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Alleviating operating temperature of concentration solar cell by air

active cooling and surface radiation

Fahad Al-Amri a,*, Tapas Kumar Mallick b,1

a College of Technology, PO Box 7650, Dammam 31472, Saudi Arabiab Environment & Sustainability Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn, Cornwall TR10 9EZ, UK

h i g h l i g h t s

A model has been developed to predict the solar cell temperature cooling by air.

Cell temperature can be remarkably reduced with the presence of surface radiation.

Cell temperature is extremely dependent on air inlet velocity and channel width.

Conjugation effect has a noticeable effect on the maximum solar cell temperature.

a r t i c l e i n f o

Article history:

Received 21 December 2012

Accepted 24 May 2013

Available online 6 June 2013

Keywords:

Concentration solar cell

Active cooling

Conjugate convection

Surface radiation

a b s t r a c t

In the present paper, a heat transfer model for a multi-junction concentrating solar cell system has been

developed. The model presented in this work includes the GaInP/GaAs/Ge triple-junction solar cell with a

ventilation system in which air is forced to ow within a duct behind the solar cell assembly and its

holders and accessories (anti-reective glass cover, adhesive material, and aluminum back plate).

A mathematical model for the entire system is presented and the nite difference technique has beenused to solve the governing equations. Results showed that the interaction of surface radiation and air

convection could adequately cool the solar cell at medium concentration ratios. For high concentration

ratios, the channel width would need to be narrowed to micro-meter values to maintain the required

efciency of cooling. The conjugation effect has been shown to be signicant and has a noticeable effect

on the maximum solar cell temperature. Furthermore, the air inlet velocity and channel width were also

found to have major effects on the cell temperature.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

The rapid growth of the worlds population and the develop-

ment of technology have led to a growing demand for energy in the

last decades. This has led to the growing importance of investing in

sources of energy other than fossil fuels, which began to be

depleted. One of the most promising sources of energy is photo-

voltaic (PV), that is, the direct conversion of solar energy into

electricity, which is expected to help ll the needs of the worlds

growing demand. One of the main disadvantages of the simple

single-junction solar cell is its lowconversion efciency. However, a

conversion efciency exceeding 43% has recently been reported,

with the advent of triple-junction cells[1]. This high efciency has

been achieved through directing a high solar ux on to the solar

cell, a system known as concentrating photovoltaics(CPV). One of

the keyparameter in the CPV systemis the concentration ratio (CR),

which is dened as the ratio between the aperture (area of the

entry optical device) and the receiver (area of the receiver i.e. solar

cell) of the device. The high solar ux at the solar cell increases the

operating temperature of the solar cell which, in turn, leads to a

negative power coefcient unless the cell is efciently cooled. An

active cooling system was found to be the most cost-effective so-

lution, using either air or water as the coolant medium [2]. Since air

has a low heat capacity, water is the favorable option and permits

operation at much higher concentration levels. Nevertheless, in

some situations the use of water is limited, so air will be the

preferred option, especially with the modern PV cells that can be

operated up to 240 C while maintaining reasonable electric con-

version efciency [3,4]. Moreover, higher temperatures are

required for some applications, such as absorption cooling, which

gives an added advantage to the use of air as a coolant medium.

* Corresponding author. Tel.: 966 38681063.

E-mail addresses: [email protected], [email protected](F. Al-Amri),

[email protected] (T.K. Mallick).1 Tel.:44 (0) 1326259465.

Contents lists available atSciVerse ScienceDirect

Applied Thermal Engineering

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 / a p t h e r m e n g

1359-4311/$e see front matter 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.applthermaleng.2013.05.045

Applied Thermal Engineering 59 (2013) 348e354


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Min et al.[5] developed a theoretical thermal model to predict

the temperature of the multi-junction solar cell based on passive

cooling systems. It was found that the heat sink area needs to in-

crease linearly as a function of the concentration ratio in order to

keep the cell at a constant temperature. Cotal and Frost[6] used a

nite difference technique to predict the temperature from variousparts of a concentrator cell assembly. The effects of the thermal

