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The Pacific Journal of Science and Technology 152http://www.akamaiuniversity.us/PJST.htm Volume 12. Number 1. May 2011 (Spring)

Parametric Study of Heat Characteristics of Fluid in Cylindrical ParabolicConcentrating Solar Collector.

Emmanuel O. Sangotayo, M.Sc.1* and Mufutau A. Waheed, Ph.D.2

1Department of Mechanical Engineering, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.

2Department of Mechanical Engineering, College of Engineering, University of Agriculture,Abeokuta, Nigeria.

E-mail: [email protected]*

ABSTRACT

This paper presents a numerical investigation ofheat transfer characteristics of fluid in CylindricalParabolic Concentrating Solar Collector inOgbomoso Climatic Conditions (lat 8

o01

I, long

4o11I). The parametric studies were conducted toinvestigate the effects of twist tape ratio,

H/D in

different fluids and length on the systemperformance as function of instantaneousefficiency in order to obtain the optimumperformance of the system.

A computer simulation program written in C++language was developed to study the effect ofReynold numbers (Re) from 2,000 to 12,000 forthe fixed value of incident solar insolation flux (Ib)of 186 W/m

2on the system thermal performance,

Nusselt number (Nu) as a function of Reynolds

number (Re) rate with variable tape twist factor (X= H/Di) for different Prandtl number, Pr in therange of 0.0001 < Pr < 100 (different fluids); liquidmetals (Pr > 1).

The results show that oil has highest heat transfercharacteristics, Nusselt number values both withand without tape twist factor. It is observed thattape twist factor enhances the heat transfercharacteristics of the fluids in cylindrical parabolicconcentrating solar collector. The higher value ofheat transfer characteristics is obtained withNusselt number (Nutw) having tape twist factor (X

= H/Di: 1, 3, 6, 9, 12 and 15) in all the fluidsconsidered. It is observed that performance of thecylindrical parabolic trough collector with twistedtape has been enhanced appreciably. Theseresults can guild practicing engineers anddesigners in the evaluation of the existing realsystems and design of future system.

(Keywords: solar collector, twist ratio factor, fluid,Prantl number)

INTRODUCTION

Flat-plate solar collectors are vastly employed inlow temperature energy technology and havedrawn the attention of a large number ofinvestigators. Several designs of solar air heaters

have been industrialized over the years in orderto improve their system thermal performance. Thethermal performance of solar air heaters isgenerally low because of the low value of theconvective heat transfer coefficient between theabsorber plate and the air, leading to highabsorber plate temperature and greater heatlosses to the surroundings.

It has been found that the main thermalresistance to the heat transfer is due to theformation of a laminar sub-layer on the heattransferring surface. Efforts of improving the heat

transfer rate have been directed towardsartificially destroying the sub-layer. The suitabledesign of solar air heaters for high temperaturesapplications have been the subject of manytheoretical and experimental investigations.

Recently, researchers have employed wirescreen matrices , expanded metal mesh, finned,corrugated and packed bed as absorbing porousmedia for directly incident solar radiation in thesolar air heater due to improve its performancebecause as the surface area and turbulenceproducing air flow path through the bed increase,

heat transfer rate increases. The high heattransfer area to volume ratio for the air flowingthrough these matrices enhances the heattransfer capability. Prasad and Mullic [7]; Momin[12]; Bhagoria [14]; Han [8]; Taslim [10]; Lau [9];Park [11]; Mital [18] and Saini [13] have carriedout investigation on the performance of solar airheater. These studies have indicated that such airheaters have superior performance as comparedto that of flat plate collectors.

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Recently, much attention has been given toconcentrating solar collectors, which are capableof reaching higher temperatures compared to flatplate collectors. Hong [1]; Kumar & Prasad [6]Sharma et al. [16]; and Togrul & Pehlivan [17]have carried out investigations on the twistedtape and reported for enhancement inperformance. These works need investigation ofthe heat and fluid flow phenomena in theabsorbing tube by evaluating friction factors,pumping power and convective heat transfercoefficients and comparisons for the alternativecases and may bring into light the factors toconstruct an economically viewable solar aircollector for high temperature applications.

The objective of this paper is to investigate theheat transfer characteristics coupled with twisttape ratio factor,

H/D in different fluids; liquid

metals (Pr > 1)

of fluid in Cylindrical Parabolic ConcentratingSolar and effect of Twist Tape factor on thesystem thermal performance Collector inOgbomoso Climatic Conditions (lat 8

o01

I, long

4o11

I).

