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An Investigation of A Novel Structure Polycrystalline Silicon Solar Cell for

Concentrated Solar Power

Conference Paper · June 2017

DOI: 10.1115/ES2017-3388

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AN INVESTIGATION OF A NOVEL STRUCTURE POLYCRYSTALLINE SILICON SOLAR CELL FOR CONCENTRATED SOLAR POWER

Ali Radwan

Energy Resources Engineering Department, Egypt-Japan University of Science and

Technology (E-JUST), Alexandria, Egypt. Ali.radwan@ejust.edu.eg

Mohamed Emam Energy Resources Engineering Department,

Egypt-Japan University of Science and Technology (E-JUST), Alexandria, Egypt.

mohamed.emam@ejust.edu.eg

Radwan M. Elzoheiry Energy Resources Engineering Department,

Egypt-Japan University of Science and Technology (E-JUST), Alexandria, Egypt.

radwan.elzoheiry@ejust.edu.eg

Mahmoud Ahmed1 Energy Resources Engineering Department,

Egypt-Japan University of Science and Technology (E-JUST), Alexandria, Egypt.

mahmoud.ahmed@ejust.edu.eg

1 On leave from mechanical Engineering Department, Assiut University, Assiut 71516, Egypt E-mail: aminism@aun.edu.eg

ABSTRACT To achieve reliable and efficient operation of generic polycrystalline silicon solar cell under concentrated sunlight, a novel structure of the cell layers is proposed along with effective cooling technique using microchannel heat sink (MCHS). In the novel structure, Boron Nitride with the volume fraction of 20%, 40%, and 60% as a filler is incorporated in the Ethylene Vinyl Acetate (EVA) matrix to form a new composite. The new composite is used instead of the conventional EVA layer in the solar cell. Various solar cell structures integrated with MCHS are studied and compared with the conventional structure. To determine the performance of the developed concentrated photovoltaic thermal (CPVT) system, a comprehensive three-dimensional model of the solar cell with heat sink is developed. The model is numerically simulated and validated. Based on the validated results, it is found that the novel structure with EVA-60% BN composite along with aluminum foil back sheet attains 30% increase in the gained solar cell electric power with 10.9 % reduction in the cell temperature compared with the conventional solar cell structure at the same cooling mass flow rate of 50 g/min and concentration ratio of 20. However at CR=20, Vw=1m/s and Ta=30oC a significant damage of the conventional solar cell structure will occurs if no effective cooling technique is used. Moreover, the developed design of solar cell achieves a higher CPVT-system thermal efficiency compared with the conventional one. 1. INTRODUCTION

The generic crystalline silicon solar cells have been the most popular commercial material that converts solar energy

directly into electricity. However, the conversion efficiency of such solar cells is limited. In addition, the high capital cost of such devices is another drawback. One proposed way to reduce the cost of solar electricity production systems is to replace some expensive solar cells with low-priced concentrating lenses or mirrors. However, sunlight concentration onto photovoltaic cells causes a significant increase in the cell temperature which decreases the system efficiency. Also, the long-term high operating temperature leads to irreversible degradation of the solar cells[1]. Another proposed way to enhance the efficiency of concentrated photovoltaic (CPV) systems is to use an efficient cooling technique that will attain a higher electrical efficiency and allow the operation of such systems under higher concentration ratio (CR). Moreover, using water as a heat extractor from the illuminated solar cells is one of the promising directions of converting solar energy into electrical energy and low-grade heat.

The objective of the current work is to present a reliable and efficient structure of polycrystalline silicon solar cell based on enhancing the thermal properties of the encapsulating material in the conventional cells along with replacement of the standard back sheet with aluminum backing foil layer. The performance of proposed solar cell structure will be compared with the conventional structure under concentrated illumination cooled with microchannel heat sink (MCHS). A comprehensive three-dimensional thermo-fluid model is developed to estimate the thermal and electrical performance of the CPVT system. The model is validated with various analytical and experimental results. The effects of CR and coolant mass flow rate on the overall performance of the CPVT system are investigated. The

Proceedings of the ASME 2017 11th International Conference on Energy Sustainability ES2017

