performance evaluation of solar air heater for various artificial roughness geometries based on...

7/28/2019 Performance evaluation of solar air heater for various artificial roughness geometries based on energy, effective

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Review

Performance evaluation of solar air heater for various artificial roughness

geometries based on energy, effective and exergy efficiencies

M.K. Gupta*, S.C. Kaushik

Centre for Energy Studies, Indian Institute of Technology, Delhi 110016, India

a r t i c l e i n f o

Article history:

Received 21 March 2008

Accepted 5 June 2008

Available online 24 July 2008

Keywords:

Solar air heater

Artificial roughness geometries

Energy efficiency

Effective efficiency

Exergy efficiency

Reynolds number

a b s t r a c t

A comparative study of various types of artificial roughness geometries in the absorber plate of solar air

heater duct and their characteristics, investigated for the heat transfer and friction characteristics, has

been presented. The performance evaluation in terms of hI, hef and hII has been carried out, for various

values of Re, for some selected artificial roughness geometries in the absorber plate of solar air heater

duct. The six roughness geometries as per the order of ability to create turbulence and a smooth surface

have been selected. The correlations for heat transfer and coefficient of friction developed by respective

investigators have been used to calculate efficiencies. It is found that artificial roughness on absorber

surface effectively increases the efficiencies in comparison to smooth surface. The hI in general increases

in the following sequence: smooth surface, circular ribs, V shaped ribs, wedge shaped rib, expanded

metal mesh, rib-grooved, and chamfered ribgroove. The hef based criteria also follows same trend of

variation among various considered geometries, and trend is reversed at very high Re. The hII based

criteria also follows the same pattern; but the trend is reversed at relatively lower value of Re and for

higher range ofRe the hII approaches zero or may be negative. It is found that for the higher range of Re

circular ribs and V shaped ribs give appreciable hII up to high Re; while for low Re chamfered ribgroove

gives more hII.

2008 Elsevier Ltd. All rights reserved.

1. Introduction

The heat transfer between the absorber surface (heat transfer

surface) of solar air heater and flowing air can be improved by

either increasing the heat transfer surface area using extended

and corrugated surfaces without enhancing heat transfer

coefficient or by increasing heat transfer coefficient using the

turbulence promoters in the form of artificial roughness on

absorber surface. The artificial roughness on absorber surface may

be created, either by roughening the surface randomly with

a sand grain/sand blasting or by use of regular geometric rough-

ness. It is well known that in a turbulent flow a laminar/viscoussub-layer exists in addition to the turbulent core. The artificial

roughness on heat transfer surface breaks up the laminar

boundary layer of turbulent flow and makes the flow turbulent

adjacent to the wall. The artificial roughness that results in the

desirable increase in the heat transfer also results in an undesir-

able increase in the pressure drop due to the increased friction;

thus the design of the flow duct and absorber surface of solar air

heaters should, therefore, be executed with the objectives of high

heat transfer rates and low friction losses. To balance useful

energy and friction losses, second law considerations are suitable,

and exergy is a suitable quantity for the optimization of solar air

heaters having different design and roughness elements.

Exergy is maximum work potential which can be obtained from

a form of energy [1,2]. Exergy analysis is a useful method, to com-

plement not to replace the energy analysis. Exergy analysis yields

useful results because it deals with irreversibility minimization or

maximum exergy delivery. Exergy analysis can indicate the possi-

bilities of thermodynamic improvement of the process under

consideration. The exergy analysis has proven to be a powerful tool

in the thermodynamic analyses of energy systems. Recently, theconcept of exergy has received great attention from scientists,

researchers and engineers, and exergy concept has been applied to

various utility sectors and thermal processes. In general, more

meaningful efficiency is evaluated with exergy analysis rather than

energy analysis, since exergy efficiency is always a measure of the

approach to the ideal. Ozturk and Demirel [3] experimentally

evaluated the energy and exergy efficiencies of the thermal per-

formance of a solar air heater having its flow channel packed with

Raschig rings. Kurtbas and Durmus [4] experimentally evaluated

the energy efficiency, friction factor and dimensionless exergy loss,

of a solar air heater having five solar sub-collectors of same length

and width arranged in series in a common case, for various values

* Corresponding author. Tel.: 91 11 26591253; fax: 91 11 26862037.

E-mail addresses: [email protected] , [email protected]

(M.K. Gupta), [email protected] (S.C. Kaushik).

Contents lists available at ScienceDirect

Renewable Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / r e n e n e

0960-1481/$ see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.renene.2008.06.001

Renewable Energy 34 (2009) 465476
mailto:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/09601481http://www.elsevier.com/locate/renenehttp://www.elsevier.com/locate/renenehttp://www.sciencedirect.com/science/journal/09601481mailto:[email protected]:[email protected]:[email protected]


2/12

of Reynolds number. The popularity of exergy analysis method has

grown consequently and is still growing [1,57].

