Pergamon Energy Convers. Mgmt Vol. 35, No. II, pp. 967-972, 1994

Copyright ~~ 1994 Elsevier Science Ltd 0196-8904(94)F_JI05-J Printed in Great Britain. All rights reserved

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T R A N S I E N T A N A L Y S I S O F A P H O T O V O L T A I C - T H E R M A L

S O L A R C O L L E C T O R F O R C O - G E N E R A T I O N O F

E L E C T R I C I T Y A N D H O T A I R / W A T E R

JAI PRAKASH Department of Physics, Ramjas College, University of Delhi, Delhi-l l0 007, India

(Received 22 May 1993; received for publication 18 April 1994)

Almract - - In this paper, a theoretical study of a hybrid photovoltaic cure thermal (PV/T) solar system is presented. The system investigated consists of a solar cell panel for electricity generation, and air/water is made to flow in a duct placed below the surface on which the solar cells are mounted to extract heat from the system, thereby cooling the cells and increasing their efficiency.

The mathematical model developed for predicting the performance of the system is based on energy balance equations written for the various nodes of the system, and the coupled differential equations obtained are solved by using the forward step marching finite difference technique. The temperatures of the solar cells and of the outlet fluid as a function of time are predicted. The performance of the PV/T system is compared with that of a conventional photovoltaic panel.

Photovoltaic-thermal solar collector Solar energy Transient analysis Co-generation

N O M E N C L A T U R E

A = Fractional area covered by solar cells C = Specific heat capacity (J/kg/'~C) h = Heat transfer coefficient (W/mr'C)

M = Mass (kg) rh = Mass flow rate through duct (kg/s)

Nu = Nusselt number S = Solar radiation intensity (W/m 2) T = Temperature (°C) U = Heat loss coefficient from duct (W/m/°C) ct = Coefficient of absorptance r /= Solar cell efficiency

= Transmittivity of glazing

Subscripts

a = Ambient f = Fluid flowing in duct g = Glass p = Absorbing plate

I N T R O D U C T I O N

High incident solar radiation on a photovoltaic panel should result in high electrical output. However, on account of the high temperatures at which the solar cells have to operate in regions of high incident solar radiation, these panels suffer a loss in efficiency. Therefore, to achieve both higher cell efficiency and higher electrical output, we must cool the cells by removing the heat in some way. This can be achieved by integrating a photovoltaic panel with a solar air/water heater. This type of system is called Photovoltaic-Thermal collector (PV/T) and can be used for the supply of electrical power along with hot air/water for domestic, industrial or agricultural applications.

In the present article, a theoretical model for the performance prediction of PV/T panels for co-generation of electricity and hot air/water has been reported. A transient analysis of the model is presented for various fluid flow rates and fluid duct depths for summer conditions prevailing in

967

968 PRAKASH: TRANSIENT ANALYSIS OF A PHOTOVOLTAIC-THERMAL SOLAR COLLECTOR

Delhi. The forward step marching finite difference technique is employed to calculate the outlet fluid temperature, cell efficiency and thermal efficiency of the system as a function of time in a day. The cell efficiency of the PV/T panel is compared with that of the conventional photovoltaic panel having no arrangement for heat removal. It is observed that the cell efficiency is marginally improved, while in addition, an average thermal efficiency of about 50-70% for water heating and 17-51% for air heating is obtained.

SYSTEM DESIGN

The design of the photovoltaic-thermal (PV/T) system studied in the present article is shown in Fig. 1. It consists of a single glazing of 3 mm thick glass sheet. The cells are assumed to be mounted on a metallic plate with an adhesive having the properties of good thermal conductivity and bad electrical conductivity. Nearly 75% of the panel area is covered with circular solar cells. The remaining 25% area of the metallic plate which is not covered with solar cells is painted black to increase the absorption of incident solar radiation. Below this plate is a duct for flow of air/water. The moving air/water in this duct collects heat from the plate above it, and useful thermal energy is extracted by removing the hot fluid from one end of the duct by allowing the cold fluid to enter at the other end. When water is used as the heat recovery fluid, we may connect the duct inlet directly to a tap, but when air is used, a pump has to be employed for air flow through the duct. The duct bottom is covered with a good insulation to minimize heat losses to the ambient.