adhesive thickness and the thermal conductivity of the adhesive on

the solar cell temperature were presented. Vincenzi et al.[7]used a

silicon wafer with micro-channels circulating water directly

beneath the cells in their active cooling system. Their photovoltaic

receiver, which operated at a concentration level of 120 sun, was

30 30 cm2 and the reported thermal resistance was

4 105 K m2/W. Moshfegh and Sandberg [8] presented both a

numerical and an experimental study for the ow and heat transfer

characteristics of natural air convection behind solar cells. It was

found that surface radiation can affect the temperature of the solar

panel and hence its efciency. Bhargava et al. [9], Garg and Adhikari

[10], and Adel [11] investigated performance analyses of hybrid

photovoltaic/thermal (PV/T) air heating collectors. In these studies,

simulation models were developed and various performance pa-

rameters were calculated. The effects of various design and oper-

ational parameters on the performance of the systems were

showed and presented. Recently, Al-Amri and Mallick[12]devel-

oped a numerical heat transfer model for a multi-junction

concentrating solar cell system to predict the maximum cell tem-

perature which could be cooled actively by water-forced convec-

tion. It was found that the maximum cell temperature was strongly

dependent on the inlet velocity and channel width. Teo et al. [13]

experimentally investigated an active cooling system for photo-

voltaic modules. A parallel array of ducts with an inlet/outlet

manifold was attached tothe back of the PV panel. It was found that

the temperature dropped signicantly, leading to an increase in the

efciency of the solar cells of between 12% and 14% through using

an air active cooling mechanism. Kumar et al.[14]presented a 3D

heat transfer model for a novel concentrating photovoltaic design

for Active Solar Panel Initiative System (ASPIS). Baig et al. [15]

presented a review of the causes and effects of the non-uniform

illumination on concentrator solar cell. They reviewed the

methods for the solar cell characterization under non-uniform heat

ux conditions and put forward several suggestions for improving

the CPV performance by reducing the non-uniformity effect on the

concentrator solar cells.

Concentrating sunlight onto small photovoltaic cells produced

the demand for the removal of a large amount of heat from a small

area. An innovative way to remove such large amounts of heat is

through incorporation of the micro-channels carrying coolant

within the cells [15,16]. Tuckerman and Pease[17]pioneered the

use of a micro-channel heat sink to cool planar integrated circuits.Later, several studies[18e20]have been performed to analyze the

heat transfer performance and pressure drop of ows in micro-

channels. Qu and Mudawar[21]investigated both experimentally

and numerically the pressure drop and heat transfer performance

of a laminar ow in a micro-channel. The dimensions of the micro-

channel were 213 mm width and 713 mm depth. They concluded that

the ow is still governed by the conventional conservation of mass,

momentum, and energy equations. Recently, Micheli et al. [1]

presented an overview of micro- and nano-technologies appli-

cable to passive CPV cooling and associated manufacturing tech-

nologies (such as monolithic applications). They found that carbon

nano-tubes and high-conductive coating are the most promising

technologies to offer the best CPV cooling performance. A critical

assessment of the technological review has also been made.In the present study, a thermal model to actively cool the

concentrator multi-junction solar cells by air convection with the

aid of surface radiation is developed and presented. This in-house

developed and validated code enabled the optimization of the

channel width for the effective removal of heat from the CPV

systems.

2. Mathematical formulations

The geometry of the triple-junction cell assembly is shown in

Fig. 1. The assembly consists of a triple-junction GalnP/GaAs/Ge

solar cell, a CueAgeHg front contact to the solar cell, a 2 mm glass

cover and a 1.5 mm thick aluminum back plate. The solar cell isattached to the cover glass and rear aluminum plate via an adhesive

material. The cooling air is forced to ow within the ducts behind

the back plate, whose external wall is assumed to be adiabatic. The

two walls of the duct are assumed to be gray, opaque, and diffuse.

Moreover, in the present study, the inlet and outlet channel areas

are assumed to be black at the ambient temperature ( TN 27 C)

and exit bulk temperature (Te), respectively. The efciency of the

triple-junction solar cell (h) is 0.38. The system dimensions and

thermo-physical properties used in the simulation are summarized

inTable 1.

The mathematical equations governing the physical situation

depicted in Fig. 1 are the energy conservation equations in the

multi-walls, the equations of continuity, momentum, energy con-

servation in the uid, and the radiation constraint equations alongeach of the two duct surfaces. Under the usual boundary layer as-

sumptions and neglecting the axial conduction of heat in both the

solid and uid regions, the corresponding dimensionless equations

Fig. 1. Schematic of the system geometry.

Table 1

Thermo-physical properties assumed in the simulation.