2. Fluid flow and heat transfer characteristic of

various type of artificial roughness geometry

The geometry of the artificial roughness has, therefore, to be

such that it should break the laminar sub-layer only without

disturbing the core to keep the pressure drop within range. The

regular geometric roughness may be classified on the basis of shape

of rib (rectangular, circular, wedge, chamfered), orientation

(transverse, inclined, V shape), arrangement on surface (continu-

ous, discrete, staggered), cavity (groove, pits/dimples) and imper-meable or porous rib. The porous rib offers lower drag force in

comparison to solid rib. Many investigators analysed various

roughness geometry [813] and attempted to develop accurate

predictions of the heat transfer coefficient and friction factor of

a given roughness geometry, and to define a roughness geometry

which gives the best heat transfer performance for a given flow

friction. Webb et al. [9] developed friction and heat transfer

correlations, for turbulent flow in tubes having repeated rib-

roughness, based on law of the wall similarity and application of

the heatmomentum transfer analogy to flow over a rough surface,

respectively. They verified the correlations with experimental data,

and argued against a single correlation for all roughness geome-

tries. Han et al. [10] investigated the rib-roughened surface for

effects of rib shape, angle of attack, spacing and pitch to heightratio. They developed the correlation for friction factor and heat

Nomenclature

Ac Collector area (m2)

Cf Conversion factor

Cp Specific heat (J/kg K)

de Equivalent hydraulic diameter of collector duct (m)

e Rib height

e Roughness Reynolds number

Ex Exergy (W)

Exc,S Exergy of solar radiation incident on glass cover (W)

Exu Exergy output rate ignoring pressure drop (W)

Exu,p Exergy output rate considering pressure drop (W)

Exd,p Exergy destruction due to pressure drop (W)

F0 Collector efficiency factor

Fr Collector heat removal factor

f Coefficient of friction

g Groove position (m)

h Enthalpy (J/kg)

hc,fb Convective heat transfer coefficient between air and

bottom plate (W/m2 K)

hc,fp Convective heat transfer coefficient between air and

absorber plate (W/m2 K)he Equivalent heat transfer coefficient (W/m

2 K)

hr,pb Radiative heat transfer coefficient between absorber

and bottom plate (W/m2 K)

hw Wind heat transfer coefficient (W/m2 K)

H Solar air heater duct depth (m)

I Radiation intensity (W/m2)

IT,c Radiation incident on glass cover (W/m2)

IR Irreversibility (W)

ki Thermal conductivity of insulation (W/m K)

ka Thermal conductivity of air (W/m K)

l Long way of mesh

L Spacing between covers (m)

L1 Collector length (m)

L2 Collector width (m)L3 Collector depth (m)

m Mass flow rate (kg/s)

M Number of glass cover

p Pressure (N/m2)

P Roughness pitch

Pr Prandtals number

Q Heat (J)

q Heat per unit area (J/m2)

Re Reynolds number

s Short way of mesh

S Absorbed flux (W/m2)

Sgen Entropy generation (J/K)

St Stanton number

T Temperature (K)

Tbm Mean bottom plate temperature (K)

Tfm Mean fluid temperature (K)

Tpm Mean absorber plate temperature (K)

Ub Bottom heat loss coefficient (W/m2 K)

Ul Overall heat loss coefficient (W/m2 K)

Us Side heat loss coefficient (W/m2 K)

Ut Top heat loss coefficient (W/m2 K)

V Velocity of air through collector duct (m/s)

VN

Wind velocity (m/s)

WP Pump work (W)

Greek symbols

aA Angle of attack for V shaped rib

aC Chamfer angle of rib

aR Rib wedge angle

b Tilt angle of collector surface

db Bottom insulation thickness (m)

ds Side insulation thickness (m)

Dp Pressure drop (N/m2)

hI Energy efficiency

hII Exergy efficiencyhef Effective energy efficiency

hpm Pumpmotor efficiency

m Viscosity of air (Ns/m2)

r Density of air (kg/m3)

s Transmissivity

sa Transmissivityabsorptivity product

j Exergy efficiency of radiation

s Stefans constant

3c Emmisivity of cover

3p Emmisivity of absorber plate

Subscripts

a Ambient

f Fluid (air)fb Fluid (air) to bottom plate

fp Fluid (air) to absorber plate

g glass

i Inlet

l Lost

o outlet/exit

p Plate

r Rough

s Smooth

S Sun

T Tilted surface

u Useful

M.K. Gupta, S.C. Kaushik / Renewable Energy 34 (2009) 465476466


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transfer, in order to define a roughness geometry which gives the

best heat transfer performance for a given flow friction. The use of

artificial roughness in solar air heaters owes its origin to several

investigations carried out in connection with the enhancement of

heat transfer in nuclear reactors [10], cooling of turbine blades and

electronic components. As in solar air heater the solar radiation is

absorbed by absorber plate,which is the main heat transfer surface;

therefore, the solar air heaters are modeled as a rectangular

channel having one rough wall and three smooth walls.

Prasad and Mullick [14] recommended protruding wires on the

underside of the absorber plate of an unglazed solar air heater used

for cereal grains drying to improve the heat transfer characteristics

and hence the plate efficiency factor.

