Solar & Wind Techmdoyy Vol. 3, No. 4, pp. 281 285,1986 0741 983X/86 $3.00+.00 Printed in Great Britain. Pergamon Journals Ltd.

ANALYSIS OF A N ACTIVELY COOLED P H O T O V O L T A I C - T H E R M A L SOLAR C O N C E N T R A T O R RECEIVER SYSTEM USING A FIN-TYPE ABSORBER*

S. N. SHARAN, S. S. MATHUR a n d T. C. KANDPAL t

Centre of Energy Studies, I.I.T. Delhi, Hauz Khas, New Delhi-110016, lndia

(Received 16 January 1986; accepted 24 February 1986)

Abst rac~A theoretical analysis of an actively cooled photovoltai~thermal solar concentrator, receiver system has been made. The mode of variation of overall electrical output, thermal output, temperature of the solar cells, and temperature of the coolant with the length of the absorber has been studied. The effect of various other design and operational parameters have also been studied. Results of some typical numerical calculations have been presented graphically and discussed.

1. INTRODUCTION

Combined pho tovo l ta i~ the rmal systems consisting of solar concentrators have been given much import- ance for the last few years. The possibility of using such a system for producing cheap electrical as well as thermal energy, as compared to the electrical energy produced by simple photovoltaic arrays, is being explored at various R & D centres [1 7].

In the present communicat ion an analygis of a typi- cal photovoltaic concentrator system has been pre- sented. The system under consideration consists of a linear Fresnel reflector, and a rectangular channel (Fig. 1) on two sides of which solar cells are mounted (referred to as a fin-type absorber in this paper). The coolant flows through the channel so as to maintain the temperature of the solar cells at a desired level. The variation of coolant and solar cell temperatures along the length of the absorber has been studied, together with the variation of electrical and thermal outputs with the absorber length. The effect of coolant mass flow rate, and that of focal length of the reflector on the coolant outlet temperature, and electrical and thermal power outputs have also been studied.

2. ANALYSIS The analysis presented here is based on the fol-

lowing simplifying assumptions : (i) both sides of the fin absorber are uniformly

illuminated;

*Paper presented at the Second Arab International Conference.

3 To whom all correspondence should be addressed.

(ii) the reflector is fully tracked, and its surface is specularly reflecting;

(iii) gaps between solar cells are negligible ; (iv) the cover glass is kept in contact with the solar

cells ; (v) the rate of heat transfer from each side of the

fin absorber to the coolant is equal. Using standard heat transfer techniques the fol-

lowing expression for the overall heat transfer

[ ~ Glass cover

Adhesive Sotor cell Metallic wall

Fig. 1. Cross-sectional view o f a combined pho tovo t t a i ~ thermal receiver system consisting ofa Fresnel reflector, solar

concentrator and a fin-type receiver.

281

282

coefficient from solar cells to the coolant, at steady state, may be obtained.

/ I' (4Zj~ 4Z~, 4Zn, U=l ' l i / tK , , . + K, + K,,,

+ hjiV2(h<,Ki, t) , .2ianh:;) (1)

with

m = \Kmt/ (2)

and the temperature of the coolant along the channel length can be shown to be given by

_ t l T a ha(Tg-lRtl0bZ,)~ ,.~ T<(x) = + T~- ; e

a - 1 h , (Tg- T,) + + I R @ "

A further extension of this analysis leads to the following expression for the temperature of the solar cells :

ha( Tg-- T~) ~ T~(x) : 11--~ -a + T, -- IR~lob J

where

and

{rhcCp } .~ a- - 1 h~(Tg- T,) e + b IRrlob x 2Ul~ s+ 1 + - ,

S. N. Stt;tR,'tN r l ,11

(4)

2biRD7 o

s = ,<c,, {1 - ,f, SRhTO~ul, J (5)

a = v#,(l -}-firTh) (6)

b = rhflr. (7)

The overall electrical power output (P,), and ther- mal power output (P,) for an absorber channel of length L, may now be calculated as

P~(L) = IRnol[L+bW{l - e " } l S ] (8)

and

P,(L ) = rhcCp { T~( L ) - T,}, (9)

where

h~(Tg - T.)) frh~Cp W = [ ( I T a + T ~ - - iRrh, b ~12Ul, S + I } I "

(lO)

3. RESULTS AND DISCUSSION

The analysis presented ill the above section ma~ now be used to study the performance of any com- bined photovoltaic thermal system comprising a linear solar concentrator and a fin absorber. We have made some numerical calculations for a typical system in which a linear Fresnel reflector [8] is used as con- centrator.