METHOD AND MATERIALS

Performance Analysis o f Cylindrical parabolicConcentrating Collector

Figure1: Cross Section of Cylindrical parabolicConcentrating Collector.

Figure 2: Energy Flow Diagram of CylindricalParabolic Concentrating Collector.

Performance Analyses

The structure of a cylindrical parabolicconcentrating collector of glass envelopeabsorber tube with selective surface (Figure 1) ofsuch system having concentrator width apertureW, length L, and tilt angle rb .

The performance of a cylindrical parabolicconcentrating collector is assumed for the sameradiation flux all along the length and thenegligible temperature drop across the absorbertube and the glass cover. The energy equationsunder the steady state conditions can be

indicated by Figure 2 and described by thefollowing expression:

( ) ( )

( )

( )dx

TTDU

aDrI

aDWrI

dq

apoL

bObb

bobb

u

+

=

(1)

The left side term represents the useful heat gainrate for a length, dx. The first term on the rightside represents the incident beam radiationabsorbed in the absorber tube after reflection, the

second term represents the absorbed incidentbeam radiation which falls directly on theabsorber tube and the third term represents theloss by convention and radiation. Also ()represents the optical properties of the system.The intercept factor, is defined as the reflectedfraction of the incident radiation on the absorbingsurface of the receiver. is the transitivity oftransparent cover. and are the absorptivity

Tf+dTfTf dx

Tp Tc

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and the reflectivity of the absorber andconcentrator, respectively.

The absorbed flux S can be given as:

( )

+=

o

O

bObbbbb DW

D

aDrIarIS )( (2)

The inlet fluid temperature (Tfi) and outlet fluidtemperature (Tfo) are established by applyingboundary conditions at inlet (x = 0. Tf = Tfi) and atoutlet (x=L, Tf= Tfo). They are written as:

=p

LO

if mC

xUDFT

1

exp (3)

=

p

LOfo

mC

xUDFT

1

exp1 (4)

Thus the useful gain rate can be expressed as:

( ) ( )

=

=

afiL

Or

fifopu

TTC

USLDWF

TTmCQ

(5)

Where Fr, the heat removal factor is expressedas:

=p

LO

LO

p

rmC

LUDF

LUD

mCF

1

exp1 (6)

Equation (5) is the equivalent of the Hotel-Whillier-Bliss equation for the flat plate collector.The Instantaneous efficiency can also bedetermined on the basis of beam radiation alone,if the ground reflected radiation is neglected and itgiven in Equation (7).

WLrI

Q

bb

ui = (7)

Heat Transfer Coefficients

In order to determine the performance ofcylindrical parabolic concentrating solar collector,the correlations are required for calculating the

values of convective heat transfer coefficientbetween the absorbed tube and cover, outsidesurface of the cover and inside surface of theabsorbed tube respectively.

The following correlations are used to calculatethe natural convection heat transfer coefficient(hp-c) for the enclosed annular surface betweenthe horizontal absorber tube and the concentriccover [Raithby & Holland].

4/1)(317.0/ RaKKeff = (8)

where Keffis the effective thermal conductivity.

The convective heat transfer coefficient (hw) onthe outside surface of the cover may becalculated by this equation [Hilpert]:

nCNu Re1= (9)

The convective heat transfer coefficient (hf) onthe inside surface absorbed tube can becalculated using Dittus-Boelter equation:

4.08.0 PrRe023.0=Nu (10)

The heat transfer coefficient for twisted tape maybe determined using the correlation given byHong and Burgles.

( ){ }[ ]5.0

7.078.1Re/Pr005484.01172.5 XNu += (11)

Where X is the Tape Twist Ratio and written as:

X=H/Di (12)

The calculation of the overall heat loss coefficientbased on convection and radiation lossesproceeds in a manner similar to that adopted forthe top loss coefficient. The absorber tube andthe glass cover around constitute a system oflong concentric tubes. The equation can bewritten as:

( )

( ){ }( ){ }1

44

/1/1/1 cOcp

cpmO

Ocpmcp

u

DD

TTD

DTThL

Q

+

+

=

( ) ( )44 skyccOOac TTDDcTThw += (13)

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WhereQu

/L is the heat loss per unit length, Tpm isthe average temperature of the absorber tube, Tcis the temperature attained by the cover and hw isthe wind heat transfer co-efficient.

A simple and flexible program, writing in C++language was developed based on models aboveto obtain results under different design andoperating conditions. The flowchart forimplementing the program is shown in Figure 3.

Figure 3: Flow Chart for Solar CollectorCalculations.