Prasad and Saini [15] developed the relations to calculate the

average friction factor and Stanton number for artificial roughness

of absorber plate by small diameter protrusion wire. They used

these relations to compare the effect of height and pitch of

roughness element on heat transfer and friction factor with already

available experimental data. The friction factor for one side rough

duct is determined byassuming that the total shear force in the one

side rough duct is approximately equal to the combined shear force

from three smooth walls in a four-sided smooth duct and the shear

force from one rough wall in a four-sided rough duct. They used thefriction similarity law and heatmomentum transfer analogy.

Saini and Saini [16] carried out experimental investigation for

fully developed turbulent flow in a rectangular duct having

expanded metal mesh as artificial roughness, and developed

correlations for Nusselt number and friction factor in terms of

geometry of expanded metal mesh.

Karwa et al. [17] carried out experimental investigation, to

develop the correlation of heat transfer and friction, for flow of air

in rectangular ducts with integral and repeated chamfered rib-

roughness on one broad uniformly heated wall, and remaining

walls insulated. They observed that the Stanton number and

friction factor take their maximum values at the chamfer angle

of 15.

Verma and Prasad [18] developed the heat transfer and frictionfactor correlation for roughness elements consisting of small

diameter wires, and evaluated the thermo-hydraulic performance

using the efficiency index suggested by Webb and Eckert [20]. The

criterion for efficiency index, which is Str=Sts=fr=fs1=3, is heat

transfer of roughened duct to smooth wall duct for same pumping

power.

Jaurker et al. [19] developed the correlations for Nusselt number

and friction factor, for rib-grooved artificial roughness on one broad

heated wall. They carried out the thermo-hydraulic performance

analysis of air duct (solar air heater), based on efficiency index [20],

andconcluded that rib-grooved arrangement is better than rib only.

Similar investigations for heat transfer and fluid flow charac-

teristics have been carried out by Gupta et al. [21] for transverse

wire roughness; Momin et al. [22] for V shaped ribs; Bhagoria et al.[23] for wedge shaped rib; Sahu and Bhagoria [24] for broken

transverse ribs; and Layek et al. [25] for chamfered ribgroove

roughness.

Gupta et al. [26] investigated the thermo-hydraulic performance

in terms of effective efficiency [27] of solar air heater with rib-

roughened surface by using the heat transfer and friction factor

correlation developed by them. The effective efficiency is ratio of

net thermal energy gain to the incident radiation. The effective

efficiency takes in account the pump work by subtracting the

equivalent thermal energy from useful heat gain by air heater to get

net thermal energy gain. The equivalent thermal energy is the

amount of thermal energy that will be required to produce the

friction power/ pump work after considering the various efficien-

cies (thermal power plant efficiency; transmission efficiency; mo-tor efficiency; efficiency of the pump) of conversion from a typical

thermal power plant to the site of collector installation. Though the

effective efficiency takes in account the pump work/equivalent

thermal energy, but it does not distinguish the quality of thermal

energy. The quality of thermal energy required in thermal power

plant is superior than obtained by air heater. For a given duct

roughness geometry they computed the effective efficiency by

varying relative roughness height and mass flow rate for different

insolation, an angle of attack 60, ambient temperature equals to

300 K and wind velocity 1 m/s. They concluded that effective

efficiency attains a maximum as flow rate is varied and effective

efficiency is found to decrease with roughness height.

Karwa et al. [28] carried out the experimental investigation for

the performance of solar air heaters with chamfered repeated rib-

roughness on the airflow side of the absorber plates, and reported

substantial enhancement in thermal efficiency over solar air

heaters with smooth absorber plates. They theoretically evaluated

the thermal efficiency using correlations [17] and concluded that

these correlations can be utilized with confidence for prediction of

the performance of solar air heaters with absorber plates having

integral chamfered rib-roughness. Based on effective efficiency,

they reported that at lower Reynolds numbers relative roughness

height should be high while at higher Reynolds numbers (>14,000)

either smooth duct or roughened duct with less relative roughnessheight performs better.

Mittal et al. [29] evaluated and compared the effective

efficiency, of solar air heaters having different roughness geometry

on absorber plate, for a set of fixed system and operating param-

eters. They determined the effective efficiency by using the corre-

lations for heat transfer and friction factor developed by various

investigators. They plotted the variation of the effective efficiency

with Reynolds number for smooth absorber plate, as well as

roughened absorber plate solar air heaters for different relative

roughness height. They reported that at higher Reynolds numbers

either smooth duct or roughened duct with less relative roughness

height performs better, and reverse for lower Reynolds number.

The Reynolds number for maximum effective efficiency was in the

range 10,00014,000 for the set of parameters investigated.Layek et al. [30] numerically calculated the augmentation

entropy generation number [31] in the duct of solar air heater

having repeated transverse chamfered ribgroove roughness on

one broad wall [25]. They evaluated the entropy generation during

heat exchange between flowing air and absorber plate.

It is evident that various investigators have developed correla-

tions for heat transfer and friction factor for solar air heater ducts

having artificial roughness of different geometries. Several

researchers carried out the thermo-hydraulic performance evalu-

ation on the basis of efficiency index or effective efficiency; but the

exergy based performance evaluation of solar air heater duct

having artificial roughness on absorber plate has not been reported

so far. Thus the aim of present investigation is to carry out the

performance evaluation of the some selected artificial roughnessgeometry (Fig. 1) on the basis of exergy analysis.

