , was known, the power

carried out by the air exiting the exchanger, x_outP , was also determined. From this

value, the output air temperature was found.

It is important to note that exchanger effectiveness is not constant and varies as

conditions for fluid flow and temperatures vary. This calculation was done as a first

order approximation based on the assumptions mentioned earlier. A detailed

justification for using a constant effectiveness is given in section 7.6.5



156

Solution process

This was a straightforward process where Equations 7.26, 7.21, 7.23 and 7.18 were

solved to obtain:

Output water temperature from exchanger, Tout_water ↓

Flow rate of water in the thermosiphon, wm&

↓ Power delivered to the water, Pin_water

↓ Output power and air temperature from exchanger, x_outP & Tout_x

The power and air temperature at the input of the exchanger were required and were

determined from the calculations for pipe losses of the previous section.

It is also important to note that the radius of the pipe used in the calculation of water

flow rate was an “effective” radius and not the actual radius of the vertical pipe.

Effective radius values were determined from experimental correlations

(Figures 7.39, 7.40, 7.46 and 7.47). The reason being that the flow path of the water

was a combination of the vertical pipe, the input and output points from the water

tank which were, in fact, reduction ports and the large number of narrow water

channels in the heat exchanger. As a result, an effective radius was obtained.

7.3.5 Centrifugal Fan-Motor

Temperature losses across the motor while recycling the air back into the collector

panel were evident during the experimental work. Heat losses in the motor were

essentially from convective air currents to the surroundings and radiation.

A simple approach in determining these losses had the motor modelled as a metal

cylinder allowing convenient determination of internal air temperature and power

drop. An overall heat loss coefficient, Umot, was determined from experimental

results and applied for all cases.

The energy balance equation was:



157

mot_outmot_lossmot_in PPP += (7.27)

(7.28a)

(7.28b)

Amot was simply the area of the motor exposed to the environment. Assuming a

cylindrical geometry, this was:

( )motmotmot

mot lDDA 22

+⋅⋅

=π (7.29)

Dmot and lmot were the diameter and length (or width in this case), respectively.

Since the motor was a relatively small object, the internal temperature was

approximated as:

2mot_outmot_in

mot

TTT

+= (7.30)

Equating and rearranging Equations 7.28 for the output air temperature and

substituting expression 7.30:

⎟⎠⎞

⎜⎝⎛ ⋅

+⋅

⋅⋅+⋅⎟⎠⎞

⎜⎝⎛ ⋅

−⋅=

2

2motmot

airair

ambmotmotmot_inmotmot

airair

mot_out AUCm

TAUTAUCmT

&

&

(7.31)

Once Tout_mot was known, mot_lossP and mot_outP were found.

Solution process

The temperature input to the motor, Tin_mot, was the temperature output from the

exchanger, Tout_x, which had been found from the previous section. The overall heat

loss, Umot, was found experimentally. The ambient temperature was known. With

these values Tout_mot was found from Equation 7.31. By knowing Tout_mot, the

temperature and power drop in the return pipe were calculated using the process

described in section 7.3.3 for pipes and bends.

( )

( )⎪⎩

⎪⎨

⎧

−⋅⋅

−⋅⋅=

ambmotmotmot

mot_outmot_inairair

mot_loss

TTAU

TTCmP

&



158

7.3.6 Water Tank heat gains and losses

The process for determining energy gain and losses for the tank of this SHWS was

similar to the one employed for the previous system of chapter 6, although simpler.

In fact, the same tank was used but without the internal heat exchange copper pipe

loop. Energy gains and losses were given by the energy gain of the water flowing

inside the compact heat exchanger and from the losses from the tank, respectively11F

#.

The power delivered to the water, Pin_water, was determined as explained in

section 7.3.4, Equation 7.23. The heat losses were found via the method explained in

section 6.4.3:

( ) ( )ambktan_water

T

T_insT

*T

ktan_loss TT

DtDln

lP −⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛ +

⋅⋅=

2

2 κπ (6.27)

Where DT , tins_T and lT are the diameter of the water tank, the thickness of the

insulation and the augmented height of the tank12F , respectively.

Finally: ktan_losswater_ineff_water PPP −= (7.32)

from eq. 7.23 from eq. 6.27

Solution process

Equation 7.32 was solved from Equations 7.23 and 6.27. For conservative purposes,

Twater_tank was equated to the maximum temperature of the water, Tout_water 13F

♦. Results

for effective power gained by the water are given in section 7.6.2.

# There are also energy losses from the thermosiphon pipe, which can be initially neglected assuming the pipes are insulated and present a very small surface contact area with the exterior.

Refer to section 6.4.3 for more information on the assessment of water tank heat losses.

♦ A more realistic approach would probably be: ( ) 2x_inwater_outktan_water TTT +=

*



159

7.3.7 Summary of solution process for the entire system

Solving for the collector meant determining the power carried by the output air. Solution included solar energy collection and heat transfer dynamics.

Solving for the downward transfer line meant

determining the effective air power going in

the exchanger after pipe losses. Losses

determined from pipe convection currents.

Solving for the heat exchanger and water tank meant determining thermosiphon output water temperature and power, exchanger output air temperature and power, tank losses and effective power delivered to the water. Solution involved the thermohydraulic assessment of the thermosiphon, the exchanger effectiveness and convective air losses from the tank.

Solving for the fan-blower meant determining motor body losses and output air temperature and power. Solution included experimental assessment of an overall heat loss coefficient and cylindrical geometry approximation of the motor.

Solving for the return transfer line meant determining the input air temperature and power to the panel. Solution as for the downward transfer line.

Collector Panel Inputs: Outputs:

Solution’s algorithm for air heating panel

(page 187)

Inputs: outpanel_airT

Outputs: Tin_x , Pin_x

Downward Transfer Line

Inputs: Tout_x , Pout_x

Outputs: Ploss_mot , Tout_mot , Ploss_mot

Fan-Blower Motor

Tout_water , Tout_x Ploss_tank

Pin_water , Pout_x Pwater_eff

Tin_x , Tin_water Tout_water

Pin_x Pin_water

Heat Exchanger Water Tank

Inputs:

Outputs:

Inputs: Tout_mot , Ploss_mot

Outputs: inpanel_airT , in

panel_airP

Return Transfer Line

(Only for closed loop operation)



160

During closed loop mode operation, the temperatures of all elements involved

increased progressively up to an equilibrium point. From there on, variations

happened due to the changing irradiance values. From a numerical perspective, this

equilibrium was reached when the input temperature of the collector panels remained

constant after several calculations for the entire loop.

All experimental and numerical results pertaining to the solution process above are

given in section 7.6.

7.4 Thermohydraulic assessment of airflow

Pressure drops in all the elements of the system strongly affect performance of the

fan-blower so it was necessary to evaluate thermohydraulic performance in order to

find the pumping/blowing power required and determine overall system

performance. Evaluation was based on the determination of head losses and minor

losses and finally the effective efficiency as explained in chapter 5.

7.4.1 Pressure losses

Head losses

The expression for head loss for each straight pipe section, hfi, was given by

Equation 5.16 and was dependent on:

- Pipe geometry (diameter, length, area)

- Airflow rate

- Kinematic viscosity of the air, ν

These head losses were related to the pipes that transported the air from the collector

output to the exchanger and in the case of closed loop operation, from the output of

the motor back to the collector input.



161

Minor losses

Calculation of minor losses was dependent on the number of fittings, valves and

other obstacles that affected the flow in any way. Therefore, in order to find these

losses it is necessary to know how many attachments of this nature were part of the

conveyance/piping system.

The minor head losses for fittings, bends and other elements are given by

Equation 5.22 and was dependent on:

- Pipe geometry (diameter, length, area)

- Airflow rate

- Loss coefficients (K-values) which are function of the geometry of the element

The “minor” losses, on occasions, can account for higher pressure losses than major

head losses. This may happen in systems containing relatively short straight pipe

sections and many contributing elements. Furthermore, the use of unconventional

devices, such as heat exchangers and collector panels, will accentuate this.

Total losses, HTOT, were the combination of all losses, major and minor, as given by

Equation 5.26.

The kinematic viscosity, ν, being temperature dependent, was a dynamic figure that

changed with changing air temperatures affecting head loss calculations. However,

since the interest lay in the performance of the system after reaching thermal

equilibrium and air temperatures did not vary greatly in the pipe sections, the

kinematic viscosity remained reasonably constant. Head losses, therefore, varied to

some extent in each pipe reaching a maximum value once in thermal equilibrium.

The results for pressure loss in the pipes allowed for performance evaluation. The

pumping power required to countervail the hydraulic losses and maintain a desired

flow rate is given by Equations 5.2 and 5.29:

TOTvmot HgCP ⋅⋅⋅Φ⋅= ρ (7.33)



162

Solution process

This was a fairly straightforward procedure in concept. It involved:

- Determination of K-values

- Calculation of minor losses

- Calculation of major losses

- Determination of total head loss, or pressure loss, in the system

- Calculation of net pumping power required

The desired flow rate, which was fixed, enabled calculation of all heat and pressure

losses and the corresponding net power required.

The determination of the K-values, in general, is not a trivial matter. For standard

pipe bends and fittings, tabulated values are available in the literature. However, for

unconventional elements, even empirical equations are seldom available.

For the heat exchanger and collector panel and a few other elements (such as

reduction/expansion joints), K-values were obtained by correlation with experimental

data obtained from the SAHS itself. The procedure for determination of pipe losses is

given in section 7.3.3. Experimental and numerical results are shown in section 7.6.3

7.5 Experimental work: construction details

The system contained:

• Air heating solar collector panel

• Air conveyance system

• Heat exchanging mechanism

• Hot water storage tank

• Fan/motor air blower

The major focus of work was the design of an appropriate solar collector and heat

exchanger subsystem.



163

7.5.1 System components

Collector Panels

1. First prototype

The design of the collector panels involved the construction of two prototypes. The

first one (Figures 7.10 and 7.11) was done to test a V-corrugated absorber

configuration with fins with the expectation that it would offer higher heat transfers

than conventional and more easily constructible flat-type absorbers (as mentioned

and modelled in sections 7.2 and 7.3, respectively).

The body was made out of 29 mm thick high-density polystyrene (32 kg/m3) sheets

serving also as insulation. The cover was a section of a Twinwall™ double-sided

polycarbonate sheet with internal slats used for protection and glazing purposes.

Figure 7.10 V-corrugated absorber panel with fins and polystyrene housing

Figure 7.11 1st prototype air heater absorber panel with air diffuser sections and double cover



164

The actual absorber shape was made out of aluminium sheeting (0.1 mm) which was

bent and cut to obtain the profile and fins desired. It was sprayed on the upper side

with a flat black paint. The entire absorber was fixed to a 6 mm thick medium

density fibreboard (MDF) sheet for ease of handling and stability, which was then

dropped into the polystyrene casing (Figure 7.11)

The internal dimensions of this prototype were 173 cm × 45 cm × 6 cm. Entrance

and exit ports were made out of polyvinyl chloride (PVC) pipe reduction/expansion

fittings to accommodate PVC pipes of 90 mm external diameter (OD). Two 6 cm

buffering zones with diffusers were set at the extremes of the panel to allow for a

more uniform heat transfer and mixing of the air throughout the panel and to reduce

low impedance pathways that could encourage the formation of hot or cold zones.

Seven thermocouples were placed at different

locations on the absorber to monitor

temperature variations. The prototype was set

on a tilted movable frame and exposed to

sunlight with the fan blowing into it

(Figure 7.12). Operation over several days and

for different airflow rates was intended as the

means for assessing performance and

determining the suitability of the absorber

profile chosen in order to construct a larger

scale prototype.

Figure 7.12 1st prototype air heater panel

on movable tilted base

Flow rates where produced by varying the applied voltage to the motor (Figure 7.13)

and were initially determined by the use of a hot wire anemometer and later by a

large cylindrical tunnel-bag of transparent and flexible polyethelene sheet, 5.15 m ×

0.59 m (Figure 7.14).

Thermocouple



165

Figure 7.13 1st prototype on work bench with fan blower and variable power supply

a) Anemometer b) Cylindrical air bag

Figure 7.14 Devices used in the determination of airflow rates

Anemometer readings of air velocity were taken at the inlet port of the motor. These

were correlated with results for airflow obtained with the tunnel-bag. It was soon

realised that the anemometer was an unreliable tool for this purpose due to the

following reasons:

- Small variations in the position of the unit’s probe in the pipes produced major

variations in recorded values.

- Limited scale for the application: maximum velocity that could be resolved was

about 10 m/s

- Temperature limited up to 50° C with errors increasing with increasing

temperatures (which made it unusable for the closed loop system)



166

Results obtained with the air bag were considered more accurate, reproducible (±5%)

and generally more reliable and that is why the anemometer was not used initially.

Construction of the unit was closely followed by simulation modelling according to

the theory described earlier, which showed good agreement between experimental

and numerical results. After due consideration from these and other modelling results

it was decided that a double cover absorber-in-the-middle panel with airflow over

and under it (Figure 7.2c) was the best option for a large-scale unit.

2 Second prototype

The second prototype was essentially a larger version of the previous one with the

following features and differences:

• External dimensions: 120 cm × 360 cm

• Double cover Twinwall™ polycarbonate sheeting

• Polystyrene case which doubled as insulation

• Flat aluminium absorber placed at midpoint height in the airflow chamber

The second prototype (Figure 7.15) was divided into two equal sections, thus

doubling the length of travel of the air. Buffer sections with diffusers at the input and

output of the panel were also provided. A buffer section of about 20 cm was located

opposite to the input and output ports for reducing friction flow losses and to

accommodate a stagnation temperature control mechanism.

Figure 7.15 2nd prototype large scale air heater panel on tilt-adjustable frame

IN

OUT



167

Actual construction of the heat absorber involved joining several flat sections of

aluminium sheeting shaped to the required profile. A total of 24 absorber sections

were made, sprayed with flat black paint and joined to compose an entire effective

absorber area of 3.7 m2 (57 cm × 650 cm).

The bottom of the collector panel was laid out with 26 plywood strips of 1 cm ×

57 cm × 0.6 cm, glued and evenly spaced out as a “bed” for affixing the absorber

sections (Figure 7.16). The absorbers where firmly fastened with nails, leaving upper

and lower airflow paths of the same dimensions.

Figure 7.16 Absorber panel profile and panel construction

An aluminium frame with 4 different tilt angle options was built to accommodate this

prototype. Measurements of air input and output temperatures were taken over

several weeks for varying irradiance values. The panel was later coupled with the

heat exchanger, water tank and associated piping and operated in open loop and

closed loop (air recycling) mode.

Stagnation temperature problems with the prototypes were foreseen before their

construction and certainly evidenced during their operation. The main drawback in

this regard was the temperature limit for structural stability of polystyrene, which is

80 °C134F

135. Under operation, even in closed-loop mode and at high flow rates (>60 L/s)

internal temperatures could actually go beyond the critical value. This issue has been

considered and discussed in section 7.7

b) Absorber sheet layering a) Cross-sectional profile of flow chamber

Absorber sections



168

Heat Exchanger

The heat exchanging mechanism was essentially a small and compact cross-flow heat

exchanger of high surface area per unit volume, typical of those used in the

automotive industry (Appendix H). The use of a readily available, mass-produced,

proven and robust compact heat exchanger, easy to use and integrate as a part of a

system, would be ideal for the purpose of a low cost, low maintenance SHWS

incorporating air as the heating fluid. Suitability would be a matter of assessing

whether the unit delivered the required power into the water or not.

The exchanger chosen (Figure 7.17a) contained a copper core 160 cm × 160 cm ×

49 cm with upper and lower header tanks. Thin flat vertical tubes ran parallel to each

other from one tank to the other. An array of V-corrugated metal sheeting with small

triangular fins interspersed between each tube made up for the rest of the unit.

Figure 7.17 Heat exchanger employed in the SHWS

The exchanger was cased in a wooden box with two openings at the bottom and top

for the input and output water pipes (Figure 7.17b) respectively, and two more

(larger) openings at the sides for the input and output air ports. Some modifications

were effected to the unit in order to provide an opening at its bottom. Pipe fittings

were fixed to these ports. The compact size can be ascertained from Figure 7.17a.

b) Exchanger inside casing and fan/blower motor attached towater tank

a) Compact heat exchanger

Back side

Front side



169

The exchanger was tested for varying air and water flow rates. Water flow rates were

provided and determined by a garden hose attached to a conventional tap valve and a

measuring cylinder. Hot air and varying airflow rates were provided by hot air

blowers.

Water Tank

The water tank used for the SAHS was the same described in chapter 6. In addition

to the input and output ports used for steam entry and condensate collection in the

system of chapter 6, there were three more access ports fitted with ball valves and

spaced evenly within 60 cm from the bottom of the tank (Figure 7.18).

Figure 7.18 Hot water tank and heat exchanger

A tube was taken from the lower of these points to the water input of the heat

exchanger, which delivered cold water from the bottom of the tank. Hot water

emerging from the top of the exchanger headed towards the upper input port. Via a

natural thermosiphon process. It is therefore noted that this tank was operating as a

storage/displacement unit, where thermal stratification was established from top to

bottom and with the intention of extracting and using the water being heated.

Valves



170

A small opening was made at the top side of the inner copper tank so that water

temperature profiles could be measured. This was done by attaching a thermocouple

to a (1 m) wooden ruler and measuring temperatures in the tank at fixed depth

positions every 5 cm. Cold and hot water temperatures were determined by fixing

thermocouples to the water input and output pipes of the heat exchanger.

Centrifugal fan/blower motor

The fan used was also sourced from the automotive industry with a nominal

operating voltage of 13.5 V and a maximum 120 W power consumption at a flow

rate of 93 L/s (Appendix H).

Figure 7.19 Upper view of centrifugal fan-blower attached to heat exchanger

The main requirement for a fan of this type was the delivery of required flow rates

despite pressure drops in the pipes. This meant selecting a unit with sufficient net

power consumption. The centrifugal fan used was able to deliver flow rates as high

as 63 L/s when operating below its nominal voltage while connected to the system in

closed loop mode. It was considered adequate for the purpose of the project.

The fan was operated by the use of two variable voltage power supplies connected in

parallel. It was used in the first prototype to determine performance under irradiation

for several flow rates. A fixed range of 2, 4, 6, 8, 10 and 12 volts was used to vary

the flow rate. In this case, air was drawn from the surroundings and pumped into the

prototype (as seen in Figure 7.12)



171

When used with the second prototype, the inlet opening of the fan was always

connected to the exit port of the heat exchanger (Figure 7.19). When operating in

closed loop mode, the outlet was connected to the return pipe driving the air back

into the collector.

Pipes, bends and fittings

Piecing together the collector panel, the heat exchanger and the fan finally formed

the complete system. This was done with standard PVC stormwater pipes of 86 mm

ID and 90 mm OD and several elbow and joining fittings.

A few images of the system operating in open loop mode are given in Figure 7.20.

Figure 7.20 2nd prototype air heater panel & SHWS in operation

As explained in the introduction, it was the closed loop mode the most favourable

mode of operation for a variety of reasons, among which are:



172

- Protection from external contamination and much less maintenance required

- Higher temperatures achievable and a more efficient system

- Smaller panel collection area required due to higher efficiency

In this operation mode, the airflow trajectory from the output of the fan/blower to the

output of the exchanger was about 18.1 m, divided in the following way:

• 9.6 m straight pipe sections (4) + 0.2 m straight section joiners

• 7 m panel compartment (including airflow turn-around at the third buffer zone)

• 0.85 m elbow fittings (10)

• 0.26 m heat exchanger compartment

• 0.2 m reduction/expansion fittings (4)

Holes were made at different points in the pipes to check for air temperatures, air

velocities and pressure drops. Air temperatures where measured with a thermocouple

by introducing the sensing tip up to the mid point of flow in the tubes. Temperatures

in the straight sections of the tube had up to a ±1.5°C variation.

Air velocities were determined in the beginning by placing the anemometer

measuring probe also at midpoint distance within the outward and return pipes, and

far from fittings that could introduce undesirable effects and produce inaccurate

results. The tunnel-bag was later used by opening the loop at the point of entry of the

collector and placing it on the return pipe.

For this system, the minor losses were the major contributors to total pressure drop.

This was due to the relatively short straight pipe sections compared to the quantity of

the other hydraulic resistive elements.

Experimental measurements of static pressure at various points in the system were

taken with a piezometer/nozzle arrangement, coupled with a differential water

manometer using atmospheric pressure as a reference point (Figure 7.21). Results

showed that the major frictional losses were due to the collector panel and the heat



173

exchanger and how correlation with calculated K-values may have indicated the

presence of large errors in pressure drop measurements (Table 7.5).

Figure 7.21 Measurement of pressure drop in mm H2O gauge across a pipe section

Reflective insulation (Astrofoil™) was provided around the pipe connecting the

output of the collector to the input of the exchanger. The insulation consisted of two

layers of aluminium foil laminated to the outsides of a sheet of heavy-duty 5 mm

thick polyethylene air-bubble cushioning. The high reflectivity and trapped air spaces

between the foil surfaces made this material a very good insulator. It was also

weatherproof, ideally suited for outdoor applications like this one.

a) No air flow (Φv = 0) b) Turbulent air flow (Φv >10 L/s)

Attachment producing pressure losses

2h1 2h2



174

7.6 Results

7.6.1 First prototype

Typical experimental and numerical results for this prototype are outlined below.

Five different scenarios were studied for four different profiles:

• Single and double cover collector with absorber at back (Figure 7.2a)

• Double cover collector with absorber in the middle (Figure 7.2c)

• Double cover collector with V-corrugated absorber (Figure 7.3b)

• Double cover collector with V-corrugated absorber, with added fins

These profiles were studied for different conditions to determine which one would

offer an overall optimum performance, from its construction to its ongoing operation.

It was decided to construct the V-corrugated profile with fins with ongoing

development of the modelling. The decision was based on the idea that high

turbulence in the collector would relate to higher heat transfer to the air.