Compon ent Mate ri al L eng th

(mm)

Thickness

(mm)

Thermal

conductivity

W/m K

Absorptivity

Solar cell GuInp 10 0.1 73 0.04

GuAs 10 0.2 65 0.40

Ge 10 0.2 60 0.50

Front contact Cu Ag Hg 2 0.025 300 0.15

Glass cover Low-iron glass 10 2 12 0.04Adhesive 10 0.5 50 0.02

Back plate Aluminum 10 1.5 238

F. Al-Amri, T.K. Mallick / Applied Thermal Engineering 59 (2013) 348e354 349


4/8


that govern the conjugate laminar mixed owand the heat transfer

in the entry eregion of the two parallel plates are:

vV

vY

vU

vZ 0 (1)

VvU

vY U

vU

vZ

dP

dZ

G*rRe

q qN v

2U

vY2 (2)

VvqfvY

UvqfvZ

1

Pr

v2qf

vY2 (3)

v2qs

vY2 0 (4)

The continuity equation(1) can be written in the following in-

tegral form:

F

Z1

0

UdY 1 (5)

The radiation constraint equations are:

Surface 1 (Y 0)

Nradq4N

1

2

ZRe

2

1 Z2Re2

12 Nradq

4e

1

2

LZRe

2

1 LZ2Re212

Z

L

0

1 3232

vqf

vY

Y1

vqsvY

Y1

Nradq4w2 Z

*

1

2

h1 Re2ZZ0

2i3=2

Re dZ0 1 31

31

vqfvY

Y0

Nradq

4w1 Z

vqfvY

Y0

(6)

where:Nrad sq31b

4=k4f.

Surface 2 (Y 1)

KRs1fvqsvY

Y1

Nradq4N

1

2

ZRe

2

1 Z2Re2

12

Nradq4e

1

2

LZ

2 Re

1 LZ2Re2

12

ZL

0

1 31

31

vq

vY

Y0

Nradq

4w1 Z

*1

2

h1 Re2ZZ0

2i3=2

Re dZ0 1 32

32

vqfvY

Y1

vqsvY

Y1

Nradq

4w2

Z vqfvY

Y1

(7)

For the limiting case of absence surface radiation (i.e. 3 0), the

above two radiation constraint equations are reduced to:

vqfvY

Y0

0 (8)

KRs1fvqsvY

Y1

vqfvY

Y1

(9)

The conjugate convection eld equations are subject to the

following dimensionless boundary conditions:

ForZ 0 and 0 < Y< 1

U 1; V P 0; q qN (10a)

ForZ> 0 andY 0

U V 0 (10b)

ForZ> 0 andY 1

U V 0 (10c)

ForZ> 0 andY YSii1 ,i 1 and 2

vqsvY

YYSii1

kRSi1ivqsvY

YYSii1

(10d)

ForY YSii1 and 0< Z< Zcor (Zc Lc)< Z< L,i 3 and 4

vqsvY

YYSii1

kRSi1ivqsvY

YYSii1

1 hasi

1 ag aad

KRsi f

(10e)

ForY YS57 and 0 < Z< Zcor (Zc Lc)< Z< L

vqsvY

YYS5

7

kRS75vqsvY

YYS5

7

1 has5

1 agaad

KRs5f

(10f)

ForY YSii1 andZc Z (Zc Lc),i 3, 4, and 5

vq

vY

YYSii1

kRSi1ivq

vY

YYSii1

(10g)

ForY YS67 andZc Z (Zc Lc)

vq

vY

YY

S67

kRS76vq

vY

YY

S67

as6

1 ag aad

kRs6f

(10h)

ForZ> 0 andY YS78

vqvY

YY

S78

kRS87 vqvY

YY

S78

as7

1 ag aad

kRs7f(10i)

ForZ> 0 andY YS8

vq

vY

YYS8

agkRs8f

(10j)

wherekRsi1i ksi1=ksi , andkRsi f ksi=kf

3. Method of solution

The solution is broken down into two sub-problems. The rst

involves treating the conjugate convection eld equations (conti-

nuity, momentum, and energy) as an initial value problem with anumerical marching technique used to obtain a solution. The sec-

ond involves the solution of equations (6) and (7) iteratively to

F. Al-Amri, T.K. Mallick / Applied Thermal Engineering 59 (2013) 348e354350


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update the wall temperatures. These updated wall temperatures

are again used to resolve the conjugate convection eld equations.