RESULTS AND DISCUSSIONS

The results obtained from the program developedare presented as profiles in Figures 4 15. Theeffect of Reynolds number (Re) ranges from 2000to 12000 on the system thermal performanceparameter were investigated for different valuesof Tape Twist Ratio, X = H/Di, (1, 3, 6, 9, 12 and15) for a fixed constant value of incident beamsolar flux (Ib = 186 w/m

2) in Ogbomoso climatic

conditions.

Figure 4 shows the plot of Nusselt number (Nu)as a function of Reynolds number (Re) ratewithout variable tape twist factor (X = H/Di) fordifferent Prandtl number, Pr in the range of0.0001 < Pr < 100 (different fluids); liquid metals(Pr > 1). It isevident that higher value of Nusselt number isobtained with corresponding higher value of

Prandtl number. It is observed that oil has highestheat transfer characteristics without variable tapetwist factor.

0

50

100

150

200

250

300

0 2 4 6 8 10 12

Renolds number, Re (x103)

Nus

seltnu

ber,

Nu

Pr=0.0001

Pr = 0.71

Pr = 10

Pr = 50

Pr= 80

Pr= 100

Figure 4: Effect of Reynolds Number, Re-

Coupled without Twist Tape Ratio Factor onNusselt Number, Nu.

Figure 5 shows the plot of Nusselt number (Nu)as a function of Reynolds number (Re) rate withvariable tape twist factor (X = H/Di) for differentPrandtl number, Pr in the range of 0.0001 < Pr 1). It is evident thathigher value of Nusselt number is obtained withcorresponding higher value of Prandtl number. It

Start

Get solar insolations

and design condition

Loop begins

Calculate incident absorbed flux

Calculate useful heat gain

Calculate outlet fluid temperature

Calculate instantaneous efficiency

Calculate Nusselt number without twist ratio factor

Calculate Nusselt number with twist ratio factor

Print the results

Stop

Loop ends

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is observed that oil has highest heat transfercharacteristics with variable tape twist factor

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12

Reynolds number, Re (x 103)

Nusseltnumber,

Nu

(w

ithtwistedtape

)

Pr=0.0001

Pr = 0.71

Pr = 10

Pr = 50

Pr= 80

Pr= 100

Figure 5: Effect of Reynolds Number, ReCoupled with Twist Tape Ratio Factor on Nusselt

Number, Nu.

Figures 6, 7, and 8 present the plots ofcomparison of Nusselt number (Nu) without tapetwist factor (X = H/Di) and Nusselt number (Nutw)with tape twist factor (X = H/Di) as a function ofReynolds number (Re) for different fluids; liquidmetals (Pr =0.0001), air (Pr = 0.71) and Oil (Pr =10). It is evident that higher value of heat transfercharacteristics is obtained with Nusselt number

(Nutw) having tape twist factor (X = H/Di) in allthe three fluids considered.

0

2

4

6

8

10

12

0 2 4 6 8 10 12

Reynolds number, Re (x103)

Nusseltnumber,Nu

Nu,Pr=0.0001

Nutw,Pr=0.0001

Figure 6: Comparison of Nusselt Number, Nuwithout and with Twist Tape Ratio Factor for Pr =

0.0001.

0

20

40

60

80

100

120

0 2 4 6 8 10 12


Nusseltn

umber,Nu

Nu, Pr = 0.71

Nutw, Pr = 0. 71


0.71.

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Reynolde number, Re (x 103)

Nusseltnumber,Nu

Nu,Pr = 10

Nutw,Pr = 10


10.

It is observed that tape twist factor enhances theheat transfer characteristics of the fluids incylindrical parabolic concentrating solar collector.

Figures 9, 10, 11 and 12 present the plots ofNusselt number (Nu) as a function of Reynoldsnumber (Re) rate with variable tape twist factor (X= H/Di: 1 ,3, 6, 9, 12, 15 ) for different fluids; liquidmetals (Pr = 0.0001), air (Pr = 0.71), and Oil (Pr =10). It is evident that higher value of Nusseltnumber is obtained with corresponding highervalue of Prandtl number.

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5

6

7

8

9

10

11

0 2 4 6 8 10 12


Nusseltnum

ber,N

u

X = 1

X = 3

X = 6

X = 9

X = 12

X = 15

Figure 9: Effect of Reynolds Number, Re

Coupled with different Twist Tape Ratio Factor onNusselt Number, Nu for Pr = 0.0001.

0

20

40

60

80

100

120

0 2 4 6 8 10 12

Reynolds number, Re ( x103)

Nusseltnum

ber,

Nu

X = 1

X = 3

X = 6

X = 9

X = 12

X = 15

Figure 10: Effect of Reynolds Number, ReCoupled with different Twist Tape Ratio Factors

on Nusselt Number, Nu for Pr = 0.71.