June 26-30, 2017, Charlotte, North Carolina, USA

ES2017-3388

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current results could provide a theoretical guidance for the industrial field to manufacture such novel solar cell structure. 2. PHYSICAL MODEL

In the polycrystalline solar cell, there are different layers; the glass cover, an anti-reflective coating (ARC), a silicon layer, ethylene vinyl acetate (EVA) layer, and tedlar polyester tedlar (TPT) layer. The whole layer of the CPV system integrated with the MCHS is presented in Fig.1 while the full dimensions of the MCHS are shown on Fig.2 and the thermal characteristics of PV layer are presented in Table.1

The typical dimensions of the commercial solar cell are 125 mm by 125 mm and the EVA interval between each cell and the adjacent cell is 2 mm. In the current study, only one cell is investigated. Therefore, the whole dimension of the computational domain is 127 mm by 127 mm. The investigated microchannel height is selected to be 100 μm[2] because it is approximately representing the mid-size range of microscale. Moreover, it was reported that the maximum heat transfer coefficient for the rectangular ducts can be obtained if the aspect ratio of the channel is eight [2]. Consequently, the designed microchannels are selected to be with dimensions of 100µm height and 800µm width. Each cooling unit is composed of 106 parallel channels. The PV layers rest on the designed MCHS. Water is used as a coolant to maintain a high cooling efficiency and avoid excessive cell temperatures with CRs up to 20.

In most of the existing numerical investigations, periodic domains were modeled to minimize the computational time. The use of periodic domain idea is suitable for the symmetrical boundaries in the integrated circuits. It is interesting to clarify that in the integrated circuits, the heat flux is uniformly distributed on the MCHS wall and periodic domain idea is suitable for such devices. On the other hand, in the polycrystalline silicon solar cell, the silicon layer is embedded in EVA due to the difference in the each layer absorptivity, thickness, and material, the heat generation in each layer is different [3]. Consequently, dealing with the periodic domains is not accurate for such application because the generated heat is not uniform over the microchannel domain. Therefore, in the current study, whole dimensions of the proposed cell area are numerically solved using parallel processing of Dell Precision T7500 workstation with Intel Xeon® processor of 3.75GH, 48-core, and 64-MB installed memory instead of using periodic domain ideas.

2.1. THEORY OF THE CURRENT INNOVATIVE

Based on energy balance on each layer of the solar cell, the absorbed solar irradiance by the silicon layer is high due to its higher absorptivity. Portion of the absorbed solar irradiance is converted into electricity depending on the cell efficiency, and the remainder part is converted to heat which increases the cell temperature. Another part of the absorbed solar irradiance is lost to atmosphere from the upper surface by conduction in EVA and glass [4] and then by combined convection and radiation from the glass cover to atmosphere. The remainder

thermal part is lost through conduction in back EVA and TPT layer and then to the coolant in the MCHS in CPVT system. Through upper heat loss, the difference between the silicon layer temperature and ambient temperature can be written as follows:-

topg

g

EVA

TopEVA

ARC

ARCtopasc UKKK

qTT 1,'' (1)

Where: Tsc, Ta, q"top, K, δ, and Utop are the solar cell, and ambient temperature, top heat loss per unit area of the cell, thermal conductivity, thickness, and overall heat transfer coefficient by combined convection and radiation from the glass cover to atmosphere respectively. Any modification on the upper layers may not be significant because the most effective parameter is the meteorological condition, i.e. wind speed and ambient temperature, at the same absorbed solar radiation.

Equation (2) represents the solar cell temperature as a function of the back heat loss per unit area of the solar cell q"bottom and the thermal resistance on the back side due to the existence of EVA, TPT back sheet and the overall heat transfer coefficient of the microchannel heat sink respectively.

fTPT

TPT

EVA

BottomEVABottomfsc UKK

qTT 1,'' (2)

Where, Uf is the overall heat transfer coefficient of the MCHS. It is well known that the thermal resistance (1/Uf) of MCHS is very small due to the high heat transfer coefficient in small size channels and high thermal conductivity of the solid channel material [5]. In more details, the sum of the first two terms on the right-hand side of equation (2) is about 0.0036(m2. K)/W while the third part is a 4.56×10-5(m2. K)/W which is equivalent to a fully developed Nusselt number of 6.49 for microchannels with aspect ratio of eight [5]. Here it worth mentioning that the most significant factor affecting on the heat transfer from the back side of the solar cell is the back EVA and TPT layer thermal resistances. Consequently, enhancing the EVA and TPT thermal conductivity is the proposed novel idea.