Figure 2 shows the variation of electrical power output, thermal power output, and that of tempera- ture of the coolant and solar cells with the distance along the length of the channel. The continuous lines correspond to a coolant mass flow rate of 0.02 kg s whereas the broken lines show the same variations for a coolant mass flow rate of 0.05 kg s L It may be noted that in the beginning both the electrical and the thermal power outputs increase rapidly, but alter a certain distance along the length of the absorber the gain in both the electrical and thermal outputs is very small. This may be attributed to the fact that in the beginning, owing to a low coolant temperature, the rate of heat transfer between solar cells and the cool- ant is more, whereas at larger distances the rate of heat transfer is less as the coolant temperature increases considerably. Another important feature to be noted is that the electrical power output is found to be slightly higher for a mass flow rate of 0.05 kg s ~. This is because of the fact that at a higher coolant mass flow rate the solar cells operate at a somewhat lower temperature and thus the overall efficiency of the solar cell panel is slightly improved. A somewhat reduced value of the thermal power output at larger mass flow rates, as obtained in Fig. 2, may also be explained on similar grounds. As regards the coolant temperature, it may be noted that it increases more or less expo- nentially along the length of the absorber.

Figure 3 shows the same variations as given in Fig. 2 for an absorber size of 5 cm. It should be noted that the Fresnel reflector is designed to give a more or less uniform illumination on both the sides of the fin absorber. Based on the geometrical optical analysis of such a typical concentrator receiver system analysed earlier [9], the concentration ratio with an absorber of size 5 cm has been found to be 6.4.

The dependence of both electrical and thermal power outputs as well as the coolant outlet tem- perature (for an inlet coolant temperature of 2 5 C ) on the coolant mass flow rate for a typical design is shown in Fig. 4. As expected, an increase in the mass flow rate results in an enhanced electrical power out- put and a slight decrease in the thermal power output. The coolant outlet temperature also decreases with an increase in the coolant mass flow rate.

Photovo l t a i c the rmal solar concen t r a to r 283

70

6O

'~ 50

0

40

o O.

- 30 0 u

u '1' 20

UJ

10

( = 0 - 0 2 m

R =11 2

- - ~c = 0.02 K g / s e c o

. . . . . . rh c = O-05Kg /sec x

I = 5 0 0 w / r n 2 o o o C o o l a n t t e m p .

0 I 0-0 0.4 0.8 1.2 1-6 2.0 2-'- 2-8 3.2

L e n g t h of t h e a b s o r b e r ( m e t e r s )

~, ,~ E lec t r , ' co l p o w e r

o o T h e r m a l p o w e r

x x So la r cel l t e m p .

3s

5OO

t ~00 .~-

30 300 ~,

o

-6 200 E

¢, . c

100

25

0

Fig. 2. Var ia t ion of electr ical power , t he rma l power, coo lan t ou t le t t empera tu re and solar cell t empera tu res a long the length of the absorber . Abso rbe r size = 0.02 m.

e = 0-05m 6 ~ ~ E iec t r l ' ca l p o w e r

70 R = 6 . 4 o o o T h e r m a l p o w e r 700

rnc= 0.02Kglse . . . . S o l a r cell t e m p .

t ' ° o0 K0/sec ° ° : ,00 -135

o 50 500 =

v

o, 13_ ~ C_

-~ ~ 30 -43o 30o

20 ~_ .o.__o__~___-o---o 200 ' -

100

~25

0 I I I I I I I I 0 0.0 0"4 0"8 1'2 1.6 2"0 2.4 2.8 3"2

L e n g t h of t he a b s o r b e r ( m e t e r s ) - - - ~ .

Fig. 3. Var ia t ion of electr ical power, the rmal power, coo lan t out le t t empera tu re and the solar cell t empera tu res a long the length of the absorber . Abso rbe r size = 0.05 m.

2~4 S . N . ~ I I A R , , \ N ('{ UI

I = 5 0 0 w / / m 2

,~ = 0 . 0 2 m

0 = 1 - O m

f = 0 , 5 m I i

20 L = 1 0 r n 135 J200 i

I E l e c l r l c o [ p o w e r I

a0 • 16 ~, o ! •

~ T h e r t o o l p o w e r 30 o

u 14 E

l e n t t e m p . uJ

12 /

10 I I I I I 25 J lO0 O-0 0.01 0.02 0-03 0-0~, 0.05

M a s s f l o w r o l e ( K g / / s e c ) - -

Fig. 4. Variation of electrical power, thermal power, and coolant outlet temperature with coolant mass flow rate.