It is observed that oil has highest heat transfercharacteristics with variable tape twist factor. It isevident that higher value of heat transfercharacteristics is obtained with Nusselt number(Nutw) having tape twist factor (X = H/Di) in allthe three fluids considered. This is due to the factthat high twisted tape inserted into the absorberincreases the friction factor and pressure dropleads to higher pumping power.

0

50

100

150

200

250

300

0 2 4 6 8 10 12

Reynolds number, Re ( x 103)

Nusseltnum

ber,

Nu

X = 1

X = 3

X = 6

X = 9

X = 12

X = 15

Figure 11: Effect of Reynolds Number, Re

Coupled with different Twist Tape Ratio Factor onNusselt Number, Nu for Pr = 10.

0

100

200

300

400

500

600

0 2 4 6 8 10 12

Reynolds number, Re ( x 103)

Nusseltnum

ber,

Nu

X = 1

X = 3

X = 6

X = 9

X = 12

X = 15

Figure 12: Effect of Reynolds Number, ReCoupled with different Twist Tape Ratio

Factor on Nusselt Number, Nu for Pr = 50.

Figures 13 and 14 present the plots of fluid inletand outlet temperature distribution as a functionof mass flow rate (m) and length (L). It is deducedthat the optimum design parameters are: length(L) is 1.30 m, mass flow rate is 0.036 kg/s, outletand inlet fluid temperature is 0.505 withinstantaneous collector efficiency of 47.38%,(Figure 15).

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0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12

Length (m)

Fluid

Tem

eretures

Tfi

Tfo

Figure 13: Effect of Length, L on Fluid Inlet and

Outlet Temperature.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1 0.15 0.2 0.25 0.3

Mass Flow Rate (kg/s)

Tem

perature

distribution

Tfi

Tfo

Figure 14: Effect of Mass Flow Rate, m on FluidInlet and Outlet Temperature.

CONCLUSIONS

The following conclusions are drawn from theparametric studies conducted investigating theheat transfer characteristics of fluids in theabsorber in Cylindrical Parabolic ConcentratingSolar Collector in Ogbomoso Climatic Conditions(lat 8

o01

I, long 4

o11

I). Oil has highest heat

transfer characteristics, Nusselt number valuesboth with and without tape twist factor.

0.473

0.4732

0.4734

0.4736

0.4738

0.474

0.4742

0.4744

0.4746

0 2 4 6 8 10 12

Length (m)

InstantaneousE

fficienc

y

Figure 15: Effect of Variation of Length, L on

Instantaneous Efficiency.

It is observed that tape twist factor enhances theheat transfer characteristics of the fluids incylindrical parabolic concentrating solar collector.The higher value of heat transfer characteristics isobtained with Nusselt number (Nutw) having tapetwist factor (X = H/Di) in all the three fluidsconsidered. This is due to the fact that hightwisted tape inserted into the absorber increasesthe friction factor and pressure drop leads tohigher pumping power. that the optimum design

parameters are: length (L) is 1.30 m, mass flowrate is 0.036 kg/s, outlet and inlet fluidtemperature is 0.505 with instantaneous collectorefficiency of 47.38%.

NOMENCLATURE

Fr Collector heat removal factor

hp-c Heat transfer coefficient betweenabsorber and cover (w/m

3- K)

hf Convention heat transfer coefficient onthe inside surface of the tube (w/m3

- K)

Instantaneous Collector efficiency

Stefan-Boltzmann constant (w/m3

- K)

X Tape twist ratio

Intercept Factor

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Ib Incident beam radiation (w/m3

- K)

UL Overall heat transfer coefficient (w/m3

- K)

Transmissivity of glass

Reflectivity of glass

Absorptivity of glass

Emissivity of the plate

Re Reynoldss Number

Nu Nusselt Number

Ra Rayleigh Number

REFERENCES

1. Bahabadi, A. et. al. 2008. Augmentation of HeatTransfer by Twisted Tape Inserts DuringCondensation of R13a inside a Horizontal Tube.International Journal, Heat and Mass Transfer.44:651-657.

2. Bhagoria, J.L., Saini, J.S., and Solanki, S.C.2002. Heat Transfer Coefficient and FrictionFactor Correlations for Rectangular Solar AirHeater Duct Having Transverse Wedge Shape-Rib Roughness on the Absorber Plate.Renewable Energy. 25:341-369.