Figures 3-a, and 3-b show the schematic of the conventional and the new solar cell structure respectively. Briefly, in the new design, the conventional EVA layer under the silicon layer is replaced by EVA mixed Boron Nitride (BN) powder as filler materials with a volume fraction of 20%, 40, and 60%. Moreover, the conventional TPT layer has a lower thermal conductivity and consequently it is replaced by aluminum backing foil in the new structure. The manufacturing process of EVA-φ%BN composite can be achieved by good mixing of BN powder with EVA granules. Using twin screw extrusion can easily form a sheet of the composite with the required thickness [6]. The mixing of polymers and ceramic powders to increase thermal conductivity is used in microelectronics, where efficient heat dissipation is necessary[7]. Both of conventional and modified solar cells are attached to MCHS to reduce its operating temperature and achieve an efficient operation under concentrated illumination.

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Channel

Inlet Plenum

Tedlar

EVASiliconGlass

A

A

Glass

Computational domain

Side-view Cross-sectional view at A-A

Concentrated solar radiation

Wch

Hch

Channel

NB: Not to scale

Outlet Plenum

Silicon

Concentrated solar radiation

Fig. 1 Schematic diagram of the CPV system integrated with MCHS.

L sc

Inlet

δg

δT

δch

Concentrated solar radiation

δsc

ARC

NHch

WchWf

x

y

z

δ intδint

δw

δw

δARC+2δEVA+δsc

δ int

Lsc +2δint

Outlet

Fig. 2. Schematic diagram of the investigated MCHS integrated with PV cell layers.

Glass

Tedlar

Conventional solar cell structure

Modified solar cell

Glass

Pure EVASilicon

(a)

(b)

SiliconEVA-φ%BN

layer

Aluminium backing foil

Cell part

Interval part

Interval part

Fig.3. Assembly sketch of the solar cell layers (a) Conventional solar cell structure, and

(b) Modified solar cell structure. Table.1 Photovoltaic/ thermal layer physical properties[3,8]

Layer Density (kg/m3) Specific heat (J/kg.K) Thermal conductivity (W/m.K) Thickness (mm)

Glass (Cover) 3000 500 2 3 ARC 2400 691 32 0.01 Encapsulation (EVA) 960 2090 0.311 0.5 Silicon 2330 677 130 0.2 Tedlar 1200 1250 0.15 0.3 MCHS (Aluminum) 2719 871 202.4 0.2 Boron Nitride powder Grade(XP)

1900 1470 71 ----

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Boron Nitride powder with particle size of 10 nm is used as a polymer filler because it is a white solid material with low porosity. In addition, it is easily machined into complex shapes using standard carbide tooling. Boron nitride is often mentioned as “white graphite” because it is a lubricious material with the same hexagonal structure as carbon graphite. Unlike graphite, BN is a good electrical insulator. Moreover, it has excellent properties such as low thermal expansion, high thermal conductivity, high electrical resistance, low dielectric constant, good thermal shock resistance, and loss tangent, microwave transparency, and nontoxic. It is commonly used for electronic parts heat sinks, substrates, and high-temperature furnace fittings and supports. In the current work, the pure grade XP of BN material which contains no binders is used because it is more efficient for the applications with extreme of temperature and where purity is important.

3. NUMERICAL MODEL

A comprehensive thermal model is developed to compare the performance of the conventional cell with the proposed structure integrated with MCHS and operating under concentrated illumination conditions. The heat transfer in CPVT system involves multiple solid domains and fluid domain. In the current three-dimensional conjugate heat transfer model, the following assumptions are adopted:

i. The flow is steady, laminar, and incompressible. ii. The solid domain properties are assumed to be

temperature independent. iii. The thermal contact resistances among each layer were

neglected.