Then, the process is repeated until convergence is achieved. The

rst iteration assumes no radiation (i.e. 3 0). Then, the obtained

wall temperatures and temperature gradients are used in the in-

tegrals of the radiation constraint equations(6) and (7)and thesetwo equations are solved iteratively by means of the Gauss-Seidel

technique. The results obtained from the solution of equations(6)

and (7) are then used to resolve equations (1) through (5). The

procedure is repeated until the difference between the old and new

values of temperatures is less than a prescribed tolerance (106

percent in the present investigation). The ow chart inFig. 2shows

the numerical solution methodology.

4. Validation

In order to validate the method of solution and the numerical

code presented in this paper, the present results have been

compared with the experimental work of Moshfegh and Sandberg

[8]. In their experiment, which was used to validate their numericalmodel developed to analyze the ow and heat transfer character-

istics of natural air convection behind photovoltaic panels, heat is

supplied to the air gap from heating foil attached to one of the two

vertical non composite walls. Thus, all the input heat ux is dissi-

pated into the coolant uid through a wall and hence ag 1,h 0

andKRs(i1)i1(for all solidesolid interfaces). A special computer

run of the present code was conducted for [ 7 m, q 20 W/m2,

KRs1f 18;000, 3 1,b0.23 m,uN 0.245 m/s andt0.01 m.

Such a comparison of the heated and adiabatic wall temperatures

obtained by the present code with those obtained experimentally

Start

Read input

parameters

Solve Equations 1-5 subject to the boundary conditions Equations

8,9, and 10 a-j (assuming =0) by using marching technique.

Iteration = iteration +1

Solve Equations 6 and 7 for the two duct wall

temperatures iteratively using Gauss-Seidel technique.

6

wwT ( noitareti 1) T ( noitareti ) 01

+

Write T values

Stop

Solve Equations 1-5 using

T ( noitareti 1)w

+ and subject

to Equations 10 a-j

Iteration = 1

Yes

No

Fig. 2. Flow chart of the numerical solution methodology.

Fig. 3. Comparison of walls temperature between present results and [8] for

b 0.23 m, t 0.01 m, uN 0 :245 m=s; 3 1 ; [ 7 m; q 20 W=m2;

KRsi1i 1,KRs1f 18 ; 000.



6/8


7/8


surfaces of the duct should be completely matt surfaces (3 1).

However, the solar cell can be operated at 240 C forC 100 even

with completely shinny duct surfaces (3 0), as shown in the gure.

Moreover, it is found that the operating cell temperature decreasesnon-linearly with increasing emissivity of the surfaces.

The effects of inlet air velocity on the variation of the maximum

cell temperature areshown in Fig. 6. Results are computed for three

selected values of the inlet air velocity, namely, 8 (Re 500), 16

(Re 1000), and 32 m/s (Re 2000). Air that enters the inlet

channel removes heat from the hot PV cell; the heatedair leavesthe

exit channel, which can be used for space heating, an absorption

cooling system, or other applications. It can be seen that the

maximum cell temperature decreases as the inlet velocity in-

creases, as shown the gure. This, in turn, improves the electrical

conversion efciency of the PV system and increases the collected

thermal qualities of the air. Fig. 7 shows the variation of the

maximum PV temperature with the concentration ratio for three

selected values of channel width. It is observed from the gure thatthere is a signicant reduction in the maximum temperature as the

channel width decreases, since the convective heat transfer coef-

cient decreases with the channel width. This means that nar-

rowing the channel width to the micro-scale value causes a great

removal of heat from the PV system. But this also leads to a sizable

pressure drop, which requires considerable pumping power [16].

Moreover, increasing inlet velocity or decreasing channel width

increases the critical concentration ratio. In the present examples

pertinent toFigs. 6and 7, the critical concentration ratio increases

by 52%, from 130 to 196, and by 82%, from 196 to 345, as the inlet

velocity increases from 8 m/s (Re500) to 32 m/s (Re 2000) and

the channel width decreases from 1 mm to 0.5 mm, respectively. In

addition, it can be noticed fromFig. 5that the solar cell cannot be

operated at 240 C or below for concentration ratio 200 or above

even though with Re as high as 2000 (uN 32 m/s) and emissivity

ashigh as 1 as long asb>1 mm. In order to operate the solar cell at

a concentration ratio higher than 200 while maintaining reason-

able conversion efciency, the channel width should be narrowed

to less than 1 mm as shown in Fig. 7.