3. Han, J.C. 1988. Heat Transfer and FrictionCharacteristics in Rectangular Channels withRib. ASME Journal Heat Transfer. 110:321-328.

4. Han, J.C. and Park, J.S. 1988. Developing HeatTransfer in Rectangular Channels with Ribs.International Journal Heat Mass Transfer. 31:83-195.

5. Hong, S.W. and A.E. Burgles. 1976.Augmentation of Laminar Flow Heat Transfer inTubes by Means of Twisted Tape Inserts. J. HeatTransfer. 98:251.

6. Kumar, A. and Prasad, B.N. 2000. Investigation

of Twisted Tape Inserted Solar Water Heaters,Heat Transfer, Friction Factor, and ThermalPerformance Results. Renewable Energy. 19:379-398.

7. Lau, S.C., et al. 1991. Heat TransferCharacteristics of Turbulent Flow in a SquareChannel.ASME Journal Turbo. 113:367-374.

8. Mazen, M. and Abu-Khader. 2006. Effect ofTwisted Tape as Tube Inserts in Shell and Tube

Heat Exchanger. Journal of Heat and MassTransfer.

9. Mital, M.K., et. al. 2005. Effective Efficiency atSolar Air Heaters Having Different Types ofRoughness Elements on the Absorbed Plate.Energy.

10. Momin, A.M. 2001. Heat Transfer and Friction inSolar Air Heater Duct with V-Shaped RibRoughness an Absorber Plate. InternationalJournal Heat & Mass Trans. 45:3383-3396.

11. Momin, A.M., Saini, J.S. and Solanki, S.C. 2002.Heat Transfer and Friction in Solar Air HeaterDuct with V-Shaped Rib Roughness on AbsorberPlate. International Journal Heat and MassTransfer. 45:3383-3396.

12. Prasad, B.N. and Saini, J.S. 1998. Effect ofArtificial Roughness on Heat Transfer. SolarEnergy. 41:555-560.

13. Prasad, K. and Mullic, S.C. 1983. Heat TransferCharacteristics of a Solar Air Heater.AppliedEnergy. 13:83-93.

14. Saini, R.P. and Saini, J.S. 1996. Heat Transferand Friction Factor Co-Relations for ArtificiallyRoughened Ducts, with Expanded Metal Mesh asRoughness Element. International Journal HeatMass. 50017-9310.

15. Sharma, P.K., et al. 2003. Laminar ConvectiveHeat Transfer with Twisted Tape Insert in aTube. Int. Journal Thermal Sciences. 42:821-828.

16. Sukhatme, S.P. 2007. Solar Energy. TataMcGraw-Hill: New Delhi, India.

17. Taslim, M.E., et al. 1996. Experimental HeatTransfer and Friction in Channels Roughenedwith Angled V-Shaped.ASME Journal Turb. 118:20-28.

18. Togrul, I.T. and Pehlivan, D. 2005. Effect ofPacking in the Air Flow Passage on thePerformance of a Solar Air Heater with ConicalConcentrator. International Journal AppliedThermal Engineering. 25:1349-1362.

ABOUT THE AUTHORS

E.O. Sangotayo, is an Assistant Lecturer ofMechanical Engineering at the Department ofMechanical Engineering, Faculty of Engineeringand Technology, Ladoke Akintola University ofTechnology, Ogbomoso-Nigeria. He received hisacademic training at Ladoke Akintola University of

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Technology (for his B.Tech. and M.Tech) and is amember of the Nigeria Society of Engineers. Heis presently undertaking his doctoral studies atthe Department of Mechanical Engineering,College of Engineering, University of Agriculture,

Abeokuta-Nigeria and his area of specialization isthermo-fluid energy studies.

M.A. Waheed, is a Professor of thermo-fluid atthe Department of Mechanical Engineering,College of Engineering, University of Agriculture,

Abeokuta-Nigeria and his area of specialization isthermo-fluid, heat and mass transfer,computational fluid mechanics, and energystudies. He undertook his academic training atthe University of Ilorin (for his B.Eng. andM.Eng.), Achem; and Germany University (for hisPh.D.). He is a member of many professionalbodies and a COREN registered engineer. He ispresently the Director of Academic Planning,

University of Agriculture, Abeokuta-Nigeria,UNAAB.

SUGGESTED CITATION

Sangotayo, E.O. and M.A. Waheed. 2011.Parametric Study of Heat Characteristics of Fluidin Cylindrical Parabolic Concentrating SolarCollector. Pacific Journal of Science andTechnology. 12(1):152-160.

Pacific Journal of Science and Technology

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