Experimental results for this prototype showed that there was close agreement with

the numerical data (Figures 7.22 – 7.23 and Table 7.6). From the modelling it also

seemed that very similar performances could be obtained between the two

V-corrugated absorber profiles (with and without fins) and the profile for the

absorber that divided the chamber into upper and lower halves. The remaining

profiles with the absorber at the back did not perform as well. Assuming then that the

model predicted well the experimental results, it was believed that in a practical

situation the corrugated absorber profile (with and without fins) and the flat

absorber-in-middle profile would behave very similarly. With this in mind,

additional analyses were performed.

A numerical analysis was undertaken to determine whether the dimensions of the

fins were a significant factor in the performance of a full-scale collector for low and

high input air temperatures. In the prototype, the maximum possible triangular fin

length (fin height) that could be made was 30 mm. Results suggested that it was

possible for relatively small irregularities in the V-corrugated profile (~1 mm) to

produce noticeable differences in output temperatures (figs 7.24 – 7.27).



175

Figure 7.22 Output air temperature vs. airflow rate for different panel configurations

Figure 7.23 Collector efficiency vs. airflow rate for different panel configurations

0 10 20 30 40 50 60 70 80 90 100 11020

30

40

50

60

70

80

90

100

110

120

Air flow rate (L/s)

Out

put t

empe

ratu

re (°

C)

Output temperature vs. flow rate for air exiting collector panel

Irradiance = 941 W/m²

Ambient temperature = 20 °C

Input temperature = 20 °C

Collector length = 1.55 m

V-corrugation V-corrugation with finsSimple single cover Simple double cover Complex double coverExp. results

0 10 20 30 40 50 60 70 80 90 100 110 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Air flow rate (L/s)

Col

lect

or e

ffici

ency

Efficiency of the collector vs. flow rate for air exiting the collector

V-corrugation V-corrugation with finsSimple single cover Simple double cover Complex double coverExp. results


Ambient temperature = 18.5 °C





176

Table 7.6 Numerical results for the complex double cover profile of Figure 7.22 for various airflow rates (Figure 7.6a absorber profile)

Airflow rates (Φ) (L/s) Calculated and given parameters 10 20 30 40

Absorber length 1.55 m Absorber width 0.45 m

Optical efficiency 0.73 Average irradiance 941 W/m2

Wind speed 5 m/s Tamb (also Tin) 20 ° C

Temperatures at exit point of panel ° C

Tc1 27.7 25.4 24.1 23.3

Tc2 45.0 38.1 34.2 31.7

Tf1=Tf 51.8 38.5 33.1 30.1

Tab 100.9 77.1 64.3 56.4

Tf2=Tf 51.8 38.5 33.1 30.1

TB 73.5 60.2 52.3 47.1

Heat transfer coefficients W/m2·°C

hQ1* 14.0 16.4 19.2 22.2

hQ2 11.4 10.4 10.0 9.8

hrabC2 8.5 7.1 6.5 6.1

hcf1C2 4.7 7.5 10.2 12.8

hcabf1 4.7 7.5 10.2 12.8

hcabf2 4.7 7.5 10.2 12.8

hcf2B 4.7 7.5 10.2 12.8

hrabB 0.8 0.7 0.7 0.6

hB 2.2 2.2 2.2 2.2

Total heat loss W/m2·°C

UL 4.3 2.9 1.8 0.8

Experimental results for the V-corrugated absorber prototype (Figure 7.22) Airflow rates (L/s) 11.3 ± 0.4 17.6 ± 0.7 23.1 ± 1.0 27.6 ± 1.2 31.3 ± 1.5

Tf (°C) 48.2 ± 0.4 41.2 ± 0.4 36.5 ± 0.4 33.6 ± 0.5 30.2 ± 1.5 * The radiation heat transfer coefficient in h1 is referenced to the ambient temperature.



177

The convection heat transfer from the absorber to the air flowing in the channels,

hcabf1 & hcabf2, is similar (is described by the same set of equations). The same

applies for the transfer between the flowing air and lower side of the top cover,

hcf1C2, and the transfer between the air and the bottom of the panel, hcf2B. These

quantities were calculated for the double-channel flat absorber profile configuration

(Figure 7.6a) as a special case of the more complex situation of heat transfer from

corrugated and finned triangular channels explained in chapter 4. The calculations

were adapted to reflect no corrugation or roughness in the channels, with an absorber

area equal to the panel aperture area. These transfer coefficients are the decisive

factors in determining useful heat. More energy is delivered to the air stream for

higher flow rates, since more heat is removed from the absorber. Conversely, less

heat is lost, so the total heat loss, UL, decreases with increasing flow rates. This can

also be seen as lower heat transfer coefficients for radiation emitted by the absorber,

hrabC2 and hrabB, and a lower figure for the combined conduction and radiation that

occurs from the lower to the upper side of the top cover, hQ2. It is important to note

that the heat transfer coefficient, hQ1, associated with the losses from the top cover is

not really an indicator of actual physical heat loss from that element. It contains the

heat transfer coefficient for forced and free convection from the cover to the ambient,

hcCA (which, incidentally, does not vary much with varying airflow rates inside the

panel). However, its radiation loss component has been referenced to the ambient

temperature instead of the sky temperature. This is done for ease of calculation of the

thermal network (section 4.2.3) and its increase with increasing airflow rates is

because of the large quotient that results as the cover temperature, TC1, approaches

the ambient temperature, Tamb (see Equation 4.42). The actual radiation transfer

coefficient from cover to sky, hrCS, decreases with increasing airflow rates.



178

Figure 7.24 Output air temperature vs. airflow rate for finned V-corrugated absorbers for an input air temperature of 20°C

Figure 7.25 Efficiency vs. airflow rate for a V-corrugated absorber of various fin lengths

0 10 20 30 40 50 60 70 80 90 100 110 60

70

80

90

100

110

120

130

140

Air flow rate (L/s)

Out

put t

empe

ratu

re (°

C)

Output air temperature vs. flow rate for a V-corrugated absorber panel

Irradiance = 900 W/m² Ambient temperature = 20 °C

Input temperature = 20 °C Collector length = 6.5 m

No fins 0.1 mm fins0.5 mm fins

1 mm fins5 mm fins

10 mm fins30 mm fins

0 10 20 30 40 50 60 70 80 90 100 110 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Air flow rate (L/s)

Col

lect

or e

ffici

ency

Efficiency of the V-corrugated absorber panel vs. air flow rate

No fins 0.1 mm fins 0.5 mm fins

1 mm fins5 mm fins

10 mm fins30 mm fins





179

Figure 7.26 Output air temperature vs. airflow rate for finned V-corrugated absorbers for

an input air temperature of 60°C

Figure 7.27 Efficiency vs. airflow rate for a V-corrugated absorber of various fin lengths

0 10 20 30 40 50 60 70 80 90 100 11085

90

95

100

105

110

115

120

125

130

135

140

Air flow rate (L/s)

Out

put t

empe

ratu

re (°

C)


Irradiance = 900 W/m² Ambient temperature = 20 °C Input temperature = 60 °C Collector length = 6.5 m


1 mm fins 5 mm fins

10 mm fins 30 mm fins

0 10 20 30 40 50 60 70 80 90 100 1100

0.1

0.2

0.3

0.4

0.5

0.6

Air flow rate (L/s)

Col

lect

or e

ffici

ency

Efficiency of the V-corrugated absorber panel vs. air flow rate

Irradiance = 900 W/m² Ambient temperature = 20 °C Input temperature = 60 °C Collector length = 6.5


1 mm fins 5 mm fins

10 mm fins 30 mm fins



180

Another analysis was done comparing all profiles for a full-size model (Figures 7.28

– 7.33). For different input temperatures there was little variation in the relative

performance of the V-corrugated profiles. The higher the input temperature and the

higher the flow rates, the smaller the difference in the collector output air

temperature and efficiency. For airflow rates above 60 L/s, the performance of both

profiles was equivalent from an operational point of view (with temperature

differences below 1.5°C). For this range of airflow rates and for medium-high and

high input temperatures, the profile for the absorber in the middle of the chamber

also showed a good performance, with temperature differences of less than 3.5°C

when compared with the other two.

This profile was considered the overall optimal for inclusion in the final full-scale

prototype, since it was much easier, faster and more reliable to manufacture and the

difference in performance could be easily compensated by increasing the length of

the collector allowing for a larger area and more input solar power.

Figure 7.28 Output air temperature vs. airflow rate for input air at 20°C and different

panel configurations

110 0 10 20 30 40 50 60 70 80 90 100

40

50

60

70

80

90

100

110

120

130

Air flow rate

Out

put t

empe

ratu

re (°

C)


V-corrugation V-corrugation with fins Simple single cover Simple double cover Complex double cover





181

Figure 7.29 Efficiency vs. airflow rate for input air at 20°C and different panel

configurations



0 10 20 30 40 50 60 70 80 90 100 1100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Air flow rate (L/s)

Col

lect

or e

ffici

ency

Efficiency of the V-corrugated collector vs. flow rate

V-corrugation V-corrugation with finsSimple single cover Simple double cover Complex double cover





0 10 20 30 40 50 60 70 80 90 100 11050

60

70

80

90

100

110

120

130

Air flow rate (L/s)

Out

put t

empe

ratu

re (°

C)


V-corrugation V-corrugation with finsSimple single cover Simple double cover Complex double cover







182

Figure 7.31 Efficiency vs. airflow rate for input air at 40°C and different panel configurations



20 30 40 50 60 70 80 90 100 110 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Air flow rate (L/s)

Col

lect

or e

ffici

ency







0 10

0 10 20 30 40 50 60 70 80 90 100 110

70

80

90

100

110

120

130

Air flow rate (L/s)

Out

put t

empe

ratu

re (°

C)









183

Figure 7.33 Efficiency vs. airflow rate for input air at 60°C and different panel configurations

Another analysis was done to determine the efficacy of the dimensions chosen for the

second prototype, namely, the ratio of the internal height of the collector, D, over the

length, L. This is known as the D/L ratio and is a parameter used in the assessment

of system efficiency113. Due to manufacturing and system constraints owing to

readily available materials, the height of the air chamber in the collector was to be 60

mm. The shortest collector length that could eventuate would be 6.4 m. With these

dimensions, D/L = 0.0094.

The result of the numerical analysis, Figures 7.34 - 7.37 show that for the profile

chosen and for mid to high input air temperatures, values of D/L below 0.0044 have

negligible effect on the efficiency and operation of the collector. The closest figure to

the design value of 0.0094 is 0.0088, which offers only slightly reduced performance

from the optimum (less than 1.5°C). It is estimated that if this design ratio is used it

would give less than 3°C output temperatures from the optimum. This is not

significant enough to require a redesign of the prototype system. In actual fact, the

D/L ratio that eventuated from the second prototype construction was 0.05/6.6 =

0.0076. The second prototype is discussed next.

0 10 20 30 40 50 60 70 80 90 100 110 0

0.1

0.2

0.3

0.4

0.5

0.6

Air flow rate (L/s)

Col

lect

or e

ffici

ency


V-corrugation V-corrugation with finsSimple single cover Simple double coverComplex double cover







184

Figure 7.34 Variation of the ouput air temperature for 20°C input air based on different

D/L ratios

Figure 7.35 Efficiency air temperature for 20 °C input air temperatures based on different

D/L ratios

0 10 20 30 40 50 60 70 80 90 100 110 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Air flow rate (L/s)

Col

lect

or e

ffici

ency

Efficiency of collector panel vs. flow rate for various D/L ratios – Low input air temperatures



Input temperature = 20 °C Collector length = 6.5 m Collector width = 0.57 m

0.00025 0.00055 0.0011 0.0022 0.0044 0.0088 0.0176 0.0352 0.0704 0.1408 0.2816

D/L

Output temperature vs. flow rate for air exiting collector panel forvarious D/L ratios – Low input air temperatures

0 10 20 30 40 50 60 70 80 90 100 110

30

40

50

60

70

80

90

100

110

120

130

Air flow rate (L/s)

Out

put t

empe

ratu

re (°

C)

Irradiance = 900 W/m² Ambient temperature = 20 °C Input temperature = 20 °C Collector length = 6.5 m Collector width = 0.57 m

0.00025 0.00055 0.00110.00220.00440.00880.01760.03520.07040.14080.2816

D/L



185

Figure 7.36 Variation of the ouput air temperature for 40°C input air based on different

D/L ratios

Figure 7.37 Efficiency air temperature for 40 °C input air temperatures based on different D/L

ratios

0 10 20 30 40 50 60 70 80 90 100 110 40

50

60

70

80

90

100

110

120

130

Air flow rate (L/s)

Out

put t

empe

ratu

re (°

C)

Output temperature vs. flow rate for air exiting collector panel for various D/L ratios – High input air temperatures




0.00025 0.00055 0.0011 0.0022 0.0044 0.0088 0.0176 0.0352 0.0704 0.1408 0.2816

D/L

0 10 20 30 40 50 60 70 80 90 100 1100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Air flow rate (L/s)

Col

lect

or e

ffici

ency

Efficiency of collector panel vs. flow rate for various D/L ratios –High input air temperatures


Ambient temperature = 20


0.000250.000550.00110.00220.00440.00880.01760.03520.07040.14080.2816

D/L



186

7.6.2 Second prototype

Temperatures at all the relevant points in the system were obtained during operation

in open and closed loop modes. This enabled estimation of power delivered to the

water, Pin_water, and its comparison with model results, constituting the decisive

figure in performance assessment. Experimental data and numerical results are given

in sections 7.6.2.1 and 7.6.2.2 for the open and closed loop modes, respectively.

Performance prediction process

The solution process for numerical prediction of Pin_water (Equation 7.23) was

explained in section 7.3.4. It required the following parameters:

- Heat loss coefficients of the system

- The exchanger effectiveness

- The effective radius of the thermosiphon coupling

Heat loss coefficients were calculated as in section 7.2. The exchanger effectiveness

was determined from Equation 7.24 and was found from the relevant input and

output temperatures, Tin_x, Tin_w, Tout_water, that were measured during system

operation. Two different values, ε = 0.73 and ε = 0.69, were obtained for open and

closed loop modes, respectively (Figures 7.39 and 7.46). (Subsequent direct

measurements on the isolated exchanger gave similar results, section 7.6.5).

The remaining parameter, the effective radius of the thermosiphon loop, was used as

a parameter to fit the experimental data. From the theory of section 7.3.4, the power

delivered to the water, Pin_water, versus Tout_water could be calculated (Equation 7.23).

The results for open and closed loop operation are given in Figures 7.40 and 7.47,

respectively. Experimental findings for Pin_water versus Tout_water were plotted on the

same graphs revealing two different radii values, r = 3 mm and r = 3.75 mm, for each

mode. (Subsequent direct measurements on the isolated exchanger gave similar

results, section 7.6.4).



187

Knowing the heat loss coefficients, the exchanger effectiveness and the effective

thermosiphon radius, Equations 7.18, 7.21, 7.23 and 7.26 were used to predict system

temperatures over a wide range of input irradiance. The predicted temperatures

versus the measured temperatures are shown in Figures 7.38 and 7.41 for open loop

mode and in Figures 7.45 and 7.48 for closed loop mode. Within the limited range of

irradiance available for measurement it is seen that the theory predicted the system

temperatures reasonably well (to within 7% of experimental results).

7.6.2.1 Open loop operation mode

The airflow rate measured was (61 ± 4) L/s. All relevant temperatures and numerical

predictions in Figure 7.38 corresponded to measurements taken for a typical run.

Figure 7.38 Experimental and numerical temperature variations vs. time of the day for the

elements of the 2nd prototype air heater panel and SHWS in open loop mode

Temperatures for 2nd prototype air heater panel & SHWS elements vs. time OPEN LOOP OPERATION

Time of the day

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

9:36 9:56 10:16 10:36 10:56 11:16 11:36 11:57 12:17 12:37

Tem

pera

ture

s (°

C)

12:57


Collector width = 0.57 m

Effective radius = 3 mm

Tin_col

Tout_col

Tin_w

Tout_w

Tin_exch

Tout_exch

Tout_exch_NUM

Tout_w_NUM

Tin_exch_NUM

Tout_col_NUM

Tamb



188

The rise in air temperature was about 40 °C – 45 °C and it dropped in the exchanger

by 11 °C – 18 °C. Assuming the entire power drop in the exchanger got transferred

to the water, no more than 40% of the gain from the collector was used.

The numerical temperature predictions were slightly lower at early stages of system

operation and slightly higher at later stages (this is explained later when numerical

predictions over a wider range of irradiances are presented).

Power delivered to the air was about 2900 W for an air mass flow rate of about

0.066 kg/s. Taking 970 W as a representative average irradiance during operation,

the average input power to the collector was about 3600 W. A quick estimation of

the efficiencies gave 80% for the collector and just under 33% for the entire system.

Heat exchanger effectiveness

The effectiveness was calculated by plotting the temperature differences ratio of

Equation 7.24 (Figure 7.39). An initial approximation of a linear fit to the data

yielded a constant exchanger effectiveness of 0.73 ± 0.04.

Figure 7.39 Experimental results and numerical fit for determination of exchanger

effectiveness (eq. 7.24) for an airflow rate of 61 L/s in open loop mode

Exchanger effectiveness plot for input and output fluid temperatures OPEN LOOP OPERATION

0 2 4 6 8

10 12 14 16 18 20 22 24 26 28 30 32 34 36

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Tin_x – Tin_water (°C)

T out

_wat

er -

T in_

wat

er (°

C)

Air flow rate = 61 L/s y = 0.726x Y-error

X-error

R = 0.81

p < 0.0001



189

The results are quite removed from the origin and there is no previous knowledge of

the variation of the effectiveness with the ratios of the varying fluid temperatures.

Therefore, the simple assumption of linear behaviour with zero intercept is very

naïve, to say the least. Calculating the effectiveness by using the average ratio of the

temperature differences would be more appropriate. It was found, however, that the

result for effectiveness in both cases was basically the same (0.726) and so the

simplification of a linear fit was kept.

Effective thermosiphon radius

Comparison between experimental and theoretical values of power delivered to the

water versus output water temperature showed that a radius of (3.0 ± 0.4) mm fitted

the data reasonably well (Figure 7.40)

Figure 7.40 Experimental measurements and numerical predictions for power delivered to

the water vs. exchanger output air temperature for various thermosiphon pipe

radii (eq. 7.22) and for an airflow of 61 L/s in open loop operation

0 10 20 30 40 50 60 0

500

1000

1500

2000

2500

3000

Tout_water (°C)

Pow

er d

eliv

ered

to w

ater

(W)

Power delivered to the water vs. output water temperature for various pipe radii OPEN LOOP OPERATION

70

RADIUS

2 mm 3 mm 4 mm 5 mm 6 mm

+


Collector input air temperature = 31.5 °C

Exchanger input water temperature = 23.8 °C



Airflow = 61 L/s

Exp. data



190

Average values for the temperatures and the irradiance were used as input parameters

for the model to produce the curves of Figure 7.40.

Temperature predictions

It was now possible to predict all system temperatures since the required parameters

were known. A plot of theoretical temperatures for a full range of irradiance values

(Figure 7.41) revealed that almost all temperatures increased with increasing

irradiance, except for the output exchanger air temperature that reached a maximum

at around 980 W/m2 and then dropped off. This seemed to indicate that at these high

irradiance values, the water flow rate was high enough to allow a higher power

transfer between the air entering the exchanger and the thermosiphon loop, therefore

lowering the output air temperature.

Figure 7.41 Experimental temperature variations and numerical predictions over a wide

range of irradiance values for the 2nd SHWS prototype in open loop mode

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 20

25

30

35

40

45

50

55

60

65

70

75

80

Irradiance (W/m2)

Tem

pera

ture

(°C

)

Temperatures for 2nd prototype heater panel & SHWS elements vs. irradiance OPEN LOOP OPERATION

Tamb

Tin_col

Tout_col

Tin_exch

Tout_exch

Tin_water

Tout water



90



191

This phenomenon was not observed experimentally, basically because of the narrow

range of irradiance values available.

Similar to the results from Figure 7.38, these plots showed that the experimental

results were less than predicted at the start and higher than predicted at the end. This

was surely an indication of thermal inertia of the system as evidenced in other

studies135F

136. Dynamic effects due to the thermal mass of the system were not included

in the steady state theory developed in section 7.2. This effect was more clearly seen

and more accurately represented in Figure 7.38, since the numerical values for those

plots were computed for actual values of ambient temperature, Tamb, input water

temperature, Tin_water, and input panel air temperature, Tin_col, for every set of

measurements. In contrast, the curves of Figure 7.41 were produced from fixed

values for these temperatures and so the differences appear more pronounced when

they are not. It is clear (Figure 7.41) that Tin_water, Tin_col and Tamb were not constant.

The limited irradiance range of operation restricted the correlation between the

model and experimental data. Measurements at lower irradiance values would have

been useful in the validation of the numerical simulation process. The solar window

for the SHWS was restricted, allowing operation from 9 am until 2 pm. However, it

is also noted that effective operation of the system would only occur for relatively

high irradiance values and even though the actual experimental range was a narrow

one, a wider irradiance range would only be useful for values above 700 W/m2,

which would happen between the expected operation times of the day (section 7.1).

Another interesting fact was that output air temperatures from the collector were

always slightly higher than numerical predictions (Figure 7.42). Since the actual

absorber profile was not smooth, imperfections and protrusions as small as 1 mm on

the surface could act as if they were “mini-fins” inducing a heightened turbulence

and contributing to the higher temperatures (Figures 7.24 and 7.26). Also, since the

real profile (Figure 7.16a) was more like a multi-channel absorber, a higher energy

exchange with the air would be expected. The wooden strips covering the bottom of

the collector, besides reducing the height by about 5 mm from the original design,

thus reducing the D/L ratio and increasing performance, (Figures 7.34 and 7.36)

might have contributed with an increase in turbulence as air flowed over them.