To study the effects of the conjugation (i.e., coupling of con-

duction and convection) on the heat transfer, three different cases

for thicknesses values (Table 2) and thermal conductivities values

(Table 3) of the holders and accessories for the solarcell (back plate,

adhesive material, and transparent front cover) are studied.Figs. 8and9show the effect of thicknesses and thermal conductivities of

the back plate, adhesive material, and transparent front cover on

the maximum temperature of the cell. It is obvious from these two

gures that the maximum cell temperature decreases as the ther-

mal conductivities of the holders and accessories increase or as the

thicknesses of these components decrease. The reason for this is

that increasing thermal conductivities or decreasing thicknesses of

the solid walls leads to a reduced overall resistance, resulting in a

large amount of heat being removed from hot PV cell and hence

improve its efciency. Thus, conductive thermal resistance has a

noticeable effect and is considerable compared to convective

thermal resistance. However, this effect has not been noticed for

water[12]because of the high value of its convection heat transfer

coefcient which mean conduction is negligible compared toconvection.

6. Conclusions

A numerical heat transfer model has been developed to predict

the maximum solar cell temperature cooling actively by air-mixed

convection with and without the interaction of radiation. It was

found that the cell temperature can be reduced remarkably with

the presence of surface radiation. The maximum cell temperature

can be reduced by as much as 50%, as the duct surfaces change from

good reectors to good emitters. In addition, results show that the

maximum cell temperature and the critical concentration ratio are

extremely dependent on air inlet velocity, channel width, and

thicknesses and thermal conductivities of the solar cell holders andaccessories. For channel width higher than or equal 1 mm, it was

found that the solar cell can be adequately cool up to concentration

Table 2

Thickness values (mm) used for the results generated in Fig. 7.

Component Case I Case II Case III

Transparent front cover 4 2 0.20

Adhesive material 1 0.5 0.05

Back plate 3 1.5 0.15

Table 3

Thermal conductivities values (W/m K) used for the results generated in Fig. 8.

Component Case A Case B Case C

Transparent front cover 3 12 24

Adhesive material 12.5 50 100

Back plate 59.5 238 476

Fig. 8. Effect of thicknesses of solar cell holders and accessories on maximum

temperature [uN 32 m/s, 3 0.5, b 1 mm].

Fig. 9. Effect of thermal conductivities of solar cell holders and accessories on

maximum temperature [uN 32 m/s, 3 0.5, b 1 mm].



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ratio 200. However, the level of concentration could be raised up to

345 by narrowing channel width to 0.5 mm.

Acknowledgements

This work was supported by King Abdulaziz City for Science andTechnology, Saudi Arabia.

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Nomenclature

b:channel width, mGr

*:modied Grashof number,gbq1b4/y2Kf

k:thermal conductivity, W/m K[: channel length, mL:dimensionless plate length, [/bRe

p:pressure ofuid at any cross section, N/m2

p0:pressure defect at any cross section, p ps, N/m2

ps:hydrostatic pressure, rNgz, N/m2

pN

:pressure of

uid at channel entrance, N/m

2

P:dimensionless pressure at any cross section, p0 pN=rNu2N

Nrad:radiation number, sq31 b

4=k4fq1:input heat ux, W/m

2

Re:Reynolds number, uob/yt: solar cell assembly thickness, mT:temperature at any point, KTN:inlet temperature,KuN:entrance axial velocity, m/su:longitudinal velocity component at any point, m/sU: dimensionless longitudinal velocity, U u/uNv:transverse velocity component at any point, m/sV:dimensionless transverse velocity,V b*v/y

y: horizontal coordinate, mY:dimensionless horizontal coordinate, y/b

z:vertical coordinate, mZ: dimensionless vertical coordinate, z/(b*Re)

Greek symbols

y: kinematic uid viscosityr: uid density, kg/m3

m:dynamic uid viscosity, kg/m sa:absorptivityh:efciency of the solar cellq: dimensionless temperature at any point [kfT/q1 b]qN:dimensionless inlet temperature at any point [kfTN/q1 b]3:wall emissivitys: StefaneBoltzmann constant 5.67 108 W/m2 K4

Subscriptsad:adhesive materialc:a CueAgeHg front contacte: exit

f: uidg:glasss:solidw:wall of the channelN: ambient or inlet1:duct wall atY 0

2:duct wall atY 1

F. Al-Amri, T.K. Mallick / Applied Thermal Engineering 59 (2013) 348e354354

ATE - Surface Cooling Air and Surface Radiation

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Transcript of ATE - Surface Cooling Air and Surface Radiation