2.1. Effect of Reynolds number and roughness geometry

on heat transfer and friction characteristics

There are several parameters that characterize the roughness

elements, but for heat-exchanger and solar air heater the most

preferred roughness geometry is repeated rib type, which is

described by the dimensionless parameters viz. relative roughness

height e/de and relative roughness pitch P/e. The friction factor and

Stanton/Nusselt number are function of these dimensionless

parameters, assuming that the rib thickness is small relative to rib

spacing or pitch. Although the repeated rib surface is considered as

roughness geometry, it may also be viewed as a problem inboundary layer separation and reattachment [9]. The rib creates

M.K. Gupta, S.C. Kaushik / Renewable Energy 34 (2009) 465476 467


4/12

turbulence, by generating the flow separation regions (vortices)

one on each side of the rib, which results in enhancement in heat

transfer as well as friction. Fig. 2 shows the various possible flow

patterns downstream from a rib, as a function of the relative

roughness pitch P/e [9]. Flow separates at the rib, forms a widening

free shear layer, and reattaches at a distance of 68 times rib-

roughness height downstream from the rib. Reattachment does not

occur for P/e less than about eight except for chamfered rib or rib

groove roughness. The local heat transfer coefficients in the sepa-

rated flow region are larger than those of an undisturbed boundary

layer and wall shear stress is zero at the reattachment point; themaximum heat transfer occurs in the vicinity of the reattachment

point. A reverse flow boundary layer originates at the reattachment

point and tends toward redevelopment downstream from the

reattachment point. The effect of various parameters of artificial

roughness geometry on heat transfer and friction characteristics

based on the literature is given below:

1. Effect of Reynolds number: as the Reynolds number increases,

the friction factor decreases due to the suppression of viscous

sub-layer and approaches a constant value; whereas the

Nusselt number increases monotonously with Reynolds

number.

2. Effect of relative roughness height e/de: the enhancement of

heat transfer coefficient depends on the flow rate and therelative roughness height. As e/de increases, both the friction

factor and Nusselt number increase. The rate of increase of

average friction factor increases whereas the rate of increase of

average Nusselt number decreases, with the increase of relative

roughness height. At very low Reynolds number the effect ofe/

de is insignificant on enhancement of Nusselt number. If the

roughness height is less than thickness of laminar sub-layer

then there will not be any enhancement in heat transfer, hence

the minimum roughness height should be of same order as

thickness of laminar sub-layer at the lowest flow Reynolds

number. The maximum rib height should be such that the fin

and flow passage blockage effects are negligible.3. Rib cross-section: it is reported that by changing the rib cross-

section from rectangular to trapezoidal the friction factor is

reduced; while there is minor effect on reduction of Nusselt

number and this effect disappears at higher values of Reynolds

number.

4. Effect of relative roughness pitch P/e: the behavior has been

explained on the basis of flow separation. Forsmall P/e the flow

which separates after each rib does not reattach before it

reaches the succeeding rib. For larger relative roughness pitch

at a P/e value of about 10 the reattachment point is reached and

a boundary layer begins to grow before the succeeding rib is

encountered. However, enhancement decreases with an

increase in P/e beyond about 10.

5. Effect of angle of attack: the induced form drag is reduced dueto change in angle of attack for ribs from 90 (transverse), and

a better thermal to hydraulic performance is obtained by hav-

ing optimum angle of attack. As the angle of attack decreases,

the friction factor reduces rapidly; however, there is marginal

decrease in Nusselt number with change in angle of attack from

90 to 45. Both the heat transfer and the friction approach the

smooth wall case as the angle of attackis decreased further. The

two fluid vortices immediately upstream and downstream of

a transverse rib are essentially stagnant relative to the

mainstream flow. The span wise secondary flow created by

inclination of the rib, and movement along the rib to

subsequently join the mainstream, is responsible for the

significant span wise variation of heat transfer coefficient.

The same concept also applies in V shape arrangement of theribs and it has been reported that such arrangement enhances

Fig. 1. Roughness geometry investigated by: [a] Saini and Saini [16], [b] Verma and

Prasad [18], [c] Momin et al. [22], [d] Bhagoria et al. [23], [e] Jaurker et al. [19], [f] Layek

et al. [30].

Fig. 2. Flow pattern as a function of relative roughness pitch.



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the heat transfer more. The apex of such rib may be up or

downstream to flow. It can be said, on the basis of flow be-

havior, that both Stanton number and friction factor are higher

for apex down. It may be pointed out that the expanded metal

mesh is a combination of apex up and down V shape ar-

rangement of the ribs.

6. Chamfering of the rib: chamfering of the rib decreases the

reattachment length by deflecting the flow and to reattach it

nearer to the rib. The decrease in reattachment length permits

to organize the ribs more closely. Chamfering of the rib also

increases the shedding of vortices generated at the rib top that

results in increase turbulence. The optimum chamfering angle

on the basis of thermodynamically performance has been

reported equal to 1518. For higher chamfer angle flow

separates from the rib top surface and generates boundary

layer, which decreases the heat transfer. The friction factor

increases monotonously due to the creation of vortices.