192

Figure 7.42 Experimental and numerical output air temperature variations for the 2nd

prototype air heater panel vs. time of the day in open loop mode

Power calculations

The power delivered to the water carried a high associated uncertainty due to the

uncertainty variations of all temperatures and the simplifications in the modelling of

the exchanger. Numerical and experimental results are given in Figure 7.43

Since a lossless exchanger was assumed, the calculated power delivered to the water

was equated to the power drop of the air in the exchanger. For open loop operation in

this particular case (3 hours of operation) this was:

Pin_water_exp: (996 ± 220) W

Pin_water_num: 923 W

With an average irradiance of (970 ± 40) W/m2 and an absorber area of 3.7 m2, total

system efficiency was about 27%, with variations between 20% to 34% due to the

high associated uncertainties. Numerical prediction gave (25 ± 1)%

Collector panel output air temperature vs. time OPEN LOOP OPERATION

60

62

64

66

68

70

72

74

76

78

80

82

9:36 9:50 10:04 10:19 10:33 10:48 11:02 11:16 11:31 11:45 12:00 12:14 12:28

Time of the day

Tem

pera

ture

(°C

)

Tout_col_NUM-RAW

Tout_col_NUM+2°

Tout_col_EXP



193

Figure 7.43 Experimental results and numerical prediction for power delivered to the water

vs. time of the day for open loop operation and for 61 L/s airflow

Water tank temperature profile

Subsequent runs with the system operating in closed loop mode included

measurements of the temperature profile of the water in the tank after a day’s

operation. These results were used to better determine the average power delivered to

the water. Since this was not implemented during the early stages of open loop

operation, special runs were done afterwards specifically to have a set of results that

would be representative of the dynamics and power delivered to the water in this

configuration mode. The results given in Figure 7.44 are for one such run where the

temperature profile was measured after 1.5 hours of system operation.

Power delivered to water vs. time – OPEN LOOP OPERATION

Pow

er (W

)

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

9:36 9:50 10:04 10:19 10:33 10:48 11:02 11:16 11:31 11:45 12:00 12:14 12:28

Pin_wat_NUM

Pin_wat_EXP

Time of the day



194

Figure 7.44 Temperature measurements for a vertical profile of the water in the storage

tank for open loop operation of the system and for 61 L/s airflow

The plot above shows obvious signs of thermal stratification with a transitional

region extending down and ending at about the centre of the tank. The assumption of

an unchanging cold water column was therefore not true. However, it was a good

starting point for the determination of an otherwise very difficult calculation.

After measuring the depth profile, the water in the tank was mixed thoroughly and a

final average temperature of 30 °C was obtained. From this Figure, and for 1.5 hours

of heating 190 L of water, it was determined that the average power delivered to the

water during operation of the system, Pin_water_exp, was: (1070 ± 150) W. Incidentally,

this figure was very close to the power measured in the open loop system operation

as shown in Figure 7.43. Despite the fact that the tank temperature profile was taken

for a different data collection time it was reasonable to expect a similar result since

operating and environmental conditions for both runs were similar.

Temperature depth profile for hot water in the tank OPEN LOOP OPERATION

20 21 22

23 24 25 26 27 28

29 30 31 32 33

34 35 36 37 38 39

40 41 42

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84

Tank height (cm)

Tem

pera

ture

(°C

)

Mixed

Unmixed



195

7.6.2.2 Closed loop operation mode

The airflow rate measured was (63 ± 4) L/s. All relevant temperatures and numerical

predictions in Figure 7.45 corresponded to measurements taken for a typical run.

Figure 7.45 Experimental and numerical temperature variations vs. time of the day for the

elements of the 2nd prototype air heater panel and SHWS in closed loop mode

The rise in air temperature was lower than for the open loop mode, about

35 °C - 37 °C, but the drop in the exchanger was higher: about 20 °C - 23 °C. This

meant that about 60% of the power in the air was transferred to the water. For

approximately 0.069 kg/s mass airflow rate, the power delivered to the air was about

2500 W. Taking 890 W as a representative average irradiance during operation, the

average input power to the collector was about 3300 W and the efficiency of the

entire system about 45%. The higher efficiency compared to the open loop

configuration was due to the larger heat transfer in the exchanger.

Temperatures for 2nd prototype heater panel & SHWS elements vs. time CLOSED LOOP OPERATION

Time of the day

Tem

pera

ture

s (°

C)

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

9:36 9:50 10:04 10:19 10:33 10:48 11:02 11:16 11:31 11:46 12:01



Radius = 3.75 mm

Tin_col

Tout_col

Tin_w

Tin_exch

Tout_exch

Tout_w_NUM

Tin_exch_NUM

Tout_col_NUM

Tamb

Tout_w

Tout_exch_NUM

Tin_col_NUM



196

Heat exchanger effectiveness

The effectiveness was calculated by plotting the temperature differences ratio of

Equation 7.24 (Figure 7.46). A linear fit to the data yielded a constant exchanger

effectiveness of 0.69 ± 0.04, lower than for the open loop mode.

Figure 7.46 Experimental results and numerical fits for determination of exchanger

effectiveness (Equation 7.24) for an airflow rate of 63 L/s in open loop mode

Similar to the effectiveness calculation in open loop mode, the average ratio of the

temperature differences was compared to the slope value from the linear fit and the

results were practically the same (less than 0.1% difference).

Effective thermosiphon radius

Comparison between experimental and theoretical values of power delivered to the

water versus output water temperature showed that a radius of (3.75 ± 0.4) mm fitted

the data reasonably well (Figure 7.47).

y = 0.691x

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52

Exchanger effectiveness plot for input and output fluid temperatures CLOSED LOOP OPERATION

Tin_x – Tin_water (°C)

T out

_wat

er -

T in_

wat

er (°

C)

Air flow rate = 63 L/s

X-error

Y-error

R = 0.775p < 0.0014



197

Figure 7.47 Experimental measurements and numerical predictions for power delivered to

the water vs. exchanger output air temperature for varius thermosiphon pipe

radi (eq. 7.56) and for an airflow of 63 L/s in closed loop operation

Average values for the temperatures and the irradiance were used as input parameters

for the model to produce the curves of Figure 7.47.

Temperature predictions

Since the air temperature input of the collector changed with time, the output

collector and exchanger air temperatures and the output water temperature increased

in a non-linear fashion (Figure 7.48), as opposed to the linearity observed in the open

loop system (Figure 7.42).

Temperature (°C)

Pow

er d

eliv

ered

to w

ater

(W)

Power delivered to water vs. exchanger output water temperaturefor various pipe radii – CLOSED LOOP OPERATION

0 5 10 15 20 25 30 35 40 45 50 55 60 650

250

500

750

1000

1250

1500

1750

2000

2250

2500

3000

70

2750


Collector input air temperature = 30.9 °C

Exchanger input water temperature = 15.6



Airflow = 63 L/s

RADIUS

2 mm 3 mm 3.75 mm 4 mm 5 mm

+ Exp. data



198

Figure 7.48 Experimental temperature variations and numerical predictions over a wide

range of irradiance values for the 2nd SHWS prototype in closed loop mode

Similar to the open loop configuration, all temperatures increased with increasing

irradiance with the exception of the output exchanger air temperature, which reached

a maximum and then dropped off. Additionally, and since the system was operating

with air recycling, the collector input air temperature experienced the same thing.

The effects of thermal inertia were also seen for this operation mode (Figures 7.45

and 7.48) for the exchanger input, exchanger output and collector input air

temperatures. Collector output air temperatures were also consistently higher than

model predictions (2 °C - 3°C).

Irradiance (W/m2)

Tem

pera

ture

(°C

) Temperatures for 2nd prototype heater panel & SHWS elements vs. irradiance

CLOSED LOOP OPERATION

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

10

15

20

25

30

35

40

45

50

55

60

65

70

75

0

5

Tamb

Tin_col

Tout_col

Tin_exch

Tout_exch

Tin_water

Tout_water

Radius = 3.75 mm





199

Power calculations

The results for power in the water versus time of the day during system operation

were higher compared to the open loop mode (Figure 7.49) and this was due to the

higher heat transference in the exchanger.

Figure 7.49 Experimental results and numerical prediction for power delivered to the water

vs. time of the day for 63 L/s airflow in closed loop mode

For 1.8 hours of operation, the results for power delivered to the water were:

Pin_water_exp: (1430 ± 200) W

Pin_water_num: 1300 W

For an average irradiance of (890 ± 40) W/m2 and an absorber area of 3.7 m2, total

system efficiency was about 40% or more which is higher than the value of 27%

found for the open loop system.

Pow

er (W

)

Power delivered to water vs. time CLOSED LOOP OPERATION

Time of the day

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

9:36 9:43 9:50 9:57 10:04 10:12 10:19 10:26 10:33 10:40 10:48 10:55 11:02 11:09 11:16 11:24 11:31

Pin_wat_NUM Pin_wat_EXP



200

Water tank temperature profile

The temperature profile of the water was measured after operation and there was also

evidence of thermal stratification in the tank with a transitional region extending

downwards by ⅔ the length of the tank (Figure 7.50).

Figure 7.50 Temperatre measurements for a vertical profile of the water in the storage tank

for 63 L/s airflow in closed loop mode

The water in the tank was mixed twice to arrive at a uniform temperature. The final

average value obtained was 23.6°C. After 1.8 hours of operation and heating 190 L

of water, the average power delivered to the water was: (1121 ± 200) W. This value

was lower than the numerical predictions and experimental data given in Figure 7.49.

System efficiency in this case was about 34%, still higher than in open loop mode.

The results for the closed loop system showed that it delivered more power than the

previous configuration.

Temperature depth profile for hot water in tank CLOSED LOOP OPERATION

Tem

pera

ture

(°C

)

Tank height (cm)

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80

Mixed

Unmixed



201

7.6.3 Determination of head loss and pressure drops in the system

Values for pipe losses in the whole system were determined both numerically and

experimentally. This was done for the closed-loop configuration, since it was the

configuration of choice for continuous operation.

A schematic of the system showing the resistive elements and pressure drop

measurement points is given in Figure 7.51. The experimental and numerical data is

given in Table 7.7 as well as the K-values for each element.

Figure 7.51 Schematic of conveyance infrastructure: pipes, elbows, fittings and other elements

The numerical calculations for pressure loss in the system were based on the theory

outlined in chapter 5, which was applied to all elements except for the heat

exchanger. Pressure measurements were taken in accordance with the description and

setup of Figure 7.21. The fan blower, used always in its medium setting, (refer to

Appendix H) was capable of producing flow rates in excess of 90 L/s when operating

against no static pressure. In closed loop operation, flow rates above 60 L/s were

obtainable. With these rates it was possible to achieve the daily hot water energy

requirements of 30 MJ (Table 1.2).

L

M J

A

B

C

D E

F

G H

I

K fan/blower

1

2

3

4 5

6

7

8



202

Table 7.7 Theoretical and experimental pipeline pressure drops

Pressure drop (Pa) Element type & ID

(Figure 7.51) Description Loss Value Calculated

Exp. (± 20)

A1 15° Kf_15 = 0.06 0.4 P2 - P1 Elbow fittings

A2 90° Kf_90 = 1.2 7.2 Straight pipe LAB A to B – join 0.2 m 1.3 42

B1 15° Kf_15 = 0.06 0.4 Elbow fittings

B2 45° Kf_45 = 0.3 1.9

11.2

P3 - P2 Straight pipe LRET B to C – join 5.1 m 33

34

C1 22.5° Kf_22.5 = 0.1 0.6 P4 - P3 Elbow fittings C2 90° Kf_90 = 1.2 7.2 58

Straight pipe LCD C to D – join 0.2 m 1.3 9.1

Reduction fitting D Collector input Kfr = 0.01 0.08 P5 - P4 Sudden

expansion E Collector inlet Kxc = 0.8 6.5

Other element F Collector panel Km ≈ 3 0.5 108 Sudden

contraction G Collector outlet Kcc = 13.7 111

Expansion fitting H Collector output Kfx = 0.02 0.16

118

I1 45° Kf_45 = 0.3 1.9 P6 - P5 Elbow fittings

I2 15° Kf_15 = 0.06 0.4 2.3 6

P7 - P6 Straight pipe LOUT I to J – join 4.1 m 26.5

26

Elbow fitting J 45° Kf_45 = 0.3 1.9 P8 - P7

Combination Fitting K1 X-changer input Kxi = 0.9 5.2

Sudden expansion K2 X-changer inlet Kxm = 0.6 3.6 72

Other element L X-changer body Kp ≈ 70 ~22 Sudden

contraction M1 X-changer outlet Kcm = 4.7 28

Combination Fitting M2 X-changer output Kco = 0.9 5.2

~66



203

The motor was never operated at its maximum voltage rating and it functioned

continuously for many hours with no apparent deterioration. Based on current and

voltage measurements, it had an average power consumption of less than 80 W, and

was able to provide the required airflow rates for this study. In a commercial

application, the call would be for a 240 VAC motor with the same physical criteria

design for this centrifugal blower, unless the system were to be used as a stand-alone

system, in which case photovoltaic panels would be used.

The results in Table 7.7 show that for an airflow rate of 63 L/s, the major losses were

due to the collector panel assembly, which included the reduction and expansion

fittings for the entrance and exit ports, and the heat exchanger. Pressure drop

calculations for straight pipe sections correlated fairly accurately with the

measurements at the different points, despite the large associated error (±20 Pa).

Correlations for the minor losses, however, indicated the presence of unaccounted

resistance factors, systematic errors, or both. It is important to note that elbow

fittings and joiners used were forced on to the straight pipe in order to obtain the

airflow pathway that the test site allowed with the hardware available at the time.

Therefore, actual airflow bends where not smooth, experiencing sharp entering and

exiting effects into and from these fittings. Even though all elbow bends were

considered as rough mitre-type bends, with sharp angles, the additional resistance

measured indicated something else was happening. Measurements with errors as high

as 100% (and higher) are not useful in practice, nevertheless the technique allowed

determining two things: the elements producing the largest pressure drops and the

possibility of determining theoretically the pressure drops for given airflow rates.

Another source of error was attributed to the measurement process, which besides

having a large uncertainty, was dependent on the actual positioning of the measuring

nozzle in the pipeline (Figure 7.19). It is possible that pressure drops were masked

and/or enhanced by the mere fact of taking measurements close to those elements

producing minor losses and by the depth at which the nozzle was inserted into the

pipes (about 10 mm). This could also explain the better correlation for head losses

from the straight pipes, where the effect of a fully developed flow would have been

prevalent. The largest discrepancy was observed for the measurement between points



204

3 and 4; the bend of the return pipe and the input to the collector. The airflow at the

entrance was confronted by a slight contraction and then suddenly by an expansion

into the collector chamber area, which could have artificially raised the expected

pressure drop between the points in question.

It is noted that the largest minor losses occurred for sudden contraction fittings,

especially from the collector exit where the airflow cross-sectional area suddenly

reduced to about 15% of its value (from about 0.034 m2 to 0.005 m2).

Of particular importance are the unconventional resistance elements: the panel and

the heat exchanger, for which the K-values were estimated. The panel proper (F),

without the input and output attachments, actually posed a relatively low resistance

due to its large cross-sectional area. Its effect was approximated to that of two 90°

degree mitre bends with an extra pressure loss at the back buffer zone where the

airflow bend actually occurred (K ≈ 1.5 x 2). The K-value assigned to the heat

exchanger was worked out from the experimental results. Since discrepancies where

found for minor losses, it is possible that the resistance posed by the exchanger was

lower than the estimation.

Finally, the so-called “combination” fittings (K1 and M2) used for the heat exchanger

were actually a special type of fitting (Figures 7.15 and 7.17). K1, for instance,

produced a partial expansion of the airflow into a relatively small space followed

immediately by a contraction into the actual exchanger chamber opening, or inlet

(where an expansion then took place as indicated by K2). The effect of M2 was the

opposite. These K-values were conservatively estimated assuming twice the value of

an expansion-contraction or (contraction-expansion) effect (K ≈ 0.45 x 2).

Since the airflow rate was 0.063 m3/s and the pressure losses in the system were

about 346 Pa, the estimated power required to overcome these losses (from

Equation 5.29) was about 22 W. Total pump efficiency was then no less than 27%

and about 58 W were consumed as part of the electro-mechanical conversion process

for airflow generation. The air pump is not very efficient. However, if these power

losses are compared with a power gain from the system of about 1000 W of hot

water, they represent less than 6% of the total, which is not a major loss. It is



205

important to note that these are worst-case scenarios, since actual motor power

measurements were not taken (80 W is an upper bound value) and the efficiency

could be higher. Also, more than 1000 W of heat into the water is expected, on

average, for daily operation as discussed in the previous section. It would appear then

that improving on motor design to increase efficiency might not be significantly

useful. More detailed assessment of power consumption is required. Keeping with

the objectives of this project, going for a higher motor efficiency could be pursued if

it is possible to source a readily available, mass produced, alternative (eg. improved

and inexpensive successor model). Compared with the power consumption of

non-solar hot water systems, this represents an insignificant loss, considering for

instance, that a typical electrical hot water system with a 160 L tank consumes about

2400 W. On the other hand, domestic solar hot water split systems that use a pump to

simulate a natural thermosiphon operation, consume less than 20 W and do not

operate continuously as the fan-motor does. Compared to these, the fan-motor is in

clear disadvantage, but putting it all in context and referring again to non-solar

systems and the project’s objectives of low-cost and ease of implementation, a

fan-blower motor efficiency of about 27 % is acceptable.

Overall, the results showed that it was possible to predetermine the hydraulic

resistance offered by a SHWS of this nature for proper sizing of the motor and

eventually finding overall efficiency.



206

7.6.4 Thermosiphon effective radius and linear fluid flow approximation

From the results for open and closed loop operation of the SHWS, two different

effective radii, 3 mm and 3.75 mm, were determined for the thermosiphon loop. This

represents a difference of 20%. The discrepancy could be explained from the high

associated uncertainties of the measurements and the simplifications used in the

analysis of the thermosiphon process, especially the assumption of a constant

effectiveness for the heat exchanger and a constant hot water column of water

driving the flow. A more detailed analysis of the relationship between water flow and

pressure drop in the exchanger was carried out in order to assess the usefulness of the

Poiseuille equation and infer a more accurate effective radius (if possible).

The experimental setup is shown in Figure 7.52 and the method consisted in the

determination of pressure drops across the exchanger for known water flow rates. A

similar approach to that of air pressure drops was done, with manometer readings in

mmH20 before and after the flow entered the exchanger. A hose was connected to the

input of the exchanger and tap water allowed to flow from 1.7 cc/s up to 46 cc/s.

Actual flow rates were determined by measuring collected fluid volume over time.

The results are shown in Figure 7.53.

Figure 7.52 Pressure drop measurement setup for water flow in the heat exchanger

Δh

Heat Exchanger



207

Figure 7.53 Experimental measurements for pressure drops vs. water flow rates in the heat

exchanger and equation fits showing a linear response below 12 cc/s

The results showed a linear response range for flow rates below 12 cc/s. This

supported the assumption made in section 7.3.4 of laminar flow under 10.5 cc/s

allowing the application of Poiseuille’s equation for flow rates under this range.

The linear fit to the points below 12 cc/s in Figure 7.53 has a high correlation

coefficient, being well approximated by an equation with zero intercept from which

the effective thermosiphon radius of the heat exchanger could be easily determined.

This assumption of linearity, however, was based on a thermosiphon radius equal to

twice the size of the calculated effective radius for the exchanger. A reduction in pipe

size would imply a reduction in the laminar flow threshold as well. For the effective

thermosiphon pipe radius (Table 7.8) and from Equation 5.18 for the Reynolds

number, this would indicate that laminar flow would be observable for flow rates

under 6 cc/s. In actual fact, and as given by the results above, fluid flow appeared to

depart from its laminar nature in the vicinity of 11 cc/s.

From Poisseuille’s equation for laminar flow (Equation 5.30):

Pressure drop vs. water flow rate for the heat exchanger

P2 = 0.168·Φ2 + 4.785·Φ

R2 = 0.998

p < 0.014

0

50

100

150

200

250

300

350

400

450

500

550

600

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

Flow rate (cc/s)

Pres

sure

(Pa)

Linear flow range (< 12 cc/s)Entire flow range

P1 = 6.094·Φ

R = 0.982

p < 0.001



208

( )fitlinearofslopear

lPL=

⋅⋅⋅

=Φ 4

8π

η (7.34)

There was excellent agreement between the calculated radius from Equation 7.34

with the value obtained from open loop operation, as shown in Table 7.8. It was also

seen that there was deviation from closed loop operation.

Table 7.8 Comparison of different values for the thermosiphon effective radius

Experimental process Effective radius (mm)

Thermosiphon process established under whole system operation in OPEN LOOP MODE (section 7.6.2.1) 3.0 ± 0.4

Thermosiphon process established under whole system operation in CLOSED LOOP MODE (section 7.6.2.2) 3.75 ± 0.4

Forced water flow under exchanger operation only (this section) 2.9 ± 0.4

The results for closed loop operation were larger than the calculation for independent

testing of the heat exchanger by about 23%. Despite the differences, the results from

the plot of Figure 7.53 were very useful, as they seemed to validate those results

obtained during open and closed loop modes. It is noteworthy that during whole

system operation, a larger pipe section was considered in the calculation of effective

thermosiphon radius and was attached to entry/exit ports of the tank that also posed

hydraulic resistance (not to mention the effects of entrant and exit losses for the fluid

as it cycles in and out the tank). This would have invariably affected the result;

specifically since the water column driving the thermosiphon was deemed constant

throughout operation and equated to the pipe section length. In actual fact, given that

other simplifications and high associated uncertainties would also account for

variations in effective radius calculation, the results obtained and compared in

Table 7.8 were in general good agreement with each other and were consistent with

the experimental work carried out earlier.

Above 12 cc/s the behaviour was clearly non-linear and Equation 7.34 was no longer

applicable. However, the 2nd order polynomial approximation for pressure drops for

this particular system was able to predict results with moderate accuracy. It is

possible it could be used in other circumstances for overall pressure drop calculations

if fluid flow were modified for active operation and water flow rates were known.



209

7.6.5 Exploring exchanger effectiveness variation under system operation

The numerical results and calculations inferred during open and closed loop

operation of the SHWS for many system parameters were obtained from several

assumptions and simplifications of the analytical theory. Of particular importance

was the determination of the following parameters:

• The thermosiphon output water temperature

• The water flow rate

• The power delivered to the hot water tank

• The exchanger output air temperature

• The effective thermosiphon radius

One such assumption was that the exchanger effectiveness remained constant

throughout operation (section 7.3.4). It is well known that exchanger effectiveness is

not constant and will vary with varying input fluid temperatures and flow rates. As a

first approximation, however, it appeared satisfactory and allowed a simple approach

to the numerical prediction of the above parameters. The values obtained were within

expected ranges and correlated reasonably well with experimental measurements. An

additional investigation was done in an attempt to more closely characterise the

exchanger effectiveness.