M A T H E M A T I C A L MO D EL

The thermal energy balance equations for the different nodes of the system are as follows: For glazing:

m c dTg g g - ~ =o~gS-.khpg(rp- Tg)-hga(Tg- Ta). (1)

For metallic plate with solar cells on it:

dTp mp C o - ~ - = zap S (1 - A ) + za s .4 ( 1 - r/¢e, , )S - hpg (rp - T,) - hpr (T o - Tf). (2)

l l l l l l Glazing

/ Solar cell kbsorbing )late

,, :- ) Fluid P -- Insulation

l / l l l l l l / l l l l l l l l l l l l l l l l / l l l / ' / / / ' / / / / / / f f ~

Fig. I. Design of the solar photovoltaic/thermat (PV/T) air/water heating system.

PRAKASH: TRANSIENT ANALYSIS OF A PHOTOVOLTAIC-THERMAL SOLAR COLLECTOR 969

For fluid in the duct:

dTt = hpf(Tp - Tf) - U(Tf - - T a ) - - rhCf(Tou, - Td). (3) mfCr-d- ~

In writing the above equations, the following assumptions are made:

- - T h e surface of the photovoltaic array facing the sun and the absorber plate have the same radiative properties. The emittance and absorptance of the black painted metallic plate are about 0.9 each, while those of the solar cell surface are about 0.7 and 0.95, respectively. For simplicity of calculations, we have taken the value 0.9 for the absorptance as well as for the emittance for both the solar cell surface and the absorbing plate.

- - A part of the incident radiation is converted into electrical energy by the solar cells, and the remainder is absorbed by the cells to increase their temperature. Thus, the part of the energy used in raising the temperature of the absorbing plate covered with cells is calculated by subtracting the energy converted into electrical energy out of the total incident radiation. In equation (2), r/ce . is the solar cell efficiency at average plate temperature Tp. A is the fraction of the area of the absorber plate occupied by the solar cells. Out of the total radiation A x S incident on the solar cells rct+A x S x qceL~ is converted into electricity while the remaining z~sA × S x (1 - qce,) is transferred to the absorber plate along with the part ~p( l - A ) x S directly absorbed by the plate.

- -Solar cell temperature is the same as that of the absorber plate. - - T h e fluid entering the duct is at ambient temperature and the fluid temperature Tf in the duct

is an average of the inlet and outlet temperatures.

The efficiency of the hybrid PV/T system is obtained in terms of the solar cell efficiency and the thermal efficiency. The solar cell efficiency depends on the cell temperature and is given by the expression [I-4]:

r /= r/r[! - flr(Tp - Tr)] (4)

where we have taken a value of 10% for q, at the reference temperature Tr = 20°C. fir is a constant given by

1 #, = - - ( 5 )

T0-T,

To is the cell temperature at which the cell efficiency drops to zero. For silicon solar cells, To = 270°C.

The instantaneous thermal efficiency is computed by

SrhCr(Tom- Tm)dt qXherm = SS dt (6)

The integration is over the period of sunshine. The Nusselt number for forced air flow through the duct is computed by the relation [5]

Nu = 0.0158Re °8 (where Re is the Reynolds number) (7)

while, for water flow which is in the laminar flow range for the selected flow rates, a fixed value, Nu = 4.86, is taken.

The coupled differential equations (1)-(3) are solved by employing the forward step marching finite difference technique. The differential equations are first converted into difference equations which are then solved simultaneously to compute the various nodal temperatures at 5 s intervals for 12 h from 7 a.m. to 7 p.m. The input parameters for the model are the solar radiation incident on the solar cell surface and the ambient temperature recorded at the Indian Institute of Technology, Delhi, on a typical summer day.

RESULTS AND D IS CU S S IO N

The results of the calculations for the performance prediction of the PV/T panel are given in Figs 2 and 3 for air heating, while those in Figs 4 and 5 are for water heating and in

970 PRAKASH: T R A N S I E N T A N A L Y S I S OF A P H O T O V O L T A I C - T H E R M A L SOLAR COLLECTOR

55 t 1 10

50

45 L) o...

=

& 40

o

O 35

30

- - I - - A - + - - B

- - x - - E - - O ' - - F

- * - - C ~ D

25 ~ 7 7 9 11 13 15 17 19

T i m e ( h )

9

L)

8

Fig. 2. Cell efficiency and the outlet air temperature as a function of duct depth for air heater. Flow rate = 100 kg/h. Duct depth for curves A, D---I cm; B, E - -2 cm; C, F - - 3 cm.