7. Combined turbulence promoter: the groove in inter rib space

and nearer the reattachment point of heat transfer surface

induces vortices in and around the groove. These vortices

increase the intensity of turbulence. The optimum relative

roughness pitch is less in comparison to simple ribbed

surface; the reported optimum relative groove position g/P isabout 0.4.

3. Thermodynamic modeling

3.1. Analysis of solar air heater

The collector under consideration consists of a flat glass cover

and a flat absorber plate with a well insulated parallel bottom plate

forming a passage of high duct aspect ratio through which the air to

be heated flows as shown in Fig. 3. The heat gain by air may be

calculated by following equations

Qu Ac

S Ul

Tpm Ta

AcsgapIT;c Ul

Tpm Ta

(1)

Qu mcpTo Ti (2)

Qu AcFrS UlTi Ta (3)

where Fr is collector heat removal factor and is given by

Fr mcpUlAc

"1 e

UlAc F0

mcp

#(4)

The collector efficiency factor F0 is

F0

1

Ulhe

1(5)

and the equivalent heat transfer coefficient he is

he hc;fp hr;pbhc;fb

hr;pb hc;fb

(6)The hc,fp and hc,fb are heat transfer coefficient due to convec-

tion from absorber plate to flowing air, and from bottom plate to

flowing air, respectively. The hr,pb is heat transfer coefficient due to

radiation from absorber plate to bottom plate.

The mean absorber plate temperature from Eqs. (1) and (3) isgiven by

Tpm Ta Ql

UlAc Ti

QuAcFrUl

1 Fr (7)

where Ql SAc Qu is heat loss from the air heater.

The mean fluid temperature is given by

Tfm 1

L1

ZL10

Tf dx Ti Qu

AcFrUl

1

FrF0

(8)

Considering solar air heater (Fig. 3) as a control volume (CV), the

law of exergy balance [2] for this CV can be written as

Exi Exc;S ExW Exo IR (9)where Exi and Exo are the exergy associated with mass flow of

collector fluid entering and leaving the CV; Exc;S IT;cAcjS [32] is

exergy of solar radiation falling on glass cover; ExW is exergy of

work input required to pump the fluid through FPSC, and IR is ir-

reversibility or exergy loss of the process. The exergy balance (Eq.

(9)) can be written as

IR Exc;S Exo Exi ExW (10)

The term in the bracket (Eq. (10)) represents the useful

exergy or exergy output rate delivered by the solar collector. As

the Exc,S, exergy of solar radiation falling on glass cover, is

fixed for a particular instant; thus minimization of entropy

generation or irreversibility is equivalent to maximization of

exergy output rate delivery of collector. Thus our aim in FPSC

must be to increase the exergy output rate delivered to

collector fluid out of the solar radiation/heat absorbed by the

absorber. The useful exergy or exergy output rate Exu

delivered by a solar collector using exergy balance equation for

collector fluid, ignoring pressure drop/pumping work Wp or

ExW, is given by

Exu mho Taso hi Tasi mho hi Taso si

(11)

For an incompressible fluid or perfect gas it can be written as

Exu mcpTo Ti Ta lnTo=Ti Qu mcpTa lnTo=Ti

(12)

The Exu,p, actual exergy rate delivered considering pressure drop

of collector fluid, is

Exu;p Exu Exd;p (13)

where the exergy destruction due to pressure drop Exd,p is

Exd;p TaTi

Wp (14)

The Wp, pump work, is

Wp mDp=hpmr

(15)

where hpm, the pumpmotor efficiency, is taken equal to 0.85.Fig. 3. Flat plate solar air heater.



6/12

Table 1

Correlations for heat transfer and coefficient of friction

Authors Types of

roughness

Correlations

Nusselt number Coefficient of friction

Saini and

Saini [16]

Expanded

metal meshNu 4:0 104Re1:22

e

de

0:625 s10e

2:22 l10e

2:66

exp

1:25

ln

s

10e

2!exp

" 0:824

ln

l

10e

2#f 0:815Re0:361

10e

de

0:591 le

0:266 s10e

0:19

Verma and

Prasad

[18]

Circular

ribsNu 0:08596Re0:723

e

de

0:072Pe

0:054for e 24

Nu 0:02954Re0:802

e

de

0:021Pe

0:016for e > 24

9=;

where e e

de

ffiffiffif

2

rRe

f 0:245Re1:25

e

de

0:243Pe

0:206

Momin

et al. [22]

V shaped

ribsNu 0:067Re0:888

e

de

0:424aA60

0:077exp

0:782

ln

aA60

2!f 6:266Re0:425

e

de

0:565aA60

0:093

exp 0:719lnaA60

2

!

Bhagoria

et al. [23]

Wedge

shaped ribNu 1:89 104Re1:21

e

de

0:426Pe

2:94aR10

0:018

exp

" 0:71

ln

P

e

2#exp

1:5

ln

aR10

2!f 12:44Re0:18

e

de

0:99Pe

0:52aR10

0:49

Jaurker et al.