The experimental setup this time required the operation of the exchanger with known

water and airflow rates and known water and air temperatures. Hot air was blown

into the exchanger at different flow rates from two hair dryers connected to a mixing

box and tap water was delivered to the exchanger at a range of different flow rates.

Water flow rates were determined by measuring volume collected over time. Airflow

rates were determined, not with the use of the air tunnel-bag, but with the

anemometer. For this purpose a better, more comprehensive, calibration was

performed as it was clear from the early stages of development of the project that the

anemometer provided unreliable results in most cases (section 7.5.1). The calibration

procedure is given in Appendix I.



210

It was explained in section 7.3.4 that the water was the fluid undergoing the

maximum temperature change available in the exchanger at all times, allowing a

simpler expression to be used when calculating exchanger effectiveness. However, if

standard operating conditions were to change (eg. low irradiance levels, different

airflow rates), this would no longer be so, in which case the general expression for

effectiveness would need to be used (Equation 4.57) with careful consideration on its

application and with the inconveniences that it presents in the determination of other

parameters of interest (section 4.5).

Since the purpose of the simulation was performance prediction, a different

expression, labelled ‘modified effectiveness’, replaced the standard effectiveness

relationship to unequivocally determine the output water temperature, Tout_water,

which was the key parameter in the determination of power:

( )( )water_inx_inairair

water_inwater_outww

water_inx_in

x_outx_in'

TTCm

TTCmTTTT

−⋅⋅

−⋅⋅=

−−

=&

&ε (4.58)

Experimental determination of flow rates and temperatures for water and air were

carried out in two sets of measurements and for two different airflow rates. The

results showed an exponential variation of ε' with increasing water flow rates

(Figure 7.54).

For very low water flow rates ( 0≈wm& ) heat transfer was negligible so there was

virtually no change in airflow temperature, i.e., Tin_x ≅ Tout_x, therefore ε’ ≅ 0. When

water flow rates were very high ( ∞→wm& ) the water temperature in the exchanger

did not change appreciably and Tout_water ≈ Tin_water. Depending on how good the heat

transfer from the collector fluid was, Tout_x would approach Tin_water but would never

be equal to it. Therefore, ε’ < 1 at all times. The variation of ε’ with wm& was fitted

reasonably well to an exponential expression (Figure7.54).

Different fit expressions were required for different airflow rates. However, the

variation of ε’ with the quotient airairww CmCm && was well approximated by a single

exponential fit for both airflow rates as given by Equation 7.35 (Figure 7.55).



211

Figure 7.54 Experimental measurements for the modified effectiveness vs. water flow rates in the heat exchanger and exponential equation fits to the data

Figure 7.55 Experimental measurements for the modified effectiveness vs. ‘ Cm ⋅& ’ product quotient between water and air. An exponential equation fits the data well.

Modified effectiveness vs. water flow rate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Water flow rate (cc/s)

Mod

ified

effe

ctiv

enes

s ( ε

')

y = 1- e-0.2062x

R = 0.98

p < 0.0001

y = 1- e-0.1158x

R = 0.983

p < 0.001

Tamb = 25 °C

1.0

44 L/s 63 L/s

airm&

Modified effectiveness vs. aaww CmCm ⋅⋅ &&

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

Mod

ified

effe

fctiv

enes

s ( ε

')

Tamb = 25 °C

y = 1-e-0.9089x

R = 0.964

p < 0.0011

44 L/s 63 L/s

airm&

aaww CmCm ⋅⋅ &&



212

From Figure 7.55: aa

ww

CmCm.

' e ⋅⋅

⋅−

−= &

&90890

1ε (7.35)

Figure 7.56 Predicted values for modified effectiveness vs. water flow rate from the

exponential expression of Equation 4.74

The exponential expression for effectiveness was able to reproduce the experimental

results for two different airflow rates up to ±13% accuracy (Figure 7.56).

In the calculation of power delivered to the water (section 7.3.4), the temperature of

the water leaving the exchanger was calculated by assuming a constant effectiveness.

The output temperature of the water was used to determine water flow rate. The

power in the water was then found from its flow rate and temperature rise. The use of

the mathematical fit shown before for the modified effectiveness would have been

better suited for these calculations since it implicitly takes into account the variable

nature of the exchanger effectiveness for varying fluid flow and temperature

conditions. Therefore, the modified effectiveness, ε’, could better characterise the

dynamics of heat transfer in the heat exchanger. From Equations 4.58 and 7.35:

( )( ) ( )water_inwater_out

airair

wwwater_inx_in

water_inx_inCmCm

.

TTCmCm

TT

TTe airair

ww

−⋅⋅⋅

−−

−=⋅

⋅⋅

&

&&

&90890

(7.36)

Prediction of modified effectiveness vs. water flow rate

Water flow rate (cc/s)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Mod

ified

effe

ctiv

enes

s ( ε

')

19.7 W/°C 28.4 W/°C

airair Cm ⋅&

Tamb = 25 °C



213

This equation has two unknowns: wm& and Tout_water, which must be determined in

order to calculate the power delivered to the water, Pin_water. The water flow rate is

also given by Poisseuille’s equation and is dependent on Tout_water:

ηπ

⋅

⋅−⋅⋅⋅≈

8

224 g)TT(Crm water_outwater_in

w& (7.21)

By substituting Equation 7.21 into 7.36, the resultant relationship is a function only

of Tout_water and even though implicit in form, it can be solved by an iteration process,

such as the one applied in the solution of Equation 7.17 for air temperatures in the

pipe. Once the output water temperature is known it can be substituted in Equation

7.21 to find wm& and ultimately the power delivered to the water, Pin_water. Additional

experimental data would be required to verify this expression for low water flow

rates and various airflow rates. This could be a point for further work.

From the modified effectiveness a direct correspondence with actual exchanger

effectiveness was obtained by recalling Equation 4.57 and noticing that:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

=⋅⋅

aa

wwCmCm

','max&

&εεε (7.37)

The effectiveness was then plotted versus water flow rates by using the relationship

for ε’ from Equation 7.35 and Equation 7.37 (Figure 7.57).

It is seen that exchanger effectiveness is certainly variable for different water flow

rates and airflow rates. For comparison, the two different effectiveness values used

for the open and closed loop configurations, and their uncertainties, are shown as a

constant band in Figure 7.57. These results were useful in the assessment of the

assumed validity of these constant effectiveness values. The first assumption made

was that the water was the fluid undergoing the maximum heat transfer at all times,

so only the right hand expression of Equation 4.57 for the effectiveness was used

(which is Equation 7.24). For the conditions of operation where airflow rates were

above 60 L/s and water flow rates below 10 cc/s, the plot shows that this was indeed

the case. Furthermore, for water flow rates between 6 cc/s and 14 cc/s, the



214

effectiveness values were all contained within the experimental band. The

effectiveness was more sensitive to changes in water flow rates and since airflow

rates were quasi-constant with no more than 5% variations, the experimental

uncertainty for effectiveness was attributed only to variations in water flow rate

during operation. Given that the SHWS operated under environmental conditions that

also remained relatively unchanged, no major variations in water flow rates were

expected anyway. This restricted even further the possible excursion of the

effectiveness values to a narrower range. Experimentally, the values determined for

effectiveness in each configuration mode (0.73 and 0.69) carried an uncertainty of

6% and also differed by the same amount.

Figure 7.57 Variation of exchanger efficiency vs. water flow rate obtained from the

experimental fit for modified effectivness

Given the above, the use of a constant effectiveness to calculate power delivered to

the water during operation of the SHWS in this study appeared justifiable.

Heat exchanger effectiveness vs. water flow rate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 Water flow rate (cc/s)

Effe

ctiv

enes

s (ε

)

Experimental ε range

= 63 L/s am& = 44 L/s am&



215

According to the model, from Equations 7.25 and 7.23 it can be seen that if the

effectiveness is higher, the temperature of the water coming out of the exchanger will

be higher and so will the power delivered to the water. A more appropriate heat

exchanger for the system would be one as compact as the unit used, but with a higher

effectiveness. It would then be a matter of selecting such a unit by estimating

effectiveness values from manufacturer technical specifications for input and output

fluid temperatures14F

*. Additionally, the pressure drop introduced in the air circulation

system by the better unit should ideally be less than the existent one, or at least

should not offset the possible extra power gain in the water by demanding an even

higher motor power expenditure. This is also possible to estimate from the

fan-blower motor specifications required and used in conjunction with these compact

exchangers (since they are originally designed for automotive applications).

There appears to be another modelling approach136F

137 for natural convection heat

exchangers that may offer additional simplicity and accuracy compared to the model

presented here. In this other method, compact heat exchangers are characterised by

two relationships:

- The pressure difference (or pressure head) driving the thermosiphon versus the

mass flow rate of the fluid: Δp vs wm&

- The modified effectiveness versus the mass flow rate: ε’ vs wm&

A correspondence can then be made between thermosiphon pressure difference and

the modified effectiveness, which in turn would allow determination of the output

water, Tout_water (from Equation 7.25), and the power delivered to the tank water.

Pressure and heat transfer characteristics are unique for every exchanger so the

pressure difference required for different water flow rates must be determined

experimentally. The pressure head can be inferred from water temperature profiles of

the tank water and natural convection loop by using the relationship between the

temperature and density (Equation G7 – Appendix G). This method therefore

requires knowledge of water temperature profiles of the thermosiphon.

* Developing a custom-tailored solution would not be in line with the objectives of low cost and

readily available materials for system construction.



216

Most of the assumptions and limitations of the model used in the project are due to

the characterisation of the convection loop flow as being laminar, so that the water

flow rate could be determined only from the input water and air temperatures to the

exchanger. For future work this alternate modelling is worth exploring with the

determination of possible relationships between pressure differences in the

thermosiphon loop and the input and output water temperatures. Computational fluid

dynamics can also be employed for a purely numerical simulation from first

principles.

7.7 Discussion

7.7.1 Air heater system elements

Collector panel

The air heating panel was designed for all day collection, as is the case with

conventional flat plate collectors. The panels were aimed at being a very low cost

alternative and did not have the complexities of the previous system (concentrating

devices, metal pipes, etc) having a thin aluminium sheet for absorber a polystyrene

body and polycarbonate cover. Ambient air was the transfer fluid and even small air

leaks would not present a problem during operation of the device137F

138 so the system

did not require leak-proof joints.

Stagnation temperature issues and robustness of collector panel structure.

During operation of open and closed loop modes, airflow rates above 61 L/s were

capable of delivering close to the required power into the water, but were not high

enough to keep collector air temperatures below 80 °C at all times. Under no airflow,

temperatures could easily reach 100 °C and beyond, melting the polystyrene walls,

dividers and air diffusers very quickly (1 min). At higher temperatures (> 120 °C) it

could also damage the polycarbonate cover.



217

Polystyrene is a very easy material to work with due to its manageability and low

weight and depending on its density it can provide excellent structural support as

well as excellent thermal insulation. It is also relatively inexpensive when compared

with other standard building materials (eg., polyurethane, wood). Despite its benefits,

it has two main drawbacks. One is the fact that its softness makes it prone to wear

and tear from exposure to physical impact. Were the material used by itself in an

open external environment such as a rooftop, it could be easily damaged by the local

wildlife (eg. possums, birds) or environmental perturbations (eg, hail storms). The

second and most significant disadvantage is the material’s low operational

temperature range. Above 80°C, the polystyrene cell structure starts to degrade. After

prolonged use at relatively high temperatures it becomes rigid and brittle. It is

affected by UV radiation which makes it turn yellow and fragile in a similar fashion

as with high temperatures, so if it were to be exposed to continuous sunlight it would

require some sort of protection. Protection from the elements and environmental

threats could be provided by using an adequate casing structure (metal sheeting,

plastics or even layering the exterior of the collector with some type of rugged paint).

However, the temperature issue cannot be easily solved.

This presented a very serious limitation to temperature operation of the device.

Temperatures in the vicinity of the polystyrene foam could not be allowed to go

beyond 80 °C for a sustained period or the structure would start to melt. Therefore,

air was not allowed to stagnate to high temperatures inside the collector when in full

sunlight so a reflective aluminium paper cover was used at all times on top of the

panel when the system was not operating.

Besides affecting the collector itself, pipe fittings and pipe sections at the entrance

and exit of the collector, would also suffer since the highest operational temperature

for the plastic piping used is 70°C under no pressure (PVC).

Considerable thought was given to the implementation of a temperature control

mechanism from the very beginning and this is why the collector was built with a

large 20 cm buffer zone as described earlier. Initially, a passive control mechanism

was considered whereby two hatches would open (via a bimetallic strip) when the

temperatures reached the undesired value. This would allow ambient air to flow in



218

the collector reducing the temperature. To assess whether natural convection

established in this manner would be sufficient, the buffer zone included two openings

on each side of the collector that could be left open or closed at will. It was soon

realised that natural convection via these hatches would not be enough to lower the

temperature of the air inside the panel to safe levels.

A second, active, control mechanism was considered using one or more axial fans to

produce the current flow required. In this case, a thermostat and associated electronic

and electromechanical devices would be required to carry on the opening and closing

of the hatches. Power would have to be available for this system to work, so the idea

of using a stand-alone low-powered solar panel was considered. Even though high

flow rates would be needed, the mechanism would only act against the internal

pressure offered by the collector and not the rest of the system. It was believed that

small fans would be able to deliver the necessary flow rate. This idea was also

discarded after a few tests since it became obvious that the added complexity of such

mechanism would not only be a disadvantage in terms of the added amount of

potential failing elements but also would increase the cost of production excessively.

A satisfactory solution to the high temperature hindrance of the system remains open.

The situation is similar with the use of PVC stormwater pipe as the air transfer

medium. A few ideas on how to tackle these problems have been suggested in

chapter 9. In any case, it is concluded that polystyrene is not suitable as a

body/insulation material per se, so if this were to be the intention, then it is

mandatory to consider a temperature control mechanism as well.

Conveyance system, heat exchanger and fan/blower motor

The stormwater PVC piping used was inexpensive, accessible and weather resistant

although a high-temperature material offering the same advantages should be used

for commercial deployment. It was a useful exercise to explore the hydraulic

resistance posed by the system allowing proper determination of motor power

requirements and overall efficiency, providing a simple method for obtaining these.

The maximum temperature drops observed for the air in the pipe was between 5-6°C.



219

The compact heat exchanger and blower motor used not only proved adequate for the

tasks at hand but being readily available and mass produced items further improved

the cost-effective quality of this system.

Water tank

The water temperature depth profiles measured inside the tank provided a more

direct way for comparison and assessment of temperatures and power delivered to

the water with numerical predictions. It was convenient to modify the same tank used

in the vapour transport system for use with the heat exchanger of this system.

Uncertainties and Inaccuracies:

All temperature measurements had large associated errors and the actual accuracy of

the digital thermometer used was no better than ±0.7°C. Therefore, the results for

power into the water carried a large associated error as well.

The temperature measurements for air exiting the collector were the most difficult to

obtain due to the variability of the temperature measured across the transverse

section of the pipe. Air temperatures at the output of the collector had variations from

65 °C up to 85 °C when the collector was receiving maximum power input.

It is thought that there were three main reasons behind this:

- The air temperature in the collector is higher under the absorber and higher than

model predictions

- Despite having the diffuser, air mixing at the end of the collector did not happen,

allowing a very distinct temperature gradient to exist at the point of exit.

- The abrupt and non-symmetrical expansion of the air at the exit point leaved an

upper, “cold “, section of the transfer pipe with much lower temperatures than the

bottom, extending and maintaining the temperature gradient. However, uniform

mixing occurred farther down the pipe.



220

Temperatures taken along the pipe were used to determine the average collector

output temperature that would result from uniform air mixing. Still, variations

recorded were between 1°-3° depending on the points of measurement. Turbulence

and the length of the pipe might not allow for these variations to be lower, meaning

that these uncertainties might be unavoidable.

Hot and cold water temperature measurements where taken by placing the

thermocouple on the surface of the uninsulated thermosiphon copper pipes. These

pipes represented a very small surface area and since power losses would be very

small it saved the inconvenience of using insulation on them.

Airflow measurements

For the closed-loop mode, once the system was “opened”, the effect of minor losses

due to the sudden presence of an entrance and exit increased the overall pressure

resistance of the piping and reduced the flow rate. An indirect approach to quantify

this effect was devised with a one-off correlation between anemometer and air bag.

The anemometer was left in a fixed position in the middle of the outer flow pipe and

velocity readings correlated for open and closed loop modes with and without the use

of the air bag. The problem with off-scale readings of the anemometer for the closed

loop mode was solved by positioning the probe against the airflow in a way that

reduced its sensitivity. By knowing the correspondence between air-bag volume flow

measurements and anemometer readings for the open loop, figures for closed loop

were inferred when the piping was opened later on. The higher pressure drop (lower

airflow) for the open loop configuration was evident.

The more accurate calibration done during the second characterisation of the heat

exchanger determined that two calibration factors had to be applied to the raw

anemometer readings in order to obtain a more realistic value of the airflow in the

pipes (Appendix I). However, the fact that its operation is limited to low

temperatures and that it cannot resolve air velocities higher than 10 m/s makes it

unsuitable in the study of these SHWS.



221

7.7.2 Economics

The system incorporating the air heater panel, even though not passive and requiring

the use of an electric fan/blower motor, was inexpensive compared to the previous

passive system. The reason lay in the materials used. This system had an inexpensive

body/insulation structure, very light and easy to work with. It also had very little

metal, since the heat absorber element was a very thin sheet of aluminium. The

conveyance system was made of plastic stormwater pipes in contrast with more

expensive copper pipes. This not only reduced material costs, but also eased

fabrication costs. By design, it was a system that could be “pieced together” from

readily available parts.

The trade-off, of course, was its active nature and a projected increase in

maintenance, particularly for the motor, and the need of an ‘on/off’ control

mechanism operating the system during useful hours of the day. The stagnation

temperature problem also remains a hurdle to overcome, while the passive system

has no problems in this regard (as long as the self-pumped mechanism works

appropriately). More on the economics of this system is given in chapter 8

7.7.3 Model prediction results

Collector panel

Results for the collector panel revealed that the model underpredicted the output air

temperature, typically by 2°C - 3°C. The obvious suggestion for this would be

inaccuracies of the model, which approximated the absorber profile as if it were a flat

absorber in the middle of the collector chamber with air flowing over and under it

(Figure 7.2c) instead of a series of absorber channels where the air went through and

over them (Figure 7.3a). At the time of construction it was not believed that the

differences between the model and actual absorber profile would result in

temperature differences as high as those observed. On closer look, it could be a

significant factor. However, at this point in time there is no assurance that a more

accurate profile model would explain the differences.



222

The results of collector output air temperatures indicated that there was a vertical

temperature gradient in the outcoming air and that the temperature was much higher

for the air flowing through the channels than above the absorber. The model used did

not explain this, with temperature predictions for the air under the absorber being

only slightly higher. This indicated that mixing by means of the diffuser and buffer

zone at the end of the collector was not occurring. It also seemed intuitively correct

since the air flowing closer to the bottom of the collector was in contact with a larger

surface from which it could extract heat. It is also true that radiation losses from the

upper side of the absorber were higher than from the inside of the channels, where

the heat was “trapped” and air flowing through them could extract more heat. The

approximate model used could not account for these facts.

Heat exchanger

A similar situation occurred in the modelling of the heat exchanger and

thermosiphon process where assumptions and simplifications such as laminar flow,

an unchanging cold water thermosiphon column and constant exchanger

effectiveness limited the accuracy of calculations. However, as an initial

approximation to the actual thermodynamic behaviour, the modelling for the heat

exchanger was satisfactory.

The use of a ‘modified’ effectiveness as a way to better characterise the exchanger

and provide more accurate modelling showed how output water temperature and

power delivered to the water could be calculated without the need to assume a

constant effectiveness or to use two different effectiveness expressions. Assessment

for more widely variable operating conditions, including low and high irradiance

values, would require the use of a ‘modified’ effectiveness.



223

7.8 Conclusions

The air heater panel SHWS that was designed and constructed proved to be a

cost-effective system capable of delivering the power needed to satisfy hot water

demands for a 4-person household (30 MJ/day) if properly sized. Based on

experimental and theoretical modelling, the large scale flat-plate absorber-in-the-

middle profile (Figure 7.2c) was the best alternative for this purpose.

With air recycling (closed loop mode), an absorber area of 3.7 m2 was able to deliver

over 1100 W into the water for an average irradiance of 900 W/m2. For 6 hours of

daily operation (9:00 am – 3:00 pm), this meant no less than 23.7 MJ gained by the

water. Higher energies would be obtained by upscaling the area of the absorber. It is

estimated that for an area of 4.8 m2 or greater, the daily average requirement of

30 MJ would be comfortably met.

Results also showed that the average efficiency of the SAHS in closed loop mode

was 33%, although the large associated uncertainties put it between 27%-40%.

Chapter 8 - Economic analysis The purpose of this chapter is to provide a general idea of the costing incurred in the

fabrication of the hot water systems developed and their feasibility as potential

commercial products. It is not intended as a comprehensive techno-economic

analysis, requiring additional knowledge of engineering and manufacturing

processes, marketing strategies, current market energy consumption trends and other

commercial and social related issues. Such an analysis is beyond the scope of this

study.

The systems proposed and costed as more realistic commercial options include

modifications, additions and improvements to the systems developed in this study.

Further explanation and details of proposed changes and improvements for future

work are given in chapter 9.

The elements for each system are outlined in Tables 8.1 and 8.2 in the next pages.

Costing is intended for the materials only, however, as most of it is retail pricing,

some labour costs and profit margins are embedded in them. This also means that the

costs are upper bound figures and it is expected that the total system manufacturing

prices would be less if mass-produced (probably by 15-20% and maybe more).