10 55

- - o - - A

6 7 9

×

+/ ./: :,, / \ . / "

- + - - B - . - - C

- -O- - F - " / ~ G

- - 5 0

- - 4 5 ° ~

- - 4 0

35 (~

x - - 30

- - O - - D

25 17 19 I1 13 15

Time (h)

Fig. 3. Cell efficiency and the outlet air temperature as a function of mass flow rate for air heater. Duct depth = 1 em. Flow rate for curves: B, E- -100 kg/h; C, F - -200 kg/h; D, G - - 3 0 0 kg/h. Curve A represents

the cell efficiency without heat removal arrangement.

PRAKASH: TRANSIENT ANALYSIS OF A PHOTOVOLTAIC-THERMAL SOLAR COLLECTOR 971

10.0 55

--o--A --+-B --*-C --D--D

[3

- x - E " ¢ " - F x ~ -- 50

•

35

0J

9.0 - ©

30

8.5 . I I I 20 9 II 13 15 17 19

Time (h)

Fig. 4. Cell efficiency and the outlet water temperature as a function of duct depth for water heater. Flow rate = 40 kg/h. Duct depth for curves: A, D - - l cm; B, E--2 cm; C, F--3 cm,

.o o ~S

10.0

9.5

9.0

8.5

\

,/"•'•X•x•X•x X ~ ~ .

- - O - - A

- × - E

I 11

55

]so

- + - - B - * - - C ,--£3-- D

- "~--" F ~ G

[ I I 13 15 17

Time (h)

45

G o

40 =

E

35

30

25

I 120 9 19

Fig. 5. Cell efficiency and the outlet water temperature as a function of mass flow rate for water heater. Duct depth = 1 cm. Flow rate for curves: A, 13----40 kg/h; B, E--80 kg/h; C, F--120 kg/h. Curve G is for

ambient temperature.

972 PRAKASH: TRANSIENT ANALYSIS OF A PHOTOVOLTAIC-THERMAL SOLAR COLLECTOR

Table 1. Thermal efficiency (%) for PV/T panels with air/water heating

Air heater Water heater

Flow rate (kg/h) Average thermal efficiency (%) Duct depth (cm) 100 200 300 40 80 120

1 34 45 51 64 66 67 2 22 33 38 57 60 61 3 17 25 31 50 54 55

Table 1. Figure 2 shows the effect o f duct depth on the cell efficiency and outlet air temperature for 12 h o f sunshine. Figure 3 shows the effect o f air flow rate on the cell efficiency and the outlet temperature. The cell efficiency for a conventional photovol ta ic panel having no heat removal arrangement is also plotted. Figures 4 and 5 are the corresponding graphs for water heating.

Table 1 shows the average values o f the thermal efficiency o f the PV/T collector with air/water heating for three flow rates and three duct depths. It is observed that, for water heating the thermal efficiency varies between 50 and 67%, while for air heating, it varies between 17 and 51%. The lower thermal efficiencies in the case o f air heating are due to poor heat transfer between the absorber plate and the flowing air.

F rom Figs 2-5 and Table l, one can easily conclude that the PV/T system has a higher cell efficiency along with the advantage o f getting hot air/water for various applications.

R E F E R E N C E S

I. L. W. Floreschuetz, On heat rejection from terrestrial solar cell arrays with sunlight consideration. Proc. IEEE Photovoltaic Specialists Conference, p. 318 (1975).

2. S. D. Hendrie, Evaluation of combined photovoltaic/thermal collectors. Int. Congress and Silver Jubilee, Atlanta, Ga, U.S.A. (1979).

3. D. J. Mbwe, H. C. Card, and D. C. Card, Sol. Energy 35, 247 (1985). 4. C. H. Cox and P. Raghuraman, Sol. Energy 35, 277 (1985). 5. H. P. Garg, Treatise on Solar Energy. Wiley, Chichester (1982).