[19]

Rib-

groovedNu 0:002062Re0:936

e

de

0:349Pe

3:318exp

"

0:868

ln

P

e

2#exp

2:486

ln

g

P

21:406

ln

g

P

3!gP

1:108f 0:001227Re0:199

e

de

0:585

P

e

7:19g

P

0:645

exp

"1:854

ln

P

e

2#exp

1:513

ln

g

P

2

0:862

lng

P

3!


7/12

3.2. Heat transfer and pressure drop

The overall heat loss coefficient Ul is sum of Ub, Us and Ut of

which Ub and Us for a particular collector can be regarded as con-

stant while Ut varies with temperature of absorber plate, number of

glass covers and other parameters. The top heat loss coefficient Ut is

evaluated empirically [33] by

Ut

264

MC

Tpm

Tpm Ta

M f0

0:252 1hw375

1

s

T2pm T2a

Tpm Ta

1

3p 0:0425M

1 3p 2M f0 1

3c M

26664

37775 16

In which f0 9=hw 9=h2wTa=316:91 0:091M,

C 204:429cos b0:252=L0:24 and the heat transfer coefficient

due to convection at the top of cover due to wind is

hc;ca

hw

5:7

3:8VN (17)

The overall loss coefficient is given by

Ul Ub Us Ut In which Ub kidb

and

Us L1 L2L3ki

L1L2ds18

The radiation heat transfer coefficient hr,pb between absorber

plate and bottom plate is given by

hr;pb

Tpm Tbm

s

T4pm T4bm

1

3p

1

3b 1

(19)

For small temperature difference between Tpm and Tbm on ab-

solute scale the above equation can be written as

hr;pby4sT3av=1=3p 1=3b 1, where Tav Tpm Tbm=2

and Tav is taken equal toTfm in iterativecalculation using thesame logic.

For smooth duct the convection heat transfer coefficients be-

tween flowing air and absorber plate hc,fp, and flowing air and

bottom plate hc,fb are assumed equal. The following correlation for

air, for fully developed turbulent flow (if length to equivalent di-

ameter ratio exceeds 30) with one side heated and the other side

insulated [34] is appropriate:

Nu hc;fpde

ka 0:0158Re0:8 (20a)

If the flow is laminar then following correlation by Mercer fromDuffie and Beckman [35] for the case of parallel smooth plates with

constant temperature on one plate and other plate insulated is

appropriate:

Nu hc;fpde

ka 4:9

0:0606

Re Pr

deL1

0:5

1 0:0909

Re Pr

deL1

0:7Pr0:17

(20b)

The characteristic dimension or equivalent diameter of duct is

given by

de

2L2H

L2 H (21)Layeketal.

[30]

Chamfered

ribgroove

Nu

0:

00225Re0

:92

ede

0

:52P e1

:72g P

1:

21

a1

:24

C

exp

"

0:

46

ln

P e2#e

xph

0:

22lnaC2i

exp

0:

74

lng P2!

f

0:

00245Re

0:

124

ede

0

:365P e4

:32g P

1:

24

exp0

:005aC

exp1

:09lnP e

2

exp0

:68lng P2

i

i

e=de:

0:

022

0:

04f0

:04g

P=e:4

:5

10f6g

g=P:0

:3

0:

6f0

:4g

aC:

5

30f18g

Re:

30

00

21

;000



8/12

For a particular Reynolds number Re, the velocity of flow is

calculated by

V mRe

rde(22)

While the mass flow rate is calculated by

m L2HVr mL2 HRe2 (23)

The pressure loss Dp through air heater duct is

Dp 4fL1V

2r

2de(24)

If Re rVde=m 2300, i.e. laminar flow, then coefficient of

friction for smooth duct is calculated by

f 16

Re(25)

otherwise the coefficient of friction f for the turbulent flow in

smooth air duct is calculated from Blasius equation, which is

f 0:0791Re0:25 (25b)

The correlations developed for heat transfer and friction

factor, for artificially roughened solar air heater of some selected

roughness geometries by their investigators are given in Table 1.

The equivalent heat transfer coefficient for roughened solar air

heater is calculated from he kaNu=de, using the Nusselt

number relation of that particular roughness geometry; similarly

the coefficient of friction f is calculated using the relation of that

particular roughness geometry. Table 1 also shows the range of

parameters investigated by the respective investigators. For Re

less than the lowest value of investigation, the correlations for

smooth duct are used even though the duct is roughened. As at

lower Re the variation in Nu with roughness parameters i.e. P/e, e/

de is insignificant, hence, for Re less than the lowest value ofinvestigation, the heat transfer and coefficient of friction corre-

lation for smooth duct are used. Also for laminar flow and

turbulent flow at low Re, as fdoes not depend on roughness, thus

as per Nuners law the correlation for smooth duct can be used

even though the duct is roughened.

3.3. Energy efficiency, effective efficiency and exergy efficiency

The energy efficiency of solar air heater based on first law of

thermodynamics is calculated by

hI Qu

IT;cAc(26)

The effective efficiency [27] of solar air heater is calculated by

hef Qu

Wp=Cf

IT;cAc

(27)

The conversion factor Cf takes in account various efficiencies

(thermal to mechanical) and is taken 0.2.