Detailed added labour costs and profit gains are not particularly discussed here since

it would be all too speculative, but as a general indication they can be classed in the

following way:

⎩⎨⎧ Assembly

- Labour costs Transportation

Installation ⎩⎨⎧ Factory

- Profit gains Distributor

Reseller


Chapter 8 - Economic analysis

225

8.1 SWHS with passive downward vapour phase heat transport

This is the most labour intensive system of the two developed. The reason being that

the absorber heater element of the panels, being made entirely of copper, required

extensive work and attention to detail, particularly with the application of the solar

selective surface.

The 3rd prototype panel constructed for the system was the most efficient and is the

one referred to here. The panel itself cost about AUD$1400 in materials, for a 2.9 m2

panel aperture and absorber collection area of 2.5 m2. The entire system cost about

AUD$2300, including the vapour transfer line, the insulation and a 200 L water tank

with an internal heat exchanger coil. Costs for a two-panel system would be around

AUD$3700. However, to satisfy the nominal requirement of 30 MJ/day of power

delivered to the water, a 16% increase in absorber area for each panel is required.

With this in mind the total costing is expected to rise beyond $4100 and considering

it is basically for the materials the system must be better costed to become a

competitive option.

The elements and pricing for a proposed, high-efficiency, commercially orientated

unit is given in Table 8.1. The pricing is substantially lower than the previous figures

and the overall cost is comparable to high-end domestic SHWS that retail around

$4500.



226

Table 8.1 Projected costing for the first system developed15F

*

Elements/Materials Cost (AUD$) Quantities Total

(AUD$)

ZincAlume® casing $16/m2 6 m2 $96 Aluminium reflectors (anodised, 0.3 mm thick) $16/m2 5.5 m2 $88

Cellulose fibre insulation $200/m3 < 0.18 m3 $36 Polycarbonate cover (6 mm thick, Twinwall)

$38/m2 3.6 m2 $137

Boiler tubules (6.4 mm OD) $5.6/m 16.1 m $90

Boiler fins (0.55 mm thick) $5.9/m 15.8 m $93

Header pipes (44.5 mm OD) $41/m 2.4 m $99

Joiners/tubes - Various $20

Abs

orbe

r-bo

iler

mat

rix

Rubber hose $10/m 4 m $40 Maxorb™ selective surface adhesive film $60/m2 2 m2 $120

CO

NC

EN

TR

AT

ING

PA

NE

L

Accessories $120 Assortment $120

TOTAL for 1 panel - 3.6 m2

$939

Copper coil pipe (12.7 mm OD) $6/m 8 m $48

Pipe fittings and joints $5 4 $20

Insulation $7/m 8 m $56

TR

AN

SFE

R

LIN

E

Aluminium tape (roll) $20 3 $60

TOTAL for transfer line $184

Plastic reservoir tank (high temperature)

(refer to text) 20 L $155

Water tank w/electrical booster and heat exchange coil (240 L) $565 1 $565

Condensate collection tank and related accessories (20 L) $40 1 $40

Other accessories $80 Assortment $80

Grand TOTAL for a 2-panel system $2902

* High-efficiency system based on the 3rd prototype panel

Wholesale/trade pricing, including tax



227

A cost of about $2900 is obtained for the two-panel system and for materials only.

Since this is a very labour intensive system, automation in its fabrication is crucial to

reduce costs. A more detailed look with suggestions for future work improvements is

given in chapter 9, but a brief look into the reason for the elements chosen will allow

for better understanding of the costing done.

The anodised aluminium reflector concentrators are to be produced as a single metal

element formed out from an industrial rolling process with the profile shape desired.

The reflector then goes into the case made out from the zincalume sheet. This leaves

empty space between them, which is filled up with cellulose fibre insulation. On top

goes the absorber-boiler matrix and the system is covered with polycarbonate

double-sheet. The insulation proposed is blown into the empty cavities and is very

economical compared with other expensive and/or labour intensive options (eg.

injected polyurethane). The water reservoir tank is ideally a high-temperature

resistant plastic tank that will not have the problem of rusting and corroding as the

zincalume™ tank had. The price has been inferred from the cost of lower

temperature-graded plastic tanks, assuming the cost for the one desired would be four

times higher.



228

8.2 SHWS incorporating an air heater collector panel and heat

exchanger-water tank coupling

The air heater collector panel system cost about AUD$1500 to put together from the

building materials and for a 4.3 m2 panel, an absorber collection area of 3.7 m2 and a

200 L water tank. The cost was much less than for the previous system, however, it

did not consider a stagnation temperature control mechanism, or the robustness

required for outdoor exposure, which is necessary for unattended operation in a

domestic environment. Additionally, for 30 MJ/day of power delivered to the water,

a minimum absorber collection area of 4.8 m2 is needed. Automatic operation of the

system was not considered either and would most probably require electronic control

circuitry.

With this in consideration, the costing for a proposed system of this type is given in

the following table where it is seen that total costs for the elements and materials is

still within a reasonable, competitive, range. A tentative solution to the temperature

limitation problem is included by considering a collector structure moulded from

fibreglass reinforced plastic and insulated with cellulose fibre. High density

polyethylene (HDPE) pipes and joints are considered instead of PVC.

This system may offer the possibility of retrofitting to existing conventional domestic

tank units. It would basically depend on the water tank providing extra ports where a

thermosiphon circuit can be attached (some tanks include draining/purging outlets

and other suitable ports)

In this case, installation costs might be higher, especially if modifications to the tank

are required, but the extra expense for a new tank is spared.



229

Table 8.2 Projected costing for the second system developed

Elements/Materials Cost (AUD$) Quantities Total

(AUD$)

Fibreglass reinforced plastic hollow body

(refer to text) 1 $245

Cellulose fibre insulation $200/m3 < 0.19 m3 $37 Polycarbonate cover (6 mm thick, Twinwall)

$38/m2 5.5 m2 $210

Aluminium absorber (0.1 mm thick)

$2/m2 8 m2 $16

Black paint spray (can) $7 10 $70

AIR

HE

AT

ER

PA

NE

L

Fasteners and washers $0.4 40 pairs $16

TOTAL for 1 panel - 5.5 m2

$594

HDPE pipes (90 mm OD)

$7/m 15 m $105

Pipe fittings and joints $10 8 $80 Insulation $11/m2 4.2 m2 $47

TR

AN

SFE

R

LIN

E

Aluminium tape (roll) $20 2 $40

TOTAL for pipes $272

Air-to-water heat exchanger $135 1 $135 Fan/blower motor (13.5 VDC, 9 A)

$230 1 $230

Power supply (12 VDC, 150 W)

$80 $80

Electronic control mechanism $50 Various $50 Other accessories $50 Assortment $50 Water tank w/electrical booster (240 L) $550 1 $550

Grand TOTAL for a 1-panel system $1961

This proposed commercial option is under $2000 and could come down by $300, or

more when mass-produced. The fibreglass body structure for the panel would

eliminate the high temperature and fragility problems of polystyrene. The figure

quoted in the table has been inferred from the costs of fibreglass reinforced plastic

Wholesale/trade pricing, including tax



230

panels used for glazing and roofing applications. The electronics include the on/off

control mechanism and associated wiring. The ‘other accessories’ include the

insulation of the thermosiphon loop, the wooden case for the heat exchanger and

miscellaneous bits and pieces.

Another possible change is the use of an AC blower motor that would eliminate the

need for a DC power supply, reducing capital costs and running/maintenance costs.

Overall economic appraisal for both systems

Assessment of an accurate final market price for these SHWS is not possible at this

stage, but an approximate indication based on the previous discussion can be given.

For some SHWS the compounded labour and profit price increase (excluding

installation) can reasonably be up to 60%16F

* the manufacturing prices (and probably

not much higher). The current rebate and renewable energy certificate schemes

offered by the state and federal governments, respectively, encourage the adoption of

this technology and these systems would certainly benefit from it, where savings of

up to $1500 on the purchase price are possible (refer to chapter 1).

The following table shows tentative “ballpark” sale prices for the systems assuming a

15% decrease in the costing prices and then a 60% increase from labour and profits:

Table 8.3 Tentative sale prices for commercial versions of the SHWS

SHWS Sale price(AUD$)

After government discount schemes17F

# 1st: Vapour transport $3950 $2450 - $3200 2nd: Hot air transport $2670 $1170 - $1920

* Information obtained from relevant sources in the industry. # $750 from state rebate scheme and up to $750 from energy certificates, depending on location



231

Installation costs can range between $250-$500. They would be less compared to

installation of conventional units, since there is no need to hoist the tank up on the

roof and reinforce the roof.

The second system is clearly more economical and for that reason probably better

suited for near-future commercial deployment. It has clear advantages over the first

one, such as making use of more readily available materials, not being affected by air

leaks, easier to handle and install. The first system, although more detailed and

expensive, is comparable in cost to high-end units on the market and with additional

improvements could become a viable alternative by offering something that no other

system can offer: a remotely coupled, and passive, domestic SHWS of minimal

maintenance.

These prices, however, might still be high and not competitive enough for market

penetration amongst current solar units. Only additional research and in-depth

costing will clarify this. Nevertheless, the general conclusions obtained from this

study and the figures shown here are encouraging. It is believed that additional work

on these systems, each for different reasons, holds potential for a domestic solar hot

water option that will increase adoption of the technology.

Chapter 9 - General discussion, conclusions and avenues

for future work The main objective of this research project was the development of alternate

solutions for domestic solar hot water systems in subtropical latitudes that would

deliver comparable performance to mainstream units and have a few advantages over

them, the major one being a reduced cost. Inexpensive domestic SHWS would

encourage and increase their market penetration and as a consequence it would have

other positive benefits (e.g., reduction in greenhouse gas emissions). The main thrust

of this study has been the production and demonstration of a complete solar hot

water system that can be manufactured inexpensively by combining readily available

materials in a smart and innovative way. To this end two different systems were

designed, built and tested.

The first system concentrated solar energy on a copper absorber-boiler array of fins

and tubes to produce steam from water supplied from a small water reservoir tank.

This steam was the heat transfer fluid that moved downward into a heat exchange

pipe within a ground level water tank, heating the water, condensing and falling into

a containment unit. The operation was entirely passive, since the condensate was

pulled up due to the partial vacuum that occurred after system cooling. Three

collector panel prototypes were built.

The second system used an air heater panel. Air was circulated in open and closed

loop configuration circuits by means of a fan/blower motor, and forced across a

compact heat exchanger coupled to the water tank. This produced a natural

thermosiphon flow heating the water. Two collector panel prototypes were built.

In order to predict performance and characterise the systems, an analytical modelling

approach was followed by simulating heat transfer modes for all the elements of the

systems (using MATLAB™). Heat gains and losses for all elements of the systems

were calculated under normal environmental conditions and system setup, such as,

geographical location, dates and times of the year, collector panel layouts and

orientation.


Chapter 9 - General discussion, conclusions and avenues for future work

233

The systems developed show potential in satisfying the objective of alternate, low

cost domestic solar hot water systems. Although additional study and research is

required in order to bring these systems to a point of commercial maturity, the

research has shown it is possible to produce SHWS with cost effective and efficient

materials, where not all of them require exclusive manufacturing processes, but can

be “off-the-shelf” type of devices in many cases. This was more so for the second

system developed. In the case of the first system, a viable economic option is

proposed for some of the elements, basically the concentrator reflector and

structure/body of the panels.

Experimental results from the operation of the systems were compared with the

simulation predictions and found to be in reasonable agreement. The analytical

approach used for characterisation of the elements of the system is useful for both

design and system prediction under varied environmental conditions, geometrical

construction and physical properties of the materials involved.

A brief discussion and concluding remarks for each system, with references to

hypothetical future work, is given next.



234

9.1 SHWS with passive downward vapour phase heat transport The design of a solar hot water system incorporating downward vapour phase heat

transport was successful, operating in self-pumped mode where water was converted

to steam and delivered down a transfer line providing over 12 MJ/day of effective

energy for domestic hot water, during the winter season. The system used a single

panel configuration (2.5 m2). During early afternoon hours, the collected condensate

was returned back into the panel assembly and reservoir tank, recharging the system,

leaving it ready for operation for the following day.

Three prototype panels were constructed, with the last panel having efficiencies

between 30% and 53% for an irradiance range of about 500-930 W/m2 and providing

the best performance in the SHWS. Radiant energy to hot water energy conversion

efficiencies over 40% were obtained above 700 W/m2.

The system is able to supply the recommended daily energy target of 30 MJ for

domestic hot water by increasing total panel area to about 5.8 m2.

System performance was predicted by the development of an analytical simulation

program that took into account solar energy collection and calculated effective

energy gained by the water based on date, time, geographical position, orientation of

the panels and heat transfer modes between elements. Numerical and experimental

results were in close agreement, and it is concluded that the model was (and is)

useful for investigation and design purposes of systems of this kind. Optical and

geometrical parameters (e.g., absorber emittance, reflectance of CPC walls,

concentration ratios) can be varied and optimised for different geographical and

layout conditions for maximum energy collection.

Compared with other collector panels, having a symmetrical and truncated CPC

profile is an advantage over more complex geometries and the use of evacuated tubes

from a fabrication point of view and is viable for building integration in a similar

way to flat plates. This self-pumped system can cope with steam production and the

reclaiming of the condensate so there is no need for consideration of non-renewable

fluids and/or fluids with hazardous properties that would require system sealing



235

(such as ethanol). Since the system operates at atmospheric pressure and is open to

the atmosphere at the condensate receptacle tank, there is no need for high-pressure

relief valves that would be necessary otherwise.

The efficiency gains relative to systems with conventional selective surface flat plate

collectors are not very significant. Therefore the advantages lie in the economic

benefits obtainable by exchanging absorber area with reflector area (increased

concentration) and by placing the water store on the ground rather than on the roof

while retaining a passive nature.

Avenues for improvement include modifications and/or use of different materials for:

Structure

- CPC Insulation

Reflectors

- Numerical simulation model

- Absorber-boiler array

- Water reservoir tank

- Hot water tank insulation and heat exchange coil

- Condensate receptacle

- Panel adjustments in situ

Numerical simulation model

The program can be enhanced to include a way of determining the optimum

orientation for year-round energy collection of a CPC, based on geographical and

placement constraints. The analytical approach can also be improved by including

more realistic simulations like multiple ray reflections, better account of truncation

effects and more accurate heat transfer modes between elements. Also, atmospheric

modelling of attenuation can be revised and updated with more accurate

relationships, and even account for regional conditions, if available.

⎩⎨⎧



236

CPC structure, insulation and reflectors

The polyurethane material used in the second and third prototype panels was very

convenient since it had a three-fold purpose: structural support, insulation and CPC

profile shaping. It was also capable of resisting temperatures up to 140°C. The

problem was its fragility and elevated cost in terms of the material itself and the

processes involved in its creation and use for prototyping. If stagnation temperatures

in the panels over 140°C are allowed, the material would not be able to endure it. It

is also not biodegradable.

The reflector material used in the third prototype was Silverlux™; expensive and

difficult to integrate in the CPC profile. It offered the highest reflectance, though.

Other materials could be used with the possibility of reducing manufacturing costs.

The structural support and shape may be given by a metal sheet rolling process,

where thin polished aluminium sheets are fed into a machine that gives them the

CPC profile required in an automated fashion. This option could also serve as the

reflecting media.

Mould-formed hollow fibreglass CPC panel structures would also be another

alternative that could then be injection-filled with expanding polyurethane, making it

also an automated process and subject to mass production. The reflector material

would then have to be added on to the fibreglass. High reflectance aluminium tape

and metalised plastics (as with the Silverlux™ used) are two options. A metal box,

similar to the one used (also from zincalume™ sheets) to house the entire panel

elements would be satisfactory.

For insulation, other materials could be used, such as glasswool. Polyester batts are

another option, although it is flammable and non-biodegradable. Cellulose fibre

thermal insulation, made out of pulverised recycled news print and used for roof

insulation, is an inexpensive option that can be applied as an amalgamated powder,

filling up completely the space where it is put. It has excellent insulation and

fire-resistant properties as well as being biodegradable.



237

There is also evidence that insulation of CPC collector panels in a plywood box has a

small effect (10% improvement) in the reduction of back heat losses compared to

dead air space behind the reflectors138F

139. As long as the reflectors are properly isolated

(physically) from the rest of the structure, it is possible that actual insulation is only

required for the header and return pipes of the panel.

Absorber-boiler array

The heat collection array for every panel was made entirely of copper tubes, pipes

and fins. The actual absorber-boiler represented a very small section of all the copper

mass used. One area of improvement in this regard would be to retain the copper fin

and tubes for heat collection and substitute header and footer pipes, return pipes and

joints by less expensive materials, such as galvanised steel pipes. High temperature

plastic header and footer pipes in a hybrid plastic-metal boiler array could be a

possibility as long as leak-proof joints are feasible. On the other hand, the advantage

of having the entire array made of copper is two-fold:

- it is a very ductile material, easy to work with

- it does not rust (although it will corrode, given the “right” conditions)

The array elements should all be brazed together, forming a much stronger bond than

soft solder can provide. This will certainly minimise vacuum leaks caused by weak

joints. It is noted that for the last prototype, the return pipes were substituted by

high-temperature rubber hosing (section 6.5.4). This should be a standard feature of

construction for any future developments.

It is desirable to have fins with indentations in the middle, as a mild centreline

depression over the entire length, so that the boiler tubes can be easily located and

soldered/brazed onto the fins. This is possible to achieve by a press mould

specifically designed for this purpose at the point of fabrication of the fins. Such

pressing could create a small circular indentation (or even a V-shaped groove)

enough to serve as a rest-point for the tubes and facilitate soldering.



238

Water reservoir tank

There was rusting of the interior and input/output junction points of the reservoir

tanks. The reasons for this were the materials chosen for the tank (zincalume™). The

use of a high-temperature plastic tank (e.g. glass reinforced polyester) would

eliminate rusting and corroding. For a SHWS of this kind operating continuously in a

domestic environment, it is necessary to use demineralised water and replenish it as

it evaporates from the condensate collection tank. This would also protect eventual

scaling of the copper absorber-boiler arrays.

Hot water tank, insulation and heat exchange coil

The first area of improvement with the tank is the insulation, since there was little on

the bottom. Ideally, the tank should be located in an easily accessible place.

The heat exchange coil used was a single copper pipe loop located at the bottom of

the tank (Figures 6.14 and 9.1a). It was short since very efficient steam heat transfer

to the water was expected for low water temperatures and it was nearly horizontal in

order to capture most of the sensible heat from the condensate before it was collected

in the receptacle. In the end, however, it appeared that even though heat transfer was

high, it was not as efficient as initially thought. Also, since the condensate was to be

pulled back into the panel assembly and reservoir tank, it was not desirable to have

this cold condensate in contact with the hot water on its way back so that there would

be minimal heat loss from the reclaim action.

However, this arrangement does not provide as efficient hot water volume per

draw-off as that of a stratified tank. The reason is that under stratification more

energy (more hot water) is available at the point of collection. In the current

situation, mixing of the water disperses the energy and lowers the temperature. A

vertical heat exchanger (Figure 9.1b) will produce this stratification with a steep

temperature gradient and is a worthwhile pursuit, especially if the system is not

relying on the self-pumped mechanism for recharge, but includes a return pipe to the

panels, where condensate is delivered with the use of a small pump.



239

Figure 9.1 Original near-horizontal heat exchanger and proposed vertical arrangement

for hot water stratification

A decision to make is whether the tank will be of the storage/displacement type, able

to withstand mains pressure, or of the heat exchange type where water is drawn via a

copper coil connected to the mains water supply and immersed in an all-copper hot

water tank. The first type is what is commonly used in commercial solar hot water

systems. One of the main reasons for this is that the heat exchange tank requires a

higher temperature in the water (about 10°C higher) to be able to provide the same

energy/day at draw-off point. For every litre of hot water in contact with the coil, an

additional 0.0413 MJ are required. For a 200 L system this equates to about 8.3 MJ

extra and this would necessitate an increase in collector panel absorber area with the

consequent increase in cost. However, a mains pressure tank is a more expensive

option, so a closer look into this issue is warranted.

Condensate receptacle

The condensate receptacle tank should not be insulated as it serves as a heat dump. It

is closed, but not airtight since it should always be at atmospheric pressure. Ideally it

would be transparent so that the level of water remaining after continued evaporation

is easily determined. It could also include a simple electronic monitoring mechanism

to detect low-levels of water and alert the user accordingly. If a condensate return

TAVG

Downcoming steam


Cold

Hot

Exchange coil

a) Horizontal exchange coil

Downcoming steam


Thot

Tcold

Condensate

return pipe

Cold

Hot

Pump

Exchange coil

b) Vertical exchange coil



240

pipe is used with a pump (Figure 9.1b), the pump can be connected to a simple mains

timer switch and operated for a few minutes everyday, long enough to recharge the

system. A self-priming diaphragm pump (as the one used) is recommended. The

return pipe would not require any insulation.

Panel adjustments

Maximising energy collection during seasonal changes will improve performance.

Once the panel is given the desired azimuth, tilt and twist angles and the orientation

is fixed, the use of the additional ρ-rotation, which is a rotation of the panel structure

about its normal (in that final position), could improve performance (section 6.3). It

is probably useful to explore incorporating into the panel base a mechanism to allow

movement of the panel in this way. Together with the adequate simulation/modelling

study, a series of predetermined ρ angles applied seasonally could optimise year

round collection. On the other hand, the financial and added complexity implications

(eg. maintenance) of this idea might prove too costly to justify it.

Economics

The last prototype, which was the most efficient, resulted in relatively high

production costs, comparable to high-end conventional SHWS. The main reasons for

this were the amount of metal (copper) and the high quality reflector and selective

surface used. Automating the production of metallic concentrators/reflectors could be

the answer to reduced costs.

There are established techniques in the fabrication of high performance CPC

collectors, with companies around the world providing products of good repute. The

merit of this study in proposing an alternate method to those already available lies

precisely in the search of a cost-effective solution that produces reasonable results by

integrating existing technologies without the need to create specialised processes.

The one issue that remains as the most contentious in this goal of integration and low

cost production is the use and type of a selective surface material.