The current thermal model is developed to compare the temperature of the conventional and new solar cell structure cooled with parallel flow MCHS. The CPV system contains a several solid domains where the energy equation is essential to be solved. While in the case of CPVT system, the continuity, momentum and energy equations for the coolant coupled with the energy equations for the MCHS body and the complete CPV system layer also should be coupled and solved. For solar cell layers

As the general form of heat diffusion equation is in Cartesian coordinates for the solid domains can be represented as follow[9]:-

1,2,.n=i0,,,,,,

2

2

2

2

2

2andq

zzyxT

yzyxT

xzyxTk i

iiii

(3)

Where the term qi and ki represents the heat generation in the layer i due to the absorption of the solar radiation and the thermal conductivity of the layer i. And in the current study, the value of n changes from 1 to 5 for glass, upper EVA, silicon, lower EVA, and tedlar layer respectively. This equation is solved five times for each layer.

Here it is worth mentioning that, the heat generation per unit volume of the layer due to the solar irradiance absorption of the CPV cell layers can be calculated by the following equation[3].

i

ijisci V

AGq

1 (4)

Where, qi is the heat generation per unit volume in the layer i; ηsc is the solar cell electric efficiency and its value changes to zero when the internal heat generation of other layers is calculated; αi, Ai, and Vi are the absorptivity, area, and volume of the layer i, respectively; τj is the net transmissivity of layers above the layer i.

In more details, for the cell part, the heat generation in the

glass cover is dependent on the glass absorptivity and the amount of net concentrated solar irradiance. By the same way, the heat generated in the top EVA layer is dependent on the transmissivity of the glass and the absorptivity of EVA and net concentrated solar irradiance as well. However, the heat generation term for the silicon layer is dependent on the transmissivity of glass, EVA layer above the silicon, net concentrated solar irradiance G, and then dependent on the solar cell efficiency which is function on the cell temperature. In meanwhile, it is interesting to elucidate that the heat generated TPT layer can be neglected in the cell part for lower transmissivity of the silicon layer[3]. On the other hand, in the interval part, the heat generation in each layer depends on the absorptivity of the layer , transmissivity of the upper layers and the reflected part from the tedlar as the tedlar material is high reflective. This idea is supported by[3].

The heat generation in the silicon layer is dependent on its efficiency which is calculated using the following equation [10–12]:-

))(1( refscrefrefsc TT (5)

Where the ref and βref are the solar cell efficiency and temperature coefficient at a reference temperature of Tref =25o C respectively. These values are provided by the manufacturer data sheet for most solar cells. And βref is taken to be 0.0045K-1 for polycrystalline silicon[13]. Deep insight into the heat generation in the silicon layer, it is dependent on the silicon layer efficiency which is function of the cell temperature, which is unknown. So two solution techniques can be applied to solve this problem. The first one can be achieved using a UDF in the energy equation of the silicon layer which is function of the silicon layer temperature. Another possible way can be achieved using iterative technique. And the second solution technique is implemented in the current study as will be explained in details in section 3.2. For MCHS substrate: -

0,,,,,,2

2

2

2

2

2

zzyxT

yzyxT

xzyxTk chchch

ch (6)

Where kch is the microchannel material thermal conductivity. In the recently available one-dimensional energy

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balance modeling techniques, the heat transfer from the back side of the CPV cells is calculated based on the appropriate Nusselt number correlations for the thermal absorbers. This way is not accurately suitable for the newly developed MCHS with unknown heat transfer and fluid flow characteristics. Instead of using this conventional way, a new modeling technique is presented via numerical solution of coolant Navier Stokes equations coupled with the whole solar cell layers’ equations. The currently solution technique can predict the heat transfer and friction characteristics in each configuration with sensitivity to each variation in the operating parameters and the design variable of the MCHS.

For fluid domain in the MCHS: -

As the fluid temperature substantially changes inside the

microchannel, especially with higher CR values. Hence, in the present calculations, the variation of water thermophysical properties with temperature is considered using the higher ordered polynomial equations presented in [14]. The fluid flow and heat transfer governing equations are described for the fluid domain as follows [15]:-

Continuity equation:

0.0zw

yv

xu

))) ((( (7)

Momentum equations [16].

zu

zyu

yxu

xxP

zuw

yuv

xuu

(8)

zv

zyv

yxv

xyP

zvw

yvv

xvu

(9)

zw

zyw

yxw

xzP

zww

ywv

xwu

(10)

Energy equation for fluid [16]

zwk

zywk

yxuk

xzTwC

yTvC

xTuC (11)

Where: u, v, and w are the velocity component in x, y, and z-direction respectively. And P, µ, , C, k, and T are the fluid pressure, dynamic viscosity, density, specific heat capacity, thermal conductivity, and temperature profile respectively. The numerical solution is achieved using FLUENT 16.2 [17].