The exergy collection efficiency based on second law of

thermodynamics, by taking exergy of sun radiation [32], can be

written as

hII Exu;p

AcIT;cjS

Exu;p

Ac

IT;c1

4

3Ta

TS

1

3Ta

TS4

(28)

4. Numerical calculations

Numerical calculations have been carried out to evaluate the

energy efficiency, effective efficiency and exergy efficiency, for

a collector configuration, system properties and operating condi-

tions.The thermal behavior of artificially roughened solar air heater

is similar to that of usual flat plate conventional air heater; there-

fore, the usual procedures of calculating the absorbed irradiation

and the heat losses are used. The set of system roughness param-

eter (shown in bracket of Table 1, column-5) for particular rough-

ness geometry, at which thermo-hydraulic behavior has been

reported best, is selected for the analysis.

In order to evaluate the efficiencies for a particular Re first

initial values of Tpm and Tfm are assumed according to inlet

temperature of air and various heat transfer coefficients are

calculated; and new values of Tpm and Tfm are calculated using Eqs.

(16)(23) and (3)(8). If the calculated new values of Tpm and Tfmare different than the previously assumed values then the iteration

0 2000 4000 6000 8000 10000 12000 14000 16000 180000

10

20

30

40

50

60

70

80

Reynolds number

Efficiency(%)

IIx10

ef

I

Bhagoria et al. (2002)

Fig. 4. Variation of energy, effective and exergy efficiencies with Reynolds number for

wedge shaped roughness geometry.

0 2000 4000 6000 8000 10000 12000 14000 16000 180000

10

20

30

40

50

60

70

80

Reynolds number

Efficiency(%)

IIx10

ef

IMomin et al. (2002)

Fig. 5. Variation of energy, effective and exergy efficiencies with Reynolds number forV shaped roughness geometry.



9/12

is repeated with these new values till the absolute differences of

new value and previous value of mean plate as well as mean fluid

temperature are less than or equal to 0.05. Air properties are

determined at Tfm by interpolation from air properties [36]. The

heat gain and outlet temperature of air are calculated from Eqs. (2)

and(3). Theexergy output rate is calculated using the Eqs. (24), (25)

and (12)(15). The various efficiencies are evaluated from the Eqs.

(26)(28).

In order to obtain the results numerically, codes are developed

in Matlab-7 using the following fixed parameters:

L1 2 m, L2 1 m, Ac 2 m2, H 3.0 cm, Ki 0.04 W/m K,

L 4 cm, db

6 cm, ds

4 cm, 3p

0.95, 3c

0.88, 3b

0.95,

ap 0.95, sg 0.88, sa 0.9, b 30, Tfi 30

C, Ta 30C,

VN 1.5 m/s, TS 5600 K and IT 1000 W/m2.

The performance evaluation has also been carried out for

various values of duct width (L2) and duct depth (H).

5. Results and discussion

Figs. 46 show the variation of efficiencies (hI, hef and hII) with

Reynolds number to show the difference in these efficiencies. The

variation ofhI with Re, for various considered geometries (rough or

smooth), is shown in Fig. 7. It is evident from Figs. 47 that the hIincreases with Re forall type of geometries, andhI of any considered

rough surface is always higher than smooth surface. It is also clear

that hI of roughened surface, at a Re, depends on ability to create

turbulence. The hI, among the considered geometries, in general

increasesin the following sequence: smooth surface, circular ribs, V

shaped ribs, wedge shaped rib, expanded metal mesh, rib-grooved,and chamfered ribgroove. The hI of expanded metal mesh geom-

etry becomes greater than hI of rib-grooved and chamfered rib

groove geometry for higher values of Re; while at low Re the hI of V

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

40

45

50

55

60

65

70

75

80

Reynolds number

I(%)

Saini and Saini (1997)

Verma and Prasad (2000)

Momin et al. (2002)


Jaurker et al. (2006)

Layek et al. (2007)

smooth duct

Fig. 7. Variation of energy efficiency with Reynolds number for various roughnessgeometries.

0 0.5 1 1.5 2 2.5

x 104

0

10

20

30

40

50

60

70

Reynolds number

Efficiency(%)

IIx10

ef

ISmooth duct

Fig. 6. Variation of energy, effective and exergy efficiencies with Reynolds number for

smooth solar air heater duct.

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

40

45

50

55

60

65

70

75

Reynolds number

ef(%)



Momin et al. (2002)



Layek et al. (2007)

smooth duct

Fig. 8. Variation of effective efficiency with Reynolds number for various roughness

geometries.

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

40

45

50

55

60

65

70

75

Reynolds number

ef(%)

L2=0.5m, H=0.03m



Momin et al. (2002)



Layek et al. (2007)

smooth duct

Fig. 9. Variation of effective efficiency with Reynolds number for various roughnessgeometries at duct width0.5 m.



10/12

shaped ribs geometry is more than hI of wedge shaped rib

geometry.

It is evident from Figs. 46 that initially the hI is nearly equal to

hef, and their difference increases with Re; though (hI hef) is not

appreciable up to very high Re.