241

9.2 SHWS with an air heater collector panel and heat exchanger-

water tank coupling

The design and operation of the air heater panel solar hot water system demonstrated

that a low cost solution for domestic SHWS can be made from readily available

materials. The system operating with air recycling under a reduced solar window of

2.5 hours over summer and spring delivered, on average, over 1100 W into the water.

Over a 6-hour period this would represent an energy gain in excess of 23 MJ (for a

3.7 m2 absorber panel).

Two air panel prototypes were built, the second one being a full-scale unit, for which

efficiencies of up to 33% for the entire system where obtained under air recycling

operation (closed loop configuration) and average irradiance values of 900 W/m2.

By adequately increasing the area of the panel (about 30%) this system can deliver

the minimum daily recommended domestic hot water power of 30 MJ.

System performance was also predicted by analytical modelling translated into a

series of computer programs developed in MATLAB™. The basic code was the

same between the two systems, although the air panel heater system had a more

comprehensive development in the consideration of the different heat transfer modes,

owing also to the fact that more elements were involved. Part of this included a first

approximation in the characterisation of the heat exchanger coupled to the water tank

and responsible for the thermosiphon process. Experimental results and model

predictions were close enough to declare the analytical model useful in system

design and performance prediction. As with the vapour transport system, virtually all

relevant environmental and system parameters were user adjustable.

The system was clearly much more cost effective that its predecessor, however, it did

remain with several unresolved issues specifically, the integrity of the panel under air

stagnation situations. The main aspects to be explored and improved if the system

were to be developed further require a re-evaluation of the material used and/or the

addition of a temperature control system.



242

Air heater panel

The high stagnation temperature of the system was the most compelling reason to

discard the use of polystyrene as the main material in a hypothetical future

construction of air heater panels of this kind. The (unsuccessful) testing of a couple

of temperature control mechanisms showed that the risks and added complexities

involved in implementing and operating such mechanisms might defeat the purpose

of the project: the cost effectiveness and simpleness intended in the original design.

If a single cover polycarbonate sheet is used, the losses due to top convection will be

higher forcing a lower air temperature inside the collector. It might be possible this

way to achieve the necessary gain-loss balance ratio by which temperatures inside

the collector will never reach 80 °C (provided the motor is in operation). On the

other hand, increased heat losses will result in a reduced efficiency for the collector,

which may be too low for the unit to deliver the necessary power into the water.

Controlling the losses might also be a matter of redesigning the thickness of the walls

of the collector. Since structural stability and robustness depend in great measure on

the amount of polystyrene used, this is not an attractive option. In any case, this is

only a palliative solution since it does not take care of the stagnation problem.

The idea of using a different material as the body/structure of the panel seems like

the most viable option to solve this problem. Additionally, the higher the

temperatures allowed, the higher the power the air can carry away and this might

allow designs of large panels or multipanel systems in series with each other.

In the following page is a comparative chart (Table 9.1) showing the properties of

several materials, their advantages and disadvantages for insulation and/or structural

support. It is not intended as a comprehensive collation of all qualifying physical and

chemical properties and commercial indicators of performance. Rather, its purpose is

to provide a glimpse of a few common building materials available “off-the-shelf”

that could be used for the construction of a solar air heater collector panel.



243

able 9.1Proposed materials for construction of the solar air hinsulation, body

Tem

pera

ture

L

imit

(°C

)

80

130

80

140

350

200

50

? 350

120 - - - - 70

90

Wea

ther

re

sist

ance

Fair

Fair

Fair

Poor

Hig

h

Poor

Poor

Fair

Hig

h

Hig

h

Fair

Fair

Hig

h

Hig

h

Hig

h

Hig

h

Fire

to

xici

ty

Fair

Fair

Fair

Fair

Nil

Nil

Fair

Low

Low

Hig

h

Nil

Nil

Nil

Nil

Fair

Fair

Fire

ha

zard

Hig

h

Low

Hig

h

Low

Nil

Nil

Hig

h

Low

Nil

Hig

h

Nil

Nil

Nil

Nil

Low

Low

Ade

quat

e fo

r st

ruct

ural

su

ppor

t Po

or

No

Yes

Poor

No

No

Yes

No

Yes

Yes

Yes

Yes

Yes

Yes

- -

Ade

quat

e fo

r in

sula

tion

Yes

Yes

Yes

Yes

Yes

Yes

Poor

Yes

Poor

No

No

No

No

No

No

No

Den

sity

(k

g/m

3 )

15

32

32

36

10

30

> 40

0

100 - - - - - - - -

Rel

ativ

e co

st

Low

Low

Fair

Hig

h

Low

Low

Hig

h

Hig

h

Fair

Hig

h

Low

Fair

Hig

h

Hig

h

Low

Low

MA

TE

RIA

L

Poly

styr

ene

foam

Poly

prop

ylen

e fo

am

Poly

styr

ene

foam

– X

Plyu

reth

ane

foam

Gla

ss w

ool

Cel

lulo

se fi

bre

(CFI

)

Woo

d

Cor

k

Fibr

egla

ss

Hig

h te

mp.

pla

stic

s

Zinc

allo

y st

eel

Gal

vani

sed

stee

l

Stai

nles

s ste

el

Alu

min

ium

PVC

Poly

ehty

lene

(HD

PE)

Tab

le 9

.1

Prop

osed

mat

eria

ls fo

r co

nstr

uctio

n of

the

sola

r ai

r he

ater

pan

el: i

nsul

atio

n, b

ody

stru

ctur

e an

d ou

ter

casi

ng



244

With the (functionally limited) exception of polystyrene, none of these materials are

capable of providing good insulation and structural stability simultaneously.

Possibly the best way to obtain the desired collector panel would be to combine the

rigidity of materials such as fibreglass composites or zinc alloy steel (Zincalume™)

with Glasswool sheets, polypropylene foam or cellulose fibre insulation. This would

eliminate the high temperature vulnerability problem that polystyrene faces with a

lightweight, easy to use, relatively inexpensive, safe, weather resistant, robust

combination of materials. Production would be a two step process since the casing of

the collector must first be made and then filled with the appropriate insulation. A

mould would be required to produce a fibreglass casing. If metal sheets were used,

then the shape could be rolled out or machine-pressed. Once the infrastructure is in

place, collector production becomes a routine process.

However, the double cover used (Twinwall®) does not tolerate temperatures above

120°C without sustaining damage so it might have to receive special attention and

maybe consideration given to an alternate cover material. This could also take care of

the warping that arose from its flexibility and high temperature gradient from the

glazing. On the other hand, this polycarbonate top cover is a cheaper alternative

compared to glass, it is easier to handle and easier to work with and carries a 10 year

warranty against loss of light transmission and a 5 year warranty against breakage

caused by hailstones up to 25 mm in diameter. It is also guaranteed UV resistant.

Another option might be to use polystyrene in conjunction with another material. For

example, a large polystyrene collector body with an oversized internal chamber can

be layered with 10 mm corkboard internally and on the top sides of the collector

walls. With this arrangement it might be possible to have very high internal air

temperatures, but the polystyrene being safely insulated by the pre-layered material.

The external polystyrene might then be painted for added robustness and general

protection. This might offer an even more cost-effective solution.

The PVC stormwater pipes would have to be changed to another piping system that

would allow higher air temperatures to be carried continuously, day after day,

without degradation of the material and also be suitable for outdoor use. The material



245

of choice would be high density polyethylene (HDPE) that can be obtained in the

form of pipes, tubes, fittings and bends as a consumer product and slightly more

expensive than PVC piping. It is also UV resistant. Finally, the insulation used for

the conveyance system would remain the same (Astrofoil™) or a similar product that

minimised both radiation and heat conduction losses and suitable for outdoor use.

Air and water flow measurements

Anemometer readings for airflow calculations were unreliable since they were

strongly dependent on the position of the probe inside the pipes, were limited in scale

(60 L/s max) and were limited to low temperature operation (50°C). Measurements

with the airbag were much more reliable and accurate (within ±5% variations),

although particularly invasive for the closed-loop mode since the piping had to be

opened up to attach the bag. A future improvement on the measurement of air

velocity and determination of airflow rates would be the use of several, more

sophisticated, flow rate meters of little invasiveness left permanently in the piping

system at different spots.

Water flow rates could not be measured due to lack of equipment and time

constraints of the project. A tiny digital water flow rate meter could be used in the

thermosiphon pipe providing instantaneous measurement of water flow rate.

Measurements of irradiance where done with a thermopile that had errors of up to

3%. An improvement here would be to have a more accurate probe and associated

meter. This is an expensive improvement and probably not warranted.

A major improvement in the measurement of all parameters would be to affix all

measuring probes permanently (or semi-permanently) at different places in the

system and couple them with a data logging mechanism.

Additionally, a way of automating daily operation is required. A very simple solution

would be to use a timer-operated relay that would give power to the motor between

predetermined hours of the day (e.g 6:00 am to 6:00 pm). Adjustments would have to



246

be done for peak summer periods where longer operation times are required and

winter periods where shorter times are sufficient. This solution, however, would have

the motor operating during overcast days and is therefore not an optimum one. A

better option for operation only when enough sunlight is available would be having

the relay switched on when a predetermined light threshold is detected. A

photovoltaic cell or a light sensitive resistor mounted on the panel frame and some

extra circuitry would probably be adequate for this.

An improvement or change in the pressure drop measuring technique for the pipe

system would allow more accurate assessment of the hydraulic resistance and a more

accurate selection of the required pumping power from the fan/blower motor.

Seasonal performance:

The system was tested during early spring and summer seasons. The collector was

tilted at about 30° and North-East orientated such that the global irradiance measured

on the top cover during operation was roughly between 700-1000 W/m2. During the

winter season, physical constraints of the test site restricted operation of the system.

An extension to the study of the effect of winter conditions can certainly be carried

out both numerically and experimentally. The numerical curves shown have been

produced with this in mind, giving an indication of how the system would perform

with a reduced irradiance for open and closed loop operations. The main factor

affecting the operation during seasonal change are the solar position and the ambient

temperature. Besides the reduced irradiance on the collector, during winter,

temperatures drop considerably meaning that losses are increased. It is easy to

simulate this situation numerically and expect to get a reasonably close result to

experimental measurements.

For the characterisation of the air heater prototype system, this extra investigation

would have to be done and the findings on operability during winter; tilt angles and

other recommendations and observations, would be part of the outcome. It would be

ideal to have a system requiring minimal maintenance where, among other things,



247

the collector panel could be set up to maximise solar contribution during winter and

left like that for all times (e.g., north facing with a tilt angle around 45°).

Numerical simulation model

As it was seen, the modelling of a collector with an absorber plate in the middle of

the chamber and airflow above and below under-predicted the experimental results

obtained from the prototype developed. Instead, the model used for more turbulent

flow (corrugation and fins) gave better results. In actual fact, the absorber-in-middle

model was an approximation to the real scenario which consisted of a series of

absorber channels and the airflow going through and over them (Figure 7.3a).

Modelling for this type of collector would improve the overall modelling scheme. It

would determine if additional investigation in heat transfer aspects were still required

in case the results still did not approximate reasonably well experimental findings.

The model would be more versatile if it took into account tilt and azimuth angles of

the collector and real-time change of irradiance over a day of operation. This was

incorporated into the model prediction for the SHWS. The benefit here would be a

closed solution to performance under real circumstances, from morning to afternoon,

for clear skies with known ambient, cold water temperatures and airflow rates.

The heat exchanger modelling done could be further improved by taking into account

that the temperature and height of the cold water column will change quite drastically

over a full day’s operation (6 hours or more). There is also dependency of the

effectiveness and the efficiency of the exchanger with airflow rates and temperatures.

Including this dynamic behaviour will certainly produce more realistic results.

This would require monitoring the changes in the cold water column, thermosiphon

water flow and water temperatures for a set of known input air power values into the

collector. Measurement of water flow rates would require the least invasive

technique possible, since any material inside the thermosiphon pipe will create

resistance and affect the flow. It is suggested that some type of magnetic flow, or

ultrasonic, transducer could be used although this might be a costly application. Also,



248

exploring other modelling techniques for the characterisation of heat exchangers is

worth considering (such as the alternate method discussed in chapter 7).

Similar to the suggested improvements for the collector, more extensive temperature

depth profile measurements would enable a better experimental evaluation of the

actual temperature gradients in the tank and assessment of the energy gained by the

water. This could be done by placing several temperature probes in strategic places,

including the thermosiphon pipes and the inside of the exchanger. Measurements

would then be recorded at real time by a data logging system.

Physical improvement and large scale systems

Besides the high temperature issue requiring changes to the materials used for

prototyping, other changes of the actual design can provide increased performance.

A higher power output can be obtained by reducing the height of the air chamber in

the collector since the efficiency increases for decreasing D/L ratios (Figures 7.35

and 7.37). For the same collector length of 6.5 m, it appears that a chamber height of

30 mm (instead of 50 mm) would certainly mean higher collector efficiency and

more power available. A reduction in height implies less material, therefore more

economical. A flatter collector would be less conspicuous and more appealing from

an architectural point of view. However, it would also mean increased pressure

losses, so careful assessment would be required to determine if the gain would be

sufficiently higher than the losses to justify doing it. Other, more practical, problems

might also arise, like the difficulty of finding appropriate reduction and expansion

fittings adequate to the reduced size of the collector.

Pipe sizes are an important factor as well. Larger pipe diameters imply higher heat

losses but lower pressure losses and vice-versa. Therefore, there is a trade-off

between these two figures and there will be an optimum size for a given airflow rate.

Bends and fittings account for minor losses, which can be quite substantial if care is

not taken in having smooth air-passage trajectories and gradual expansions and



249

reductions. A deeper exploration into the piping layout and the different connections,

in conjunction with the optimum pipe size, might result in a noticeable decrease in

pressure drops and the system requiring less pumping power or achieving higher

flow rates (and more power transferred as a result).

It was assumed that the efficiency of the exchanger is very high in relation to the

power gained by the water and this might not be the case so better insulation for the

heat exchanger would be another area of improvement.

The possibility of using this system for industrial applications is also feasible and

would imply rescaling of the collector panels and a careful study of the hydraulic

resistance of the transfer pipes and high temperatures issues.

Final words

Both systems developed satisfied the aims and objectives of the project to different

degrees. The vapour transport system has an advantage over the air heating system in

its passive nature. While the air heating system still requires investigation into the

temperature limitation problem, this is not so with the vapour system. Stagnation in

the concentrator panels would be a consequence of the self-pumped mechanism not

working properly, where the reservoir tank would run dry. It is very easy to

determine if this is happening and correct the problem before it is allowed to

continue for an extended period. Under day-after-day operation as evidenced with

the first prototype, this will never happen. Even in the event of this problem ocurring,

localised high temperatures around 200 °C in the vicinity of the absorber boilers

would not be a problem for a brazed structure with the selective surface used. The

top cover would probably require additional assessment under the potential of high

temperatures, but metal reflectors would not be affected by elevated heat inside the

concentrator cavity. On the other hand, the air heater was clearly much easier to

fabricate and much more cost-effective. It is also easier to manipulate, install and

service. Provided the temperature limitation problem is solved, these advantages

might make a future commercial deployment more feasible over the first one.

Appendix A – Mathematical relationships and calculations

in solar geometry and CPC orientation A1 Panel orientation

The qualitative process described in Chapter 2 for orientating and positioning of the

CPC plane involves rotations about preselected axes. These can be accomplished by

3×3 rotation matrices applied to the unit vectors that define the orientation of the

panel (VN) and position of the CPC (VP). The azimuth rotation is a rotation about the

z-axis, while the tilt and twist rotations about the transverse and longitudinal axes of

the plane are actually rotations about the x- and y-axis, conveniently chosen to obtain

the same outcome.

Step 0: Defining unit vectors and matrices

VNpol = (1, 90°, 0) – vector normal to the CPC plane

VPpol = (1, 0, 90°) – vector parallel to the plane and normal to the CPC line-axis

(refer to Figures 2.5 - 2.7)

These vectors can be transformed into their Cartesian form (VN,VP) in order to apply

the rotations required:

( )ϕθ ,,VV mpolar =

( )θϕθϕθ sinV,coscosV,sincosVV mmmcart ⋅⋅⋅⋅⋅= (A.1)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=

xx

xx

cossinsincosX

θθθθ

00

001 – rotation about the x-axis (A.2)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−=

yy

yy

cossin

sincosY

θθ

θθ

0010

0 – rotation about the y-axis (A.3)


Appendix A – Mathematical relationships and calculations in solar geometry and CPC orientation

252

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡ −=

10000

xz

zz

cossinsincos

Z θθθθ

– rotation about the z-axis (A.4)

For a rotation θu about an arbitrary vector, ( )w,v,uVU = :

( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ⎥

⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−⋅+−⋅⋅+⋅−⋅⋅+⋅−−⋅⋅+⋅−⋅+−⋅⋅+⋅−⋅⋅+⋅−⋅⋅+⋅−−⋅+

=

uuuuuu

uuuuuu

uuuuuu

coswcoscoswvsinucoswusinvcoswvsinucosvcoscosvusinwcoswusinvcosvusinwcosucos

Uθθθθθθ

θθθθθθθθθθθθ

111111111

2

2

2

(A.5)

Step 1: Applying azimuth, tilt and twist rotations to the CPC panel

For illustration purposes, only vector VN will be used. The same applies for VP.

a) Order of the rotations: azimuth tilt twist:

These operations are equivalent to applying first a rotation in the y-axis, then in the

x-axis and finally in the z-axis.

NN VYXZ'V ∗∗∗= (A.6)

b) Order of the rotations: azimuth twist tilt:

These operations are equivalent to applying first a rotation in the x-axis, then in the

y-axis and finally in the z-axis.

NN VXYZ'V ∗∗∗= (A.7)

The resulting vectors are then transformed back into their polar form to obtain the

effective azimuth and tilt angles that redefine the position of the CPC plane.

( )eff'effN ,,V ϕθ1= (A.8)

The actual tilt angle of the panel is: 'effeff θθ −°= 90 (A.9)



253

Step 2: Applying ρ-rotation about the normal to the panel

In section 2.5 it was mentioned that rotations about this angle would not affect the

orientation of the panel, but would change the position of the CPC. It would

therefore be necessary to calculate the new position and this could be done by

applying the rotation matrix of Equation A.5 to vector VP’.

'VU'V PP ∗= δρ (A.10)

Step 3: Determining incidence angle, θinc, on the plane of the CPC panel

The cosine of the incidence angle for direct solar radiation on flat tilted surfaces may

be obtained by one of the following expressions139F

140:

SeffeffSeffeff

Seffeffeffeffinc

hsinsinsincoscoshcossininscos

coshcoscoscoscossincossincossinsincos

⋅⋅⋅+⋅⋅⋅⋅+

⋅⋅⋅+⋅⋅⋅−⋅⋅=

ϕθδϕθφδ

θφδϕθφδθφδθ (A.11a)

( )effSeffzeffzinc cossinsincoscoscos ϕϕθθθθθ −⋅+⋅= (A.11b)

Since the incidence angle will change throughout the day, the final objective is to

determine when this angle will fall within the admittance criterion of the CPC, which

will then indicate energy collection times.

Step 4: Determining solar azimuth, ϕS , altitude, α, and zenith, θz, angles, and

other quantities of interest.

The parameters of Eqs. A.11 have been defined in Table 2.1. Of interest are the

declination, δ, solar altitude and zenith angles, α and θz, solar azimuth angle,ϕs, and

the hour angle, hs. These can be found from different relationships available in the

solar literature, with the later-developed algorithms22 appearing to be the most

accurate and simple to use.

It was also mentioned in Chapter 2 that the solar altitude angle could be determined

from Equation A.11a by considering a flat horizontal surface (θeff = 0°). The

resulting angle in this case is the zenith angle, where α = 90-θz.



254

Step 5: Collection angle, θc and collection times are found

From the solar azimuth and altitude angles, solar vectors, VS, for each position of the

sun from dawn to dusk can be obtained (and converted to Cartesian coordinates). To

determine collection times, it was mentioned in Chapter 2 that the collection angle,

θc, must be found. It was also said that this is the angle between the projection of the

solar vector on the transverse plane perpendicular to the panel, VST, and the vector

normal to the surface, VN’, as seen in Figure 2.9. The vector VST therefore has

components on the axes that contain VN’ and VP’. These components are VSP’ and

VSN’, respectively.

It is easy to see that: 'V

'Vtan

SN

SP

c =θ (A.19)

Vectors VSP’ and VSN’ are also the direct projections of the solar vector, VS, on the

said axes via the angles θSP and θSN, respectively. These angles can be obtained from

the scalar product between Vs and VP’, and, Vs and VN’. So one way of determining

the collection angle is the following:

1) Projection angles between VS, and VN’ and VP’ are found:

(A.20)

(A.21)

2) Vector components VSN’ and VSP’ are found:

(A.22)

(A.23)

SNSNNSNS coscos'VV'VV θθ =⋅⋅=•1

1

SPSPPSPS coscos'VV'VV θθ =⋅⋅=•

SNSNSSN coscosV'V θθ =⋅=

SPSPSSP coscosV'V θθ =⋅=



255

3) The collection angle is found from these components

'VV'VV

coscos

'V

'Vtan

NS

PS

SN

SP

SN

SP

c•

•===

θθθ (A.24)

⎟⎟⎠

⎞⎜⎜⎝

⎛

••

= −

'VV'VVtan

NS

PSc

1θ (A.25)

Since these are unit vectors, and their coordinates are known, the collection angle can

be readily found. Finally, calculation of irradiance during collection times is done:

If Collection Occurs

Irradiance –Gcb (from Eq. 2.9)

ac θθ ≤ catm cosG θτ ⋅⋅0

ac θθ > 0

The process outlined here was implemented in a MATLAB™ program as part of the

development of this project. A summary of the input and output data for the program

is given in Table A1.

Table A1 Input/Output data for solar geometry modelling program

INPUT DATA OUTPUT DATA

General parameters Internal calculations

• CPC geometrical data (aperture, etc) • CPC optical data (reflectance, etc) • Geographical data (latitude, etc) • Date and time

• Atmospheric attenuation • Effective azimuth and tilt angles • Angle of incidence • Solar azimuth and altitude angles • Energy on collector plane over a day• Collection times

User-defined panel layout Graphs and plots • Azimuth, tilt and twist angles • ρ-rotation (ρ angle)

• Irradiance profile • Collection times

Appendix B – Etendué invariant and optical concentration B1 The etendué invariant and upper limit for concentration

Consider a very general optical system bounded by homogeneous media of different

refractive indices (n and n’ ) (Figure B1).