In order to attain a relatively constant inlet coolant

temperature, an open loop cooling system is proposed in the current study. That’s mean the coolant is taken from a large reservoir with a constant temperature and then allowed to pass in the MCHS using pump to cool the CPV system. And then the outlet heated water is used directly in domestic or industrial application.

The electrical power produced by the CPVT system, Pel is

expressed by the following equation [18]:-

scscscgscel lwtGP .)( (12)

Where:sc, τg , G(t), wsc, lsc are the solar cell efficiency, glass transmissivity, the net concentrated solar radiation incident on the surface of the solar cell regardless of the concentrator optical losses, width and the length of the solar cell respectively.

The gained rate of thermal energy is calculated using the following equation:

)(.,,, infoutfinpfth TTCmP (13)

Where: Pth, Cp,in , Tf,out, Tf,in are the rate of thermal energy, specific heat capacity of the water, and the average fluid temperature at the outlet and inlet of the MCHS respectively. Through the results discussion, the terms Reynolds number, hydraulic diameter, thermal efficiency, net concentration ratio, coolant mass flow rate, friction power, and the net power are calculated using the following equations respectively: -

in

hinin DV

Re (14)

chch

chchh WH

WHD

2 (15)

sc

thth AtG

P.)(

(16)

2/1000,)( mwGG

tGCR refref

(17)

NVWHm inchchin (18)

infrict mPP /.. (19)

2

2inin

h

VDlfP

(20)

.frictscnet PPP (21)

Where; in, Vin, µin, Dh, Hch, Wch, Asc, N, ∆P, Psc, Pfrict., Pnet are the water density, velocity, viscosity, channel hydraulic diameter, the channel height, channel width, solar cell area, number of channels, pressure drop, solar cell electric power, MCHS friction power, and the net gained electric power respectively. In the current study, the equivalent density, specific heat capacity, and thermal conductivity of the EVA polymer mixed with Boron Nitride are specified by the following equations[19]:- Density

pmcomposit )1( (22)

Specific heat

ppmpcompositp CCC )1( (23)

Thermal conductivity[20] pmpm

pmpmmcomposit KKKK

KKKKKK

222

(24)

Where m and p refers to the matrix material (continuous phase) and the filler phase, i.e. Boron Nitride.

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In the present study, the solar energy absorption of all layers is taken into consideration to simulate the actual situation. Due to the silicon layer is embedded in the EVA layer, and the existing of the adjacent solar cell, so the heat generation in the interval part between each cell and the adjacent one is also considered. The simulated model is divided into cell part and the interval part as displayed in Fig.3-a. In the cell part, the layers under the silicon layer are not directly exposed to the concentrated solar flux due to the lower transmissivity of the silicon layer. Consequently, the generated heat in the EVA and tedlar layer under the silicon layer can be neglected. Moreover, due to the existence of ARC layer and the low silicon layer reflectivity, the reflected solar irradiance absorption by glass and EVA above the silicon layer is also neglected [3]. So, only the absorption of net concentrated solar irradiance by glass, EVA above the silicon, and the silicon layer are considered. While in the interval part, all the layers are directly exposed to the net concentrated incoming irradiance. Both the incident irradiance and the reflected irradiance by tedlar layer are considered due to the high reflectivity of the tedlar. Table 2 and table 3 shows the optical properties and computational domain dimensions respectively.

Table 2 indicates the optical properties of each layer.

Material (ρ) (α) (τ) (ε)

Glass 0.04 0.04 0.92 0.85

EVA 0.02 0.08 0.90 Silicon 0.08 0.90 0.02

TPT 0.86 0.128 0.012 0.9 Aluminum --- ---- ---- 0.9

Table 3: Computational domain design parameters

Factor Value Factor Value Lsc 125 mm Wsc 125mm Hch 0.1mm Wch,flat 125.6 mm Wch 0.8mm N 106 δw 0.2mm δch 0.5mm Asc 125×125 mm2 δint 1mm

3.1. Boundary conditions

Generally, at the inlet of the computational domain, the fluid velocity component (w) is identified and assumed to be uniform, and it is varied according to the value of the coolant mass flow rate. Moreover, the channel flow Reynolds number is checked to be within the laminar flow regime Re<2300. In addition, a uniform inlet temperature is assumed at the inlet. In the meantime, zero gage pressure is identified at the microchannel outlet section. Since water molecular mean free path is about 0.25 nm. Hence, Knudsen number (Kn) falls in the no-slip regime (Kn<0.001). So, no-slip and no temperature jump boundary conditions are considered at the solid–fluid interfaces. The thermal boundary condition for the upper wall of the glass layer is combined convection and radiation loss. The convective

heat transfer coefficient, ambient temperature, surface external emissivity, and the external radiation temperature should be accurately specified. The energy generation in each layer is added as a source term in the energy equation for each solar cell layer. Finally, the side walls of the computational domain are assumed to be adiabatic. The lower wall of the computational domain is also assumed to be completely insulated. For all existing solid-solid interfaces, thermally coupled boundary conditions are applied.

For the glass cover thermal boundary conditions, the

equivalent radiative heat transfer coefficient is calculated using the following correlation[10]:-

2244

, sgsggsg

sggsgrad TTTT

TTTT

h

(25)

And the surface external emissivity is taken to be the same value for the glass emissivity while the external radiation temperature is calculated using the sky temperature with the following correlation[21,22]: 5.10522.0 as TT (26)

In addition, the convection heat transfer coefficient due to the wind effect is calculated by the empirical correlation[3]:

wagcon Vh 07.482.5, (27) Where; Vw is the wind speed, it was taken to be 1m/s

through all results and the ambient temperature and the inlet fluid temperature are taken to be 30oC. It is worth mentioning that the wind effect, ambient temperature, and fluid inlet temperature effect on the performance of the CPVT system are investigated in the author earlier work [23].

3.2. Numerical method

The governing equations were simulated using the implicit method. The second order upwind scheme is used to solve the convective terms in the momentum and energy conservation equations. Moreover, the SIMPLE algorism is applied for the coupling of pressure and velocities. In the existing governing equations, the solar cell temperature is dependent on its efficiency. On the other hand, the solar cell electrical efficiency decreases with the operating temperature which is mainly unknown at a particular climatic condition. Consequently, an iterative solution technique is adopted in the current work. The solution steps are presented in the author earlier work [1] with two convergence criteria of 10-3 for solar cell temperature and 10-6 for fluid equations. Furthermore, the grid independence test is performed, and the validation of numerical simulation through comparison of the predicted results with the available experimental, analytical, and numerical data is carried out. A mesh independence test is performed and it is found that increasing the number of cells greater than 30370272 will not effect on the solar cell temperature and consequently this number of cells is adopted through all the simulations.

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4. Model validation The current model is validated using different sets of the

available experimental and analytical results available in the literature. The first set of results is used to verify the solution of Navier-stokes equations with the existing analytical solution for the same aspect ratio channels[24]. The second set of results is used to validate the comprehensive thermal model of the cooled concentrated solar cell (CPVT) with the available experiments and numerical results published in[25].

4.1. Fluid flows validation

The predicted outlet velocity profile is validated with the available analytical data. The analytical fully developed profile is determined using a series solution of equations (28) to (30) [24]. In house-MATLAB code is performed to compute the three dimensional fully developed velocity profile of the rectangular channel and then compared with the predicted values via the solution of the three-dimensional Navier-stokes equations.

+ ,)28(

2cos

)2/cosh()2/cosh(1)1(16),(

,...5,3,13

2/12

3

0

0

0≅

♣

≅

0

axn

abnayn

na

dzdpyxu

n

n σσσ

πσ

Where the pressure gradient dp/dx is related to the inlet mean velocity regarding the following correlation: -

(29)2

tanh1192131

,...5,3,155

2

0

0≅

♣

≅nmean a

bnnb

aadzdpu σ

σπ

22chch HbandWa ≅≅ (30)

In Fig.4, the comparison between the predicted and the analytical results of the fully developed velocity profile is presented. The velocity profiles are drawn at a line located in mid-height and mid-width of the microchannel outlet section in Fig.4-a and 4-b respectively. The comparison indicates an excellent agreement with the analytical velocity profile. It is found that the predicted velocity profile deviates from the analytical value by a maximum error of 0.84% at the center of the channel. Moreover, the predicted Poiseuille number is 20.67, while the analytical value is 20.58 for the channel aspect ratio of eight [24]. Based on the current validation, the present model accurately predicts the fluid flow behavior with a precise solution of Navier-Stokes equations.

4.2. Photovoltaic–Thermal model validation.

The current validation step is conducted using a set of experimental data to validate the comprehensive model of the PV/T system. In this comparison, the measured average cell temperature at various metrological conditions is compared with the predicted. Figure 5 compares between the hourly calculated the average cell temperature and those measured and predicted[25] at two different days in different seasons. Excellent agreement between the computed temperature and those measured and predicted is shown. In this validation, the same dimensions and affected variables were used as the used in the experiment of [25].

Fig.4 Predicted fully developed velocity profile validation (a) mid-

height (B)mid-width at the microchannel outlet [24].

Fig.5 Predicted average cell temperature validation with the

experimental results of [25].

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5. Results and discussion This section is organized into five general subsections.

The first subsection compares the proposed new structures with the conventional one. The second subsection presents the average cell temperatures of the novel and the traditional structure. The third one compares the electric, friction, and net gained the electric power of both systems. In the fourth subsection, the temperature uniformity of both structures is compared. Finally, the solar cell electrical efficiency and CPVT system thermal efficiency of both structures are compared.

The efficient operation of the generic polycrystalline silicon solar cell is limited by its maximum operating temperature of 85oC [26] which can be reached at CR<2.15, Vw=1m/s, and Ta=30oC[1]. Consequently, modification of the cell structure along with efficient cooling technique is a crucial aspect. The comparison offered at the wind speed of 1m/s, inlet and ambient temperature of 30oC. The effect of wind speed, coolant inlet and ambient temperature variation on the performance of CPVT system are investigated in the author earlier work [23].

5.1. The new proposed solar cell

The average solar cell temperature and the gained electric power for various cell structures are compared in Figs.6 and 7 respectively. The comparison is performed at CR=20 and minimum m where maximum solar cell temperature can be achieved. The compared structures are the conventional structure with the common TPT and EVA layer (A), the modified structure with the conventional TPT (B) while the EVA under the silicon layer is mixed with 20%BN, (C) conventional TPT, while the EVA under the silicon layer is mixed with 40%BN, (D) conventional TPT, while the EVA layer under the silicon layer is mixed with 60%BN, and the final structure (E) the EVA under the silicon layer is mixed with 60% BN. Moreover, the conventional TPT layer is replaced with aluminum foil sheet with the same thickness. The selection of best structure is accomplished based on lower cell temperature, and higher gained electric power.

Based on Figs.6 and 7, it is clear that increasing the percent of BN in the composite decreases the solar cell temperature along with a significant increase in the gained electric power. In more details, the structure (E) of EVA-60% BN and the replaced TPT with aluminum foil can achieve reliable and efficient operation of solar cell. It is found that the gained power is about 40.3W and the temperature is of 70.5 oC at CR=20 and m=50g/min while for the conventional structure the solar cell temperature and gained electric power are about 112.2oC and 30.77W respectively. A 30% increase in the gained electric power is achieved along with 10.9 % decrease in the cell temperature at m=50g/min and CR=20. In the meantime, the structure (E) is able to attain efficient operation of CPVT system with silicon layer temperature under the operating limit of 85oC at CR=20, and m=50g/min. Consequently, the structure (E) is used through all of the coming subsections.

5.2. Comparison of average cell temperature.

The effect of varying coolant mass flow rate on the average cell temperature for the conventional and the novel structure (E) at CR=5 and CR=20 is presented in Fig.8. The solar cell temperature significantly decreases with the increase of the coolant mass flow rate (m) until a certain value of m that depends on the CR. Further increase in m beyond that value results in a slight decrease of solar cell temperature for both structures. This trend was observed by several researchers[27], [25],[28], and [29]. There are different points of view to interpret the reason for this trend. It is reported that at a lower mass flow rate, the heat transfer mechanism between the microchannel wall and cooling fluid is dominated by convection, while at a higher m range, the heat transfer mechanism is dominated by conduction within the thin boundary layer of the laminar wall region [27]. Another point of view that relates this trend to the reduction of contact time between the fluid and the microchannel upper wall is due to higher velocity associated with higher flow rate [25]. The last point of view is that at high m, the heat extracted by the cooling water reaches the saturated level and therefore the cell temperature slightly increases[29].

Fig. 6 Variation of average solar cell temperature for various cell

structures in CPVT systems.

Fig. 7 Variation of solar cell gained electric power for various

solar cell structures in CPVT systems.

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In addition, the solar cell temperature increases with the increase in the solar CR due to the increase in the absorbed solar radiation with increasing CR. Moreover, the novel structure of EVA-60%BN composite and aluminum back sheet attain lower solar cell temperature compared with the conventional structure over all range of investigated ṁ at the same CR. In more details, at ṁ=1015 g/min, the solar cell temperature at CR=5 is 42oC and 31.6oC while they are 80oC and 36.2oC at CR=20 for the conventional and novel structure respectively.

Fig. 8 Effect of coolant mass flowrate on the solar cell temperature

for conventional and new cell structure in CPVT system.

5.3. Comparison of the gained electric power. The variation of MCHS consumed friction power (Pfric.)

along with the CPVT-system electric power (Pel) and net gained electric power (Pnet) for both investigated solar cell structures are presented in Figs.9-a and 9-b at CR=5 and 20 respectively. It is found that increasing the coolant mass flow rate leads to an increase in the consumed pumping power for the two examined structures due to the increase in the pressure drop with the increase in ṁ. Moreover, the effect of CR on the consumed friction power is a not significant because the effect of CR can be observed on the thermophysical properties of the coolant. In the meantime, the MCHS consumes nearly the same power in both proposed structures.

The net CPVT system output power (Pnet) is calculated by Eq. (21). Increasing the coolant flow rate causes a significant decrease in the solar cell temperature, and the gained solar cell electric power (Pel) significantly increases the coolant flow rate up to a certain limit. On the other hand, the consumed friction power dramatically increases with the increase of mass flow rate. Consequently, the net gained electric power which is the difference between the solar cell electric power and the friction power will increase up to a certain limit and then decrease again

as presented in Fig.9. This trend is in good agreement with the experimental results of [25] and the numerical results of[27]. Furthermore, Pnet increases until a critical mass flowrate (ṁ-c) and then decrease a gain. The value of ṁ-c is dependent on CR and the MCHS design. The value of ṁ-c is about 155.4g/min and 404.6g/min at CR=5 and 20 respectively and nearly the same for both structures. The net gained electric power at ṁ-c for the conventional structure is about 11.49W and 37.1W at CR=5 and 20 respectively. While the net gained electric power is about 12.1W and 47W at CR=5 and 20 respectively for the new proposed structure. An increase of 5.3% and 26.6% at ṁ-c were achieved through the use of the new structure at CR=5 and 20 respectively.

Fig. 9 Variation of Pfric., Pel, and Pnet of the conventional and new structure operated in CPVT system at (a) CR=5, and (b) CR=20.

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5.4. Comparison of the solar cell temperature uniformity. The cell efficiency declines because of the cell non-uniform

temperature distribution. That’s because the cell temperature non-uniformity causes a reverse saturation current [30]. Moreover, the thermal expansion depends on the local cell temperature, so CPV cell temperature non-uniformity implies a mechanical stress and reduces the life time of the solar cell. Table 4 show the maximum temperature difference on the silicon layer at CR=5 and 20 for both investigated structures. In both investigated structures, it is found that the conventional structure achieves a better temperature uniformity than the new structure because in the new structure, the thermal resistance of the layers between the silicon layer and MCHS is very small compared with those in the conventional structure which makes a large temperature difference on the silicon layer. In more details, at ṁ-c, ΔT is about 6.66oC and 7.65oC for conventional and new structure respectively at CR=20.

Table 4 temperature uniformity of silicon layer for

conventional and new structure