The variation ofhef with Re, for various considered geometries

(rough or smooth), is shown in Fig. 8. It is evident that hef follows

the trend, of variation among various considered geometries,

indicated by variation ofhI with Re (Fig. 7), up to very high value

(>20,000) of Re. The hef attains maximum, and then decreases

with Re; though this is not clear from Fig. 8 with the taken value

of duct width (L2) and duct depth (H). As the frictional pressure

drop/pump work through a duct strongly depends on flow cross-sectional area, thus the simulation has been done for various

reduced values of L2 and H; and the variation of hef with Re for

various reduced values of L2 and H is shown in Figs. 911. It can

be concluded from Figs. 911 that effect, on hef, of reduction in H

is more dominant than reduction in L2. The hef, for lower duct

depth, reaches maximum value at reduced value of Re; for values

of Re greater than 12,00014,000 the roughness geometry which

creates less turbulence gives more hef. The trend, of variation

among various considered geometries, for lower value of L2 and H

is reversed even at low Re as pump work becomes significant. It is

also evident that at higher Re only circular ribs and V shaped ribs

become effective, as there is no appreciable gain in effective

efficiency (for Re 12,00018,000) from other geometries. The

maximum hef of roughened geometries, which creates greater

turbulence, decreases with decrease in duct depth. The hef of

roughened geometries creating greater turbulence becomes less

than that of smooth surface duct at higher Re.The hII (Figs. 46) first increases, reaches maximum value

corresponding to Re in laminar flow regime (for low inlet tem-

perature of air) and then decreases with Re. The useful heat gain

will be less corresponding to Re in laminar flow regime, thus the

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

5

10

15

20

25

Reynolds number

L2=0.5m, H=0.03m



Momin et al. (2002)



Layek et al. (2007)smooth duct

Fig. 13. Variation of exergy efficiency with Reynolds number for various roughnessgeometries at duct width0.5 m.

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

5

10

15

20

25

Reynolds number

IIx10(%)



Momin et al. (2002)



Layek et al. (2007)

smooth duct

Fig. 12. Variation of exergy efficiency with Reynolds number for various roughness

geometries.

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

45

50

55

60

65

70

75

Reynolds number

ef(%)

L2=0.5m, H=0.02m



Momin et al. (2002)



Layek et al. (2007)

smooth duct

Fig. 10. Variation of effective efficiency with Reynolds number for various roughness

geometries at duct width0.5 m and duct depth0.02 m.

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

45

50

55

60

65

70

75

Reynolds number

ef(%)

L2=0.3m, H=0.02m



Momin et al. (2002)



Layek et al. (2007)

smooth duct

Fig. 11. Variation of effective efficiency with Reynolds number for various roughnessgeometries at duct width0.3 m and duct depth0.02 m.



11/12

flow may be made turbulent at the cost of decrease in hII. The hIIdecreases with Re in turbulent flow regime for low inlet tem-

perature of air, as quality of collected heat decreases and pump

work increases.

The variation ofhII with Re, for various considered geometries

(rough or smooth), is shown in Fig. 12. It is evident that initially hIIalso follows the trend, of variation among various considered

geometries, indicated by variation ofhI with Re (Fig. 7), but only up

to value ofRe around 14,000. The trend, of variation among various

considered geometries, is reversed for value of Re higher than

around 14,000. For higher Re around 20,000 the hII of considered

geometries, except smooth duct, circular ribs and V shaped ribs,

approaches zero. The reason for this is that at higher Re the Exd,papproaches Exu due to increase in pumping power requirement.

Figs. 1315 show the variation of hII with Re for various reduced

values ofL2 and H. It is also evident from Figs. 1315 that thehII may

be negative at even lower value of Re. The hII, for lesser duct depth,

decreases rapidly with Re for wedge shaped rib, expanded metal

mesh, rib-grooved, and chamfered ribgroove i.e. in the order of

ability to create turbulence. The hII also follows the trend, of

variation among various considered geometries, as indicated by

Figs. 911; but the trend is reversed at further low value of Re in

comparison to hef trend. The maximum hII of roughened geome-

tries, which occurs at low Re, increases with decrease in duct depth.

The hII of roughened geometries, creating greater turbulence, at

higher Re becomes less than that of smooth surface duct.

6. Conclusion

The efficiencies are improved by using roughened geometries in

the duct of solar air heater. The hef based criterion suggests to use

the roughened geometries for very large value of Re. The hII based

criterion shows that at very large value ofRe the hII may be negative

or exergy of pump work required exceeds the exergy of heat energy

collected by solar air heater. Thus hII provides the meaningful cri-

terion for performance evaluation. There is not a single roughened

geometry which gives best exergetic performance for whole range

ofRe. For largerflow cross-section area of solar air heaterduct along

with low Re the roughened geometry should create more turbu-

lence; while smooth surface, circular ribs and V shaped ribs are

suitable for smaller flow cross-section area of solar air heater duct

and high Re.

Acknowledgement

The first author gratefully acknowledges Ujjain Engineering

College, Ujjain, M.P. (India) and IIT Delhi (India), for sponsorship

under quality improvement program of government of India.

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x 104

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Momin et al. (2002)



Layek et al. (2007)

smooth duct

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Momin et al. (2002)



Layek et al. (2007)smooth duct

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12/12

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