Figure B1 General optical system and the étendue invariant

P represents the origin of an incident ray on the system from the input media.

P’ is the end point of the same ray after emerging at the output media.

The incident and emerging ray segments are specified in each media by:

- Coordinates P(x,y,z) and P’(x’,y’,z’)

- Direction cosines (L,M,N) and (L’,M’,N’)

The positions of the origins and the directions of the axes for the cartesian

coordinates of each medium are arbitrary. Small spatial displacements for each ray

are, therefore, given by differential increments dx, dy, dx’ and dy’. Similarly, small

changes in angular direction are given by dL, dM, dL’ and dM’. There is then a

two-dimensional spatial displacement for the position of the rays given by the

differential areas dx·dy, dx’·dy’ and of angular extent dL·dM, dL’·dM’ (Figure B2).

The expression for étendue invariance is given by:

n2·dx·dy·dL·dM, = n’2·dx’·dy’·dL’·dM’ (B.1)

P

n

P’

n’

x

y

z

x'

y'

z'


Appendix B – Etendué invariant and optical concentration

257

Figure B2 The étendue for a general optical system (measure of angular displacement

shown for y-coordinate)

Integrating B.1 over the spatial and angular variables allows determination of optical

relationships between input and output rays that depend on the collection and exit

angles and the input and output aperture dimensions.

Consideration is now given to a 2D concentrating system of input and output

apertures 2w and 2w’, and acceptance and exit angles 2θ and 2θ’ (Figure B3).

Figure B3 Two dimensional concentrator of acceptance angle 2θ and output angular

range 2θ’

Since this is a 2D system with rays varying in position and angular displacement

only in the y-coordinate (no x component), the étendue expression of Equation B.1

reduces to:

n·dy·dM, = n’·dy’ ·dM’ (B.2)

In other words, concentration only occurs in the y-dimension. The origin of the

cartesian axes, being arbitrary, is conveniently located about the axis of the system.

This way, the spatial position, y, varies over ±w, which is the extent of the input

aperture. The angular displacement, M, which is the direction cosine for the rays in

P

dy

dx

dM

2θ

2θ

2w 2w’

2θ’

n n' z

y


Appendix B – Etendué invariant and optical concentration

258

the y-direction, varies over the angular collection range ±θ. A similar argument

applies to rays emerging in the output media.

In the system, θsinry ⋅= , where r is the magnitude of the vector representing the

incident ray. Therefore, θsinM = and θθ dcosdM ⋅= .

The integral for the étendue relationship is then:

∫∫∫∫−−−−

⋅⋅⋅=⋅⋅⋅'

'

'

'

w

w

''''w

w

dcosdyndcosdyn ϕϕϕϕθ

θ

θ

θ

(B.3)

( ) ( ) ( ) ( )''' sinwnsinwn θθ ⋅⋅⋅⋅=⋅⋅⋅⋅ 2222 (B.4)

''' sinwnsinwn θθ ⋅⋅=⋅⋅ (B.5)

Relating this to the previous definition of concentration (Equation 3.3)

θθ

sinnsinn

wwC

''

' ⋅⋅

== (B.6)

For fixed values of n and n’, and for any input acceptance angle, θ, the maximum

concentration will be obtained when 2πθ =' , the maximum emergence angle. The

expression for maximum concentration for a 2D system is given by:

θsinwwC '

Dmax

12 == (B.7)

For a 3D system with axisymmetric properties and circular entrance and exit

apertures, w in Equation B.7 becomes the aperture radius, a, and the maximum

concentration is given by (Equations 3.4 and 3.7):

223

⎥⎦

⎤⎢⎣

⎡⋅

=⎟⎠⎞

⎜⎝⎛=

θsinnn

aaC

'

'D

max (B.8)

Appendix C – Mathematical formulation for the design of

the CPC shape and the horizontal fin profile C.1 The CPC reflector shape

Figure C1 Construction of the CPC profile

In Figure C1, the CPC segment (black) is represented as the plot of the function for

that profile in the Cartesian coordinate system with origin O. The polar form equation

for the parabola allows calculation of the vector magnitude for each point on the

segment and to later determine the equivalent (x,y) pair for easy plotting and

representation.

(C.1)

Equation C.1 is later parameterised into the corresponding x and y coordinates to

achieve this. It is therefore necessary to determine the focal length, f, of the parabola

P’ P

θ

2w’

θ

ϕ

2w

L

R r

f

y

x

O

Q

O

( )⎟⎠⎞

⎜⎝⎛

=−

⋅=

21

22 ϕϕ sin

fcos

fr


Appendix C - Mathematical formulation for the design of the CPC shape and horizontal fin profile

260

that generates the segment of interest. As discussed in Chapter 3, this is a parabola

with focal point at P’, vertex O and axis as defined in Figure C1,

with: ⎥⎦⎤

⎢⎣⎡ +∈ θπθϕ

22 ,

Focal point calculation

To find f, the known value of 'wr ⋅=+=

22

θπ

ϑ is used and substituted in Equation C.1:

⎟⎠⎞

⎜⎝⎛ +−

⋅=⋅=

+=θπθ

πϑ

21

222 cos

fwr ' (C.2)

( )θsinwf ' +⋅= 1 (C.3)

Concentration ratio

Firstly: ( )( )

θθ

θθϑ 221

212

sinsinw

cosfQ'Pr

' +⋅=

−⋅

=== (C.4)

Then: ( ) '''

' wsinw

sinsinwsinQ'Pww +=

+⋅=⋅=+

θθθθ 1 (C.5)

Which takes it back to the theoretical maximum for concentration:

Csinw

wsinww '

'

==⇒=θθ

1 (C.6)

Concentrator length (or height)

( ) ( ) θθθ

θθθθθϑ cotww

sincos

sinsinwcosQ'PsinrL '

'

⋅+=⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

+⋅=⋅=⋅= =

12 (C.7)

The x and y coordinates for every point on ( ) 'wsinrx −−⋅= θϕ (C.8)

the concentrator’s surface are given by: ( )θϕ −⋅= cosry (C.9) {



261

The x-coordinate has been biased due to the selection of the origin in the middle of

the exit aperture, while all values of r originate from P’, located at -w’ from the

origin. The angles have also been biased due to a similar argument, since the axis of

the parabola is tilted by -θ° from the coordinate axes. Plotting Equations C.8 and C.9

will result in the CPC profile shape of Figure 3.10 for the right side reflector wall. A

mirror image about the axis (-x,y) will yield the second segment. This procedure can

be readily employed to fabricate concentrators with plane absorber shapes. The

construction of the horizontal absorber profile of Figure 3.7b, used for the second

and third prototypes is detailed below.

For many convex absorbers (eg. circular cross-section absorbers) obtaining the

required CPC shape can be done via an extension of the edge-ray principle, by

stating that extreme rays at the aperture of the collector must be tangent to the

absorber after one reflection. For plane absorbers, it can be seen that this reduces to

focusing to a single point as already discussed. Its application is more demanding for

absorbers other than plane absorbers however, since it requires specifying and

solving a set of differential equations that characterise the concentrator profile18F

*.

C.1.1 Truncation

In practical applications, the CPC profile is often truncated to reduce size and cost.

The penalty for doing so is small, since the upper half of the reflector in a full-sized

CPC is nearly parallel to the optical axis and has very little contribution to

concentration. The reflector area can be reduced by about 50% without any

significant loss in concentration and even though some rays outside the acceptance

angle can reach the absorber, the resulting gain in radiation at the absorber is very

small 140F

141,141F

142 (Figure C2).

* In the case of 3D problems, the application of this principle is more limited. Other, more general methods of design have to be applied to assure that ideal concentration is reached.



262

Figure C2 Comparison of the fraction of radiation incident on the aperture of a CPC for

different CPC scenarios (assuming perfect reflectivity)

C.2 The horizontal absorber CPC profile

This section describes the detailed construction of the profile of choice for the

concentrators used in the 2nd and 3rd prototypes for the SHWS (Figure 3.7b).

The profile of the compound parabolic sections for this CPC is shown in Figure C3.

Figure C3 Compound parabolic profile for the horizontal absorber concentrator

3

2

1

P’

SS’

R’ R

Q’ Q

O

A’

B’

C’

x

θ

ϕ3 θ

ϕ1

ϕ2

P

1.0

0.5

ΔΔ

+θ -θ +θ’-θ’

Full CPC

Full CPC with angular surface error Δ Truncated CPC



263

Following the edge-ray principle, 3 different sections are identified for this profile.

Since the system is a mirror image about its axis, consideration is only given to one

side and then the treatment can be duplicated for the other

C.2.1 Sections of the CPC profile

Section 1: Below the absorber where there is no direct illumination from

extreme rays

This section is made up by curve OS (blue). An involute of the absorber drawn from O

to S and centred at P will result in an arc of a circle.

Section 2: Below the absorber level where direct illumination from extreme

rays is available

This section is defined by curve SR (green). Extreme rays falling on this segment

must be focused on the edge, P, of the absorber. In this case it can be seen that SR is

part of a parabola with focus at P and axis Q’PS

Section 3: Above the absorber level

This section is given by curve RQ (brown). In this case, extreme rays must be

focused on edge, P’, of the absorber. Again, a parabolic section will satisfy this

condition, with a parabola with focus at P’ and axis A’P’B’, parallel to Q’PS.

Similar arguments apply to the construction of the other half of the CPC.

C.2.2 Mathematical formulation of the CPC profile

The origin of the coordinate system is located at the centre of the absorber, O. All

Cartesian equations for the different sections are referred to these coordinates.

Section 1: Arc of a circle with centre at P and radius OP

The equations for this segment are straightforward, noting that the x and y

components are the projections of the radius on each coordinate axis.



264

ϕcoswwx ''S ⋅−=1 (C.10)

ϕsinwy 'S ⋅−=1 (C.11)

The coordinates are biased according to the displacement from the origin of the

system (at O) since the vector that defines that arc originates from P.

Section 2: Section of parabola with focus at P, focal length PS and axis Q’PS

The parametric equations are determined from the polar equation for the parabola,

( )ϕcosfr

−⋅

=1

2 (C.12)

The focal distance is required, which is given by segment PS. Note that this is the

radius of the arc from section 1.

So the equation for the parabola is:

( )ϕcoswrS −

⋅=

12

2 (C.13)

And the x and y components are then:

( ) wsinrx SS +−⋅= θϕ22 (C.14)

( )θϕ −⋅= cosry SS 22 (C.15)

Bias is only in the x coordinate since the origin for the calculation of rS2 is displaced

+w from the origin of the system.

Section 3: Section of parabola with focus at P’, focal length P’C’ and axis A’P’B’

The focal length for this section is the distance P’C’ which is calculated in the

following way:

Data: ⎥⎦⎤

⎢⎣⎡ +∈ θθπϕ 2

2,

Rearranging Equation B.1:

( )2

1 ϕcosrf −⋅= (B.16)

⎩⎨⎧Data:

⎥⎦

⎤⎢⎣

⎡+∈ θπϕ

20,

'woP =

⎩⎨⎧

Data: 'wPSf ==

⎥⎦

⎤⎢⎣

⎡+∈ θππϕ

22 ,



265

Also: PRPPr ' +=+θπ

2

, with P'P = 2w and θθπ sin

w

cos

fPR S

+⋅

=⎟⎠

⎞⎜⎝

⎛+−

⋅=

12

21

2 2

Substituting in Equation 3.27 and solving for f:

( )θsinwf 'S +⋅= 23 (C.17)

Finally: ( )ϕ

θcos

sinwr'

S −+⋅⋅

=1

223 (C.18)

With x and y components given by:

( ) wsinrx SS −−⋅= θϕ33 (C.19)

( )θϕ −⋅= cosry SS 33 (C.20)

Bias is now –w in the x coordinate.

Plotting the parameteric equations for these sections will result in the profile shape of

Figure C3 for positive x-values (right hand side). The rest of the profile is obtained

by reflection of these values

C.2.3 Truncation

Truncation was implemented in the

design by limiting the length of

section 3 of the CPC in accordance

with a reduced input aperture

dimension

The final shape of the horizontal CPC

profile is shown, to scale, in Figure C4

the solid black section. The truncated

sections are given by the dotted curves.

Figure C4 Truncated CPC

2θ

Appendix D – Heat transfer parameters and pipe friction Many different parameters have been used in the heat transfer

modelling of both the SHWS developed in this study. The following

relationships and definitions complement the theory developed in

Chapter 4

D1 – Convection transfer and quantities of interest (section 4.2.1)

( )

t

fluidsurface

Pr

LTTgGr

αν

νβ

=

⋅−⋅⋅= 2

3

( )

( )2D

1D

.

.

tfff

LTgPrGrRaαν

β⋅

⋅Δ⋅⋅=⋅=

3

(D.3)

Where: g = 9.8 m/s2

T1

=β

ν = kinematic viscosity (m2/s)

αt = thermal diffusivity (m2/s)

The Prandtl number, Pr, expresses the relative magnitudes of diffusion of

momentum (ν) and diffusion of heat (αt) in a fluid as convection is established. The

subscript f indicates that the properties of Equations D.1 and D.3 are evaluated at the

film temperature, Tf:

( )2

fluidsurfacef

TTT

+= (D.4)

Thus: f

f T1

=→ ββ , ν → νf and ftt αα →


Appendix D – Heat transfer parameters and pipe friction

267

It is advisable to use the film temperature since the properties of the fluid may vary

considerably between surface and free-stream conditions. The characteristic length,

L, in this case is the ratio of the surface area over the perimeter: PAL = .

For a horizontal arbitrary tilted plate (section 4.2.1.1) the parameters used are:

(4.9)

(D.5)

(D.6)

(D.7)

(D.8)

(D.9)

(D.10)

The characteristic length for this case is also: PAL = .

In forced convection over flat plates (section 4.2.1.2), the Reynolds number is given

by:

(D.11)

Where: =mv mean fluid velocity (m/s)

ρf = mass density (kg/m3)

μf = dynamic viscosity (kg/m·s)

x = distance from leading edge of plate (m)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+

=

T

lH

HNu.ln

.Nu411

41

418350 Hl

T RaC.Nu H θ⋅⋅=

( ) 94

169

49201

6710

⎥⎦⎤

⎢⎣⎡ +

=

Pr.

.Cl

( )αν

βθθ ⋅

⋅Δ⋅⋅=

30 LTcos,gRa maxH

31

HtHtH RaCNu θ⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+

⋅+⋅=

Pr.Pr..CtH 0101

010701140

( ) 1011010

lHtHH NuNuNu +=

νμρ xvxv m

f

mfx

⋅=

⋅⋅=Re



268

D2 – Pipe friction and the Moody diagram

The characteristic length for convection arising from fluid flow in ducts is called the

Hydraulic Diameter, Dh, which is defined as:

d

dh P

AD ⋅= 4 (D.12)

Where Ad is the flow cross-sectional area and Pd is the wetted perimeter of the duct.

A friction factor that accounts for the frictional resistance in pipes is defined in its

general form as:

2v

f 2m

w

⋅=

ρτ (D.13)

Where: τw = wall shear stress (kg/m·s2)

The relationship for friction used in this study was:

( )[ ] 2

7781750−

⋅= Reln.f (D.14)

The Moody diagram142F

143 that is presented next shows the relationship between friction

and the Reynolds number and how friction is affected by the nature of the flow

(whether its laminar, transitional or turbulent) and by the pipe roughness and

diameter.

The curves in Figure D1 are the result of plotting the implicit equation known as the

Colebrook equation for friction143F

144:

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅+

⋅⋅−=

D.fRe.log

f 7351221 ε (D.15)

Where the quantities Re, ε and D have been defined in Chapters 4 and 5.



269

Figu

re D

1 Fr

ictio

n fa

ctor

s fo

r vs

. Rey

nold

s nu

mbe

r fo

r va

riou

s pi

pe r

ough

ness

and

dia

met

er r

atio

s an

dfo

r la

min

ar, t

rans

ition

al a

nd tu

rbul

ent f

low



270

For very large Reynolds numbers, the first term in brackets in Equation D.15 is very

small and the resulting equation is that for complete turbulent flow. For smooth pipes

(ε ≈ 0), the second term in brackets is negligible and the result for friction is an

implicit form of f. Similar results are obtainable by the use of Equation D.14 (the

expression used in this study).

The Moody diagram and Equation D.15 are amply referred to in heat transfer, fluid

mechanics and hydraulics literature for pipe system design and fluid flow studies.

Appendix E – Analytical expressions for the heat transfer

dynamics of the CPC panel SHWS E1 – Convection and radiation heat transfer relationships for the

elements of the CPC collector panel system

The expressions used for heat transfer in the determination of power gain and losses

from the CPC panel described in Chapter 6 were based on the simplified heat

exchange modelling between elements, given by Table E1, and the sources and

theory provided in Chapter 4. All relationships refer to the concepts and process

explained in section 6.4.

Table E1 Modelling relationships

Heat transfer modes Configurations used for modelling

Convection Radiation Absorber-Sheath Absorber-Sheath

Two concentric cylinders Sheath - Cover Sheath – Cover

Flat horizontal plate Cover-Surroundings -

Small object in large enclosure - Cover-Sky

1. Convection and radiation from top cover to the environment (hcCA & hrCS)

Convection:

To calculate hcCA, expressions for forced and free convection from the panel open to

the atmosphere were used. To be conservative, the maximum of these two was

selected.

• Free convection calculation:

From Equations 4.7, 4.8 and C1-C4: PA

RaChc

mfCA

CAfree

κ⋅⋅= (E.1)


Appendix E - Analytical expressions for the heat transfer dynamics of the CPC panel SHWS

272

CCA and m are dependent on the Rayleigh number, Raf, evaluated at the film

temperature Tf. A and P are the area and perimeter of the cover, respectively and κ is

the thermal conductivity of the air.

• Forced convection calculation:

From Equations 4.7, 4.10, 4.11 and D.1-D.4:

lRePr.

hc xCAforced

κ⋅⋅⋅=

21

316640

(E.2)

Pr and Re are the Prandtl and Reynolds number, respectively and l is the length of

the cover (which was basically the same as the length of the collector panel).

The final result for convection heat transfer coefficient from the top cover to the

environment, hcCA, was:

[ ] maxCAforcedCAfreeCA hc,hchc = (E.3)

Radiation:

From Equations 4.28, 4.29:

( )( )ambC

skyCcCS TT

TThr

−

−⋅=

44

εσ (E.4)

The equivalent thermal resistance for both convection and radiation heat transfer

from the top cover to the surroundings and to the sky was (from Equation 4.36):

⎥⎦

⎤⎢⎣

⎡+

⋅=CSCA

C hrhcAcR 11 (E.5)



273

1 Convection and radiation between sheath and top cover (hcFC & hrFC)

Heat transfer modes between the sheath and CPC cavity with top cover were

modelled assuming a similar behaviour to heat transfer between concentric cylinders.

Convection:

From Equations 4.21, 4.22:

⎟⎠⎞

⎜⎝⎛⋅

⋅⋅=

FF

nFC

CFC

rrlnr

RaCkhV

δ (E.6)

CFC and n are dependent on the Rayleigh number, Raf. rF and rV are the “effective”

radii for the sheath and CPC cavity, respectively. In the modelling process and

numerical simulation, rV = 0.11m and rF = 0.05 m.

The thermal resistance for this heat transfer mode was (from Equation 4.36):

FCFCFC hcA

R⋅

=1 (E.7)

Radiation:

For radiation transfer, it was assumed that all radiation emanating from the sheath

eventually ended up on the cover (FFC = 1).

From Equation 4.34:

( ) ( )

C

F

C

C

f

CFCFFC

AA

TTTThr⋅

−+

+⋅+⋅=

εε

ε

σ11

22

(E.8)

AF and AC represent the areas of sheath and top cover, respectively.



274


FCFFCR hrA

R⋅

=1 (E.9)

The equivalent thermal resistance for convection and radiation modes from the

sheath to the top cover, RF, was:

⎥⎦

⎤⎢⎣

⎡+

⋅=FCFCF

F hrhcAR 11 (E.10)

3. Convection and radiation between absorber and sheath (hcAF & hrAF)

Interaction between these two elements was also modelled like two concentric

cylinders exchanging heat. The previous equations are also applied in this case.

Convection:

As for 6.9: ⎟⎠⎞

⎜⎝⎛⋅

⋅⋅=

A

FA

nCF

CabF

rrlnr

RaCkh δ (E.11)

The value for rA was obtained from the original area of the absorber by equating this

value to the area of the modelled cylinder of equal radius:

πWrA = (E.12)

It is noted that this sheath had an oval cross-section because it was a tight fit to the

shape of the absorber-boilers (Figure 6.22).


AFACAF hcA

R⋅

=1 (E.13)



275

Radiation:

As for 6.11: ( ) ( )

AFA

TTTThrA

F

F

A

FAFAabF

⋅−

+

+⋅+⋅=

εε

ε

σ11

22

(E.14)

The equivalent thermal resistance for this heat transfer mode is (from Equation 4.36):

abFARAF hrA

R⋅

=1 (E.15)

The equivalent thermal resistance for convection and radiation heat transfer from the

absorber to the sheath, RA, was:

⎥⎦

⎤⎢⎣

⎡

+⋅=

AFAFAA hrhcA

R 11 (E.16)

Appendix F – Analytical expressions for the heat transfer

dynamics of the air heater panel SHWS

F1 – Convection, conduction and radiation relationships for heat

exchange between the elements of the air heater SHWS

All expressions used for heat transfer assessment in the SHWS incorporating the air

heater panel are based on the modelling and construction setup described in

chapter 7. The sources used were given and explained in chapter 4.

1. Convection and radiation coefficients from upper side of cover to the

environment (hcCA & hrCS)

Convection coefficient:

To calculate hcCA, expressions for forced and free convection for a horizontal panel

of arbitrary tilt open to the atmosphere were used and the maximum value between

them selected as a conservative measure.

• Free convection calculation

From Equations 4.14, and D.5-D.10:

( )A

PNuNuhchc lHtH

HAfreeQ⋅⋅+

==κ

θ

1011010

1 (F.1)

10tHNu and 10

lHNu are empirical relationships dependent on the Rayleigh and Prandtl

numbers, as well as the tilt angle, θ. A and P are the area and perimeter of the top

cover, respectively. κ is the thermal conductivity of the air.


Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS

277

• Forced convection calculation

From Equations 4.7, 4.10,4.11 and D.1-D.4:

lRePr.

hc xAforcedQ

κ⋅⋅⋅=

21

316640

1 (F.2)

Pr and Re are the Prandtl and Reynolds number, respectively and l is the length of

the cover (which was basically the same length of the collector panel).

The final result for convection heat transfer coefficient from the top cover to the

environment, hcQ1A, was:

[ ] maxAforcedQAfreeQAQ hc,hchc 111 = (F.3)

Radiation coefficient:

From Equation 4.29:

( )( )ambC

skyCcskyQ TT

TThr

−

−⋅=

1

441

1 εσ (F.4)

The equivalent thermal resistance for both convection and radiation heat transfer

from the top cover to the surroundings and to the sky was (from Equation 4.36):

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+⋅=

skyQAQCQ hrhcA

R11

111 (F.5)

2. Convection and radiation coefficients from lower side to upper side of cover

(hc21 & hr21)

Convection and radiation relationships between flat plates with tilt angles between 0°

and 75° were used in this case, considering also possible convection suppression (or

enhancement) due to the slats present in the collector’s double cover.



278

Convection coefficient:

From Equations 4.17, 4.19, 4.20, D.3:

(F.6a)

(F.6b)

Where a tilt angle, θ, of 45° for the panel was used for simplicity and to be

conservative. The ‘+’ superscript of the brackets means that non-zero values are to be

taken.

If Ra < 2415, Nuno_slats = 1, there would have been no convection between the plates

and the slats had no effect. Instead, heat transfer would have been via conduction

through the air space. This can be seen from Equation 4.7, which reduces Equation

4.6 to Equation 4.1; that of pure conduction heat transfer:

←=⇒⋅= LkhL

kNuh TT

1

conduction heat transfer coefficient

Note that if Nuno_slats > 1, the ratio from Equation 7.21a above is independent of the

Rayleigh number and the slats may actually enhance convection by up to 50%.

The average temperature of the air between the plates was above 30 °C at all

operational times, since the temperatures of the air exiting the panel were close to

75 °C. It was estimated that the temperature difference, ΔT, between the upper and

lower sides of the cover would rarely reach 40°C. The interplate distance, HS, was

6 mm.

With these values and from Equation D.3, an upper limit value for the Rayleigh

number was found:

slats_noNu44444444 344444444 21

↓

[ ][ ]

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

=⎥⎦⎤

⎢⎣⎡ −⋅+⎥

⎦

⎤⎢⎣

⎡−⋅⎥

⎦

⎤⎢⎣

⎡−⋅+

>⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦⎤

⎢⎣⎡ −⋅+⎥

⎦

⎤⎢⎣

⎡−⋅⎥

⎦

⎤⎢⎣

⎡−⋅+⋅

⋅

⋅

=++

++

1105024151236814411

110502415123681441111070

1160

31

31

280

280

slats_no

slats_no

max.

max.

slats

NuifRa.RaRa

.

NuifRa.RaRa

.,Ra.

,Ra.

Nu



279

<→⋅

⋅Δ⋅⋅= max

t

Sf RaHTgRa

ανβ 3

800

Therefore, the Nusselt number was always unity and there was no convection arising

between the plates.

Radiation coefficient:

Radiation was calculated by approximation from the formula for radiation exchange

between two infinite parallel plates

From Equation 4.32:

( ) ( )12

2122

21

21−

+⋅+⋅=

C

CCCC TTTThrε

σ (F.7)

The equivalent thermal resistor for these heat transfer modes was:

( )21212

1hrhcAc

RQ +⋅= (F.8)

3. Convection coefficient from airflow in upper channel to lower side of cover

(hcf1C2)

The heat transfer mode in this case was approximated by that of air flowing in a

triangular duct.

From Equations 4.23, 4.24, D.14:

[ ] 21

70240036021

21

71

92211 Cf_smooth..

h

CfCf NuPrRe.

Dhc ⋅

⎭⎬⎫

⎩⎨⎧ ⋅⋅+⋅= −κ

(F.9)



280

The corrugation parameters that defined the dimensions and layout of the fins in the

channels are the following: αr = 90°, pr = 0.09 m, dr = Dh, er = 0.02 m. These values

were used in Equation 4.24 and the result is given in Equation 7.24.

Nusmooth was determined from Equation 4.23 and was dependent on the Reynolds and

Prandtl numbers. It was also dependent on the friction factor.

( )( ) ( )18712071

83

22

1−⋅⋅+

⋅⋅=

Prf..PrRefNusmooth (F.10)

The equivalent thermal resistor for this heat transfer mode was:

( )2121

1

CfCCf hcA

R⋅

= (F.11)

Note that this was the same relationship for:

- Convection heat transfer between fluid in lower channel to back of collector

- Convection heat transfer between absorber and fluid in upper and lower channels

However, also note that BfabfabfCf hchchchc 22121 ≠≠≠ in the most general sense,

because the thermal conductivity, κ, is dependent on the temperatures of the heat

exchanging elements.

4. Radiation coefficient from absorber to lower side of cover (hrabC2)

The area of the V-corrugated absorber, Aab, was larger than that of the collector

aperture, AC.

From Equations 4.4 and 4.34:

( ) ( )

2

222

2

2 11C

ab

C

C

ab

CabCababC

AA

TTTThr⋅

−+

+⋅+⋅=

εε

ε

σ (F.12)



281


( )21

1

abCab hrAR

⋅= (F.13)

A radiation shape factor, F12 = 1, was used. In reality, F12 < 1. It can be readily seen,

since the corrugated nature of the absorber necessarily meant that part of the

radiation emitted was re-absorbed, so not all the radiation reached the bottom side of

the cover.

5. Convection coefficient from absorber to airflow in upper channel (hcabf1)

As for Equation 7.24:

[ ] 1

7024003601

1

71

92211 abf_smooth..

h

abfabf NuPrRe.

Dhc ⋅

⎭⎬⎫

⎩⎨⎧ ⋅⋅+⋅= −κ

(F.14)


( )1

11

abfab

abfhcA

Rc⋅

= (F.15)

6. Convection coefficient from absorber to airflow in lower channel (hcabf2)


[ ] 2

7024003602

2

71

92211 abf_smooth..

h

abfabf NuPrRe.

Dhc ⋅

⎭⎬⎫

⎩⎨⎧ ⋅⋅+⋅= −κ

(F.16)


( )2

21

abfab

abfhcA

Rc⋅

= (F.17)



282

7. Radiation coefficient from absorber to back cover (hrabB)

As for Equation 7.26

( ) ( )

B

ab

B

B

ab

BabBababB

AA

TTTThr⋅

−+

+⋅+⋅=

εε

ε

σ11

22

(F.18)


( )abBab hrAR

⋅=

12 (F.19)

8. Convection coefficient from airflow in lower channel to back cover (hcf2B)


[ ] Bf_smooth..

h

BfBf NuPrRe.

Dhc 2

7024003602

2

71

92211 ⋅⎭⎬⎫

⎩⎨⎧ ⋅⋅+⋅= −κ

(F.20)


( )BfC

BfhcA

R2

21

⋅= (F.21)

9. Conduction coefficient from back cover (hB) and the sides (he) of the

collector to the environment

A total conduction loss was calculated as a combination of back losses and side

losses in the following way:

• Losses from the back



283

B

BB x

hΔ

=κ (F.22)

BxΔ = thickness of insulation

• Losses from the sides

These losses were estimated by assuming one-dimensional heat flow around the

perimeter of the collector and referencing them to the collector aperture area93:

( ) TAhAhQ eeCBeB_loss_total Δ⋅⋅+⋅=+ (F.23)

( )C

CS

e

e

C

e

e

e'e wl

wlHxA

Ax

h⋅

+⋅⋅⋅

Δ=⋅

Δ=

2κκ (F.24)

(F.25)

(F.26)

( )C

CS

e

e

b

b

wlwlH

xxhB

⋅+⋅⋅

⋅Δ

+Δ

=2κκ (F.27)

If κe = κB (same material) and Δxe = ΔxB (same thickness), then:

( )⎥⎦

⎤⎢⎣

⎡

⋅+⋅⋅

+⋅Δ

=C

CS

wlwlH

xhB 21κ (F.28)


( )eBB AA

xR+⋅

Δ=

κ (F.29)

( ) TAhh C'eB Δ⋅⋅+

TAchB Δ⋅⋅

wC = collector width

44 344 21



284

F2 – Equations and calculations for heat loss in the pipe system of

the air heater SHWS

From the design rationale of section 7.1.1, (airflow rates of 60 L/s at 50°C, air

temperatures above 30°C) and for a pipe diameter of about 90 mm and from

Equation D.11 for the Reynolds number, airflow should always be turbulent (even if

it were to drop to a tenth of its value, i.e., 6 L/s => Re > 4400).

Considering this and since the downpipe to the exchanger was surrounded by a very

good insulator, it was assumed that the temperature of the internal wall, Twin, was

close to the temperature of the fluid, Tf. Therefore, Tf ≅ Twin.

Energy available at the end of a pipe section is given by Q1 (Figure 7.8):

1QQQQ effolossoo ==− −− (F.30)

From Equation 4.35, conduction losses through the walls of a long cylinder are:

( )ooutw

o

outwo

o

outwlosso TT

rrln

LT

rrln

LQ −⋅⎟⎠⎞

⎜⎝⎛

⋅⋅⋅=Δ⋅

⎟⎠⎞

⎜⎝⎛

⋅⋅⋅= −

−−−

κπκπ 22 (F.31)

Furthermore, Qo-loss, is dissipated in the environment mainly by convective currents:

( )outwamb'

cv''

cvo

o

outwlosso TTAhTAhT

rrln

LQ −−

− −⋅⋅=Δ⋅⋅=Δ⋅⎟⎠⎞

⎜⎝⎛

⋅⋅⋅=

κπ2 (F.32)

Where: o

outw'

rat rr

DD

AAA −=

+==

ς2 ; =ς thickness of the insulation

Finally, the resultant energy balance equations are:

( ) ( ) ( ) ( )ambpoutworat

ambop TTCmTTAln

LTTCm −⋅⋅=−⋅⋅⋅⋅

−−⋅⋅ − 12 κπ (F.33)

( ) ( ) ( )amboutw'

cvoutworat

TTAhTTAln

L−⋅⋅=−⋅

⋅⋅⋅−−

κπ2 (F.34)

Appendix G – Polynomial approximations of select

physical properties of air and water G1 - Approximations used in the application of heat transfer theory

for analysis and performance prediction of the SHWS

developed in this study.

In the development of the passive downward vapour phase transport SHWS

(Chapter 6) the numerical simulations and performance prediction of the heat transfer

theory developed required the use of the thermal conductivity, κ, kinematic viscosity,

ν, and thermal diffusivity, αt, for air of varying temperatures within the CPC cavity.

Likewise, the development of the solar air heater panel and associated SHWS

(Chapter 7) also required these quantities to be known, plus the specific heat and

density for the air flowing through the system. Additionally, it required a way of

determining the density and kinematic viscosity of the water in the thermosiphon

loop for varying temperatures.

Numerical calculation of these quantities was done in the programs developed by

approximating accepted values from data tables available in the literature to adequate

polynomial equations.

In this regard, the variation of thermal diffusivity, kinematic viscosity and thermal

conductivity for air vs. temperature were well approximated by linear fits with no

more than 2.5% deviation. The specific heat and density required 2nd order

polynomial fits giving errors below 0.2%. Water density versus temperature was

also approximated by a 2nd order polynomial with excellent results, also giving errors

below 0.2%. Water viscosity required a 3rd order polynomial fit in order for errors to

be below 6% in the range of operating temperatures of the system. Refer to the

tables and plots that follow.

All “accepted” tabulated values are taken from Holman (refer to bibliography).


Appendix G - Polynomial approximations of select physical properties of air and water

286

Table G1 Thermal diffusivity and kinematic viscosity for air at atmospheric

pressure

Temperature Thermal diffusivity, αt Kinematic viscosity, ν (K) (°C) (m2·s-1·10-5) (m2·s-1·10-5)

Fit Fit

250 -23 1.568 1.532 1.131 1.105 300 27 2.216 2.267 1.569 1.595 350 77 2.983 3.002 2.076 2.085 400 127 3.760 3.737 2.590 2.575

Error (max) 2.3% 2.4%

Table G2 Thermal conductivity, specific heat and density for air at

atmospheric pressure

Temperature Thermal conductivity, κ Specific heat, Cp Density, ρ (K) (°C) (W·m-1·°C-1) (kJ·kg-1·°C-1) (kg·m-3)

Fit Fit Fit

250 -23 0.02227 0.02225 1.0053 1.0048 1.4128 1.4137 300 27 0.02624 0.02605 1.0057 1.0058 1.1774 1.1761 350 77 0.03003 0.02985 1.0090 1.0087 0.9980 0.9985 400 127 0.03365 0.03365 1.0140 1.0136 0.8826 0.8809 Error (max) 0.8% 0.05% 0.2%

Fit equations: 57 1087110471 −− ⋅+⋅⋅= .T.airα (G1)

58 1033110809 −− ⋅+⋅⋅= .T.airν (G2)

25 1040210607 −− ⋅+⋅⋅= .T.airκ (G3)

00511071104 527 .T.TCairp +⋅⋅+⋅⋅= −− (G4)

297110841021 325 .T.T.air +⋅⋅−⋅⋅= −−ρ (G5)



287

(a)

(b)

Figure G1 Plots of the linear fits for thermal diffusivity, kinematic viscosity and thermal conductivity of air vs. temperature

Thermal conductivity of air vs. temperature

y = 7.6E-05x + 2.4E-02

R = 0.9995

0.021

0.023

0.025

0.027

0.029

0.031

0.033

0.035

-40 -20 0 20 40 60 80 100 120 140

Temperature (°C)

Ther

mal

con

duct

ivity

(W/m

·°C

)

Temperature (K)

Physical properties of air vs. temperature

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

-30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

Kin

emat

ic v

isco

sity

& T

herm

al d

iffus

ivity

(m2 /s

)·10-5

y = 1.469E-07x - 2.142E-05

R = 0.9991

y = 9.768E-08x - 1.333E-05

R = 0.9993

Kinematic viscosity

Thermal diffusivity



288

(a)

(b)

Figure G2 Plots of polynomial fits for specific heat and density of air vs. temperature

Specific heat of air vs. temperature

y = 4E-07x2 + 1.7E-05x + 1.005 R = 0.9985

1.004

1.005

1.006

1.007

1.008

1.009

1.01

1.011

1.012

1.013

1.014

1.015

1.016

-40 -20 0 20 40 60 80 100 120 140 Temperature (°C)

Spe

cific

Hea

t (kJ

/kg·

°C)

y = 1.2E-05x2 - 4.8E-03x + 1.297 R > 0.9995

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

-30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130

Density of air vs. temperature

Temperature (°C)

Den

sity

(Kg/

m3 )



289

Table G3 Selected properties for water at atmospheric temperature

Temp. Dynamic viscosity, η Density, ρ (°C) (kg/m·s)·10-4 (kg/m-3)

Fit Fit

0 17.9 17.6 999.8 998.0 4.44 15.5 15.6 999.8 997.9 10 13.1 13.3 999.2 997.6

15.56 11.2 11.4 998.6 997.0 21.11 9.80 9.85 997.4 996.2 26.67 8.60 8.53 995.8 995.2 32.22 7.65 7.44 994.9 993.8 37.78 6.82 6.56 993 992.3 43.33 6.16 5.87 990 990.5 48.89 5.62 5.32 988.8 988.4 54.44 5.13 4.89 985.7 986.1

60 4.71 4.56 983.3 983.6 65.55 4.30 4.28 980.3 980.8 71.11 4.01 4.04 977.3 977.8 76.67 3.72 3.79 973.7 974.5 82.22 3.47 3.52 970.2 971.0 87.78 3.27 3.19 966.7 967.2 93.33 3.06 2.76 963.2 963.2 Error (max)

5.5% 0.2%

Fit equations: 0017601085410261092 52739 .T.T.T.wat +⋅⋅−⋅⋅+⋅⋅−= −−−η (G6)

9980040 2 +⋅−= T.watρ (G7)



290

(a)

(b)

Figure G3 Plots of the polynomial fits for selected physical properties of air vs. temperature

Water density vs. temperature

y = -0.004x2 + 998

960

965

970

975

980

985

990

995

1000

1005

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Temperature (°C)

Den

sity

(kg/

m3 )

Water viscosity vs. temperature

0

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0 10 20 30 40 50 60 70 80 90 100 Temperature (°C)

Vis

cosi

ty (k

g/m

·s)

y = -2.90E-09x3 + 6.20E-07x2 - 4.85E-05x + 1.76E-03

Appendix H – Air/water heat exchanger and fan-blower

motor H1 – Compact heat exchanger (heater core) used in the air-to-water

heat exchanger-water tank coupled SHWS

The heat exchanger core used is fabricated for cabin air heating of motor cars,

specifically: Toyota Corona vehicles from 1983 through 1996, Nissan model 200B

and Toyota Camry ST141.

Table H1 Specifications for the heat exchanger core

Manufacturer Denso Pty Ltd – 0Hwww.denso.com.au Part No. ND803 (also HTR 803.N8T) Body construction Copper core Heater core dimensions 160cm × 160cm × 49cm Top header dimensions 160cm × 59cm Bottom header dimensions 160cm × 59cm

Figure H1 Picture-schematic of original heater core used as a heat exchanger


Appendix H - Air/water heat exchanger and fan/blower motor

292

H2 – Centrifugal fan-blower motor used in the air-to-water

heat exchanger-water tank coupled SHWS

This unit is used as a source of pressurised air for ventilation and heating systems,

particularly for cabin heating of buses and trucks.

Table H2 Specifications of the fan/blower motor

Manufacturer Torin Fans & Blowers Pty Ltd

Model No. H30730 Nominal voltage 13.5 Volts DC

Low 65 Medium 93 Nominal airflow –

free discharge (L/s) High 130 Low 5.2 Medium 9 Nominal current

(A) High 16.8 A 106 × 106

Dimensions (mm) B 90

Figure H2 Picture-schematic of the fan/blower

B

A

Appendix I – Anemometer calibration

I1 – Two-step calibration process for accurate anemometer readings For the final study of variations in exchanger effectiveness with changing

temperatures and flow rates of the fluids (section 7.5.2) the anemometer was used to

determine airflow rates. Since its operation was deemed unreliable at the early

stages of the project, a more comprehensive look into the anemometer readings and

more accurate calibration with known airflow rates was obtained.

The calibration was done in a two step process:

1- First the velocity profile for airflow across the transverse area of the pipes was

measured. Readings of air speed were taken at different distances from the wall

of the pipe. A polynomial expression was fitted to the experimental data

(Figure I1) and an average flow rate was determined by integration over the

transverse area of the pipe. The ratio between this average and the value

obtained from the peak reading at the centre of the pipe resulted in a primary

calibration factor, cal1. Since experimental measurements were taken with the

anemometer in the centre of the pipe, this calibration allowed for a more accurate

account of the (real) average airflow speed. The result, however, required

another calibration against known air speed values since there was no way of

knowing if the absolute readings of the anemometer were accurate or not.

2- The anemometer was then fixed to the outer edge of a rotary clothesline (Hills

Hoist) of 2.6 m radius, which was rotated at a constant pace for different periods.

The tangential speed at its periphery was easily determined from the number of

turns it was given over the period of measurement. Several runs were made for

increasing air speeds and the results were compared with the values for airflow

speed obtained from the anemometer. A linear correlation between the data was

obtained and from there a secondary calibration factor, cal2 (Figure I2).



294

Figure I1 Speed profile for airflow in the pipes vs. transverse distance and polynomial fit

The ratio of the average flow rate to the maximum flow rate obtained from the peak

speed measured at the centre of the pipe gives the first calibration factor.

From Equation 5.19: pipepeak_airpeak_air Areav ⋅=Φ (I.1)

Where: sL

sm

peak_airpipe

sm

peak_air.

m.Area

v290290

1085

53

23 =≈Φ⇒⎪⎭

⎪⎬⎫

⋅=

=−

From the polynomial fit: [ ] 5080010 24 +⋅−⋅−= r.r.vs

m)r( (I.2)

The average flow rate is found by integrating over the area:

drrv )r(

.

air ⋅⋅⋅=Φ ∫ π234

0 (I.3)

sL.

sm.rr.r.

.

air 118018101050403010 3

4

34

0

246 =≈×⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⎥⎦

⎤⎢⎣

⎡⋅+⋅−⋅−⋅=Φ −π

6201 .calpeak_air

air ≈Φ

Φ= (I.4)

Transverse speed profile of airflow in the pipe system

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Distance from the centre of the pipe (cm)

Air

spee

d (m

/s)

y = -0.01x4 - 0.08x2 + 5 R2 > 0.99

Pipe radius = 4.3 cm



295

Figure I2 Correlation between anemometer readings and known air speed values

showing a strong linear fit to the data.

The linear fit to the data allows a more accurate determination of real airflow speeds

from the anemometer:

250650 .v.v anem_airreal_air −⋅≅ (I.5)

The second calibration factor is the ratio of the two airflow speeds:

anem_airanem_air

real_air

v..

vv

cal 2506502 −== (I.6)

This factor is not static and should be built into the calculations for each anemometer

reading. However, for simplicity, it is possible to use a constant value provided

airflow rates do not change much. For the calculations of section 7.5.2, where two

different airflow rates were used (10.8 m/s and 7.5 m/s), a constant calibration factor

of 0.62 was applied

Calibration curve for anemometer against known airflow speeds

y = 0.65x - 0.25

R2 > 0.99

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

Anemometer readings (m/s)

Acc

urat

e ai

r spe

ed m

easu

rem

ents

(m/s

)

Bibliography

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