The effect o f the geometrical design parameters of the linear Fresnel reflector on both the electrical and thermal power outputs as well as the outlet tem- perature of the coolant may be seen in Figs. 5 and 6. Figure 5 shows the effect o f a variation in the focal

t = O02m

D = 1.Ore

rn c = O-02Kg/sec

L = 1.Ore

I : 500 w / m 2

E lec t r ica l power

I 20 }5 200

f

25 ~ o

30 = 150 a

Cu '-

u

Focol l e n g t h ( m e t e r s ) ~-~-

Fig. 5. Variation of electrical power, thermal power, and coolant outlet temperature with the focal length of the

Fresnel reflector ; D = 1.0 m.

length of the Fresnel reflector on the above-mentioned parameters for a concentra tor aperture diameter of I m, while Fig. 6 shows similar variations for an aper- ture diameter of 1.5 m. From these figures it may be noted that with an increase in the focal length of the

t

cl

o~

._w

uJ

! = 500 w / m 2

= O.02m

D = t - 5 m

r~ c = 0 - 02 Kg/ /sec

L = I , O m

Elec tr ical power

Coo lan t t e m p .

Focol l e n g t h ( m e t e r s )

35 ~; I 20O

i

u o

g

o 1

Fig. 6. Variation of electrical power, thermal power, and coolant outlet temperature with the focal length of the

Fresnel reflector ; D = 1.0 m.

Photovoltaic-thermal solar concentrator 285

l inear Fresne l ref lector these p a r a m e t e r s increase at the beginning , reach a m a x i m u m , and finally s tar t decreas ing. The reason for such b e h a v i o u r lies in the fact tha t wi th a change in the focal length the c o n c e n t r a t i o n ra t io o f the c o n c e n t r a t o ~ r e c e i v e r sys- tem changes , thus caus ing a c o r r e s p o n d i n g change in the a b o v e pa rame te r s .

NOMENCLATURE

T,c temperature of the solar cell ( 'C) U overall heat transfer coefficient from solar cells to the

coolant (W m : ~'C) fir fractional decrease in solar cell efficiency per degree

rise in solar cell temperature r/~ optical efficiency r/r reference efficiency of solar cell

Z,, thickness of adhesive (m) Zj~ thickness of solar cell from its junction to bottom

(m) Zm thickness of metallic wall (m)

B half width of the absorber (m) Cp specific heat of coolant (J kg i "C) D aperture width of Fresnel reflector (m) F focal length of Fresnel reflector (m) 1 solar radiation per unit area per unit time ( W m :)

h~ heat transfer coefficient from glass cover to the ambi- ent a i r ( W m zoC)

hc heat transfer coefficient from metallic wall to the cool- ant (W m 2 C )

K,, conductivity of adhesive (W m 2 ~C) Kj~o conductivity of solar cell material (W m 2 C ) K~ conductivity of metallic wall of the absorber

(W in ~ C ) Kg conductivity of glass (W m 2 C ) L length of the channel (m) l height of the absorber (m) l, effective height of the absorber through which the

heat transfer from metallic walls to coolant is taking place (m)

rh, mass flow rate of the coolant (kg s ~) P~ overall electrical power output from the absorber

(W) P~ thermal power output from the absorber (W) R concentration ratio t thickness of the metallic wall (m)

Ta ambient air temperature ( C ) T~. coolant outlet temperature (~C) T~ temperature of the surface of the glass in contact with

the air ( 'C) T~ coolant inlet temperature (~C)

REFERENCES

1. S. S. Mathur, T. C. Kandpal and R. N. Singh, Solar Concentrators: A Bibliography. Innovative Information Inc., USA (1982).

2. L. W. Florschuetz, Extension of the Hottel Whillier model to the analysis of combined photovoltaic/thermal flat plate collectors. Solar Energy 22, 367 (1979).

3. U. H. Kurzweg, On a class of axisymmetric concen- trators with uniform flux concentration for photo- voltaic applications. Solar Energy 24, 507 (1980).

4. D. L. Evans and L. W. Florschuetz, Cost studies on terrestrial photovoltaic power systems with sunlight con- centration. Solar Energy 19, 255 (1975).

5. S.N. Sharan, S. S. Mathur and T. C. Kandpal, Economic evaluation of concentrator photovoltaic systems. Solar Wind Technol. 2, 195 (1985).

6. S.N. Sharan, S. S. Mathur and T. C. Kandpal, Economic feasibility of photovoltaic-concentrating systems. Solar Cells 15, 199 (1985).

7. M. J. O'Leary and L. Davis dements, Thermal-electric performance analysis for actively cooled, concentrating photovoltaic systems. Solar Energy 25, 401 (1979).

8. M. S. Sharma, S. S. Mathur and T. C. Kandpal, Geo- metrical optical performance studies of a linear Fresnel reflector. Opt. Appl. 14, 549 (1984).

9. A. K. Singhal, R. N. Singh, T. C. Kandpal and S. S. Mathur, Geometrical concentration characteristic of a linear Fresnel reflector using a fin receiver. Opt. Appl. 12, 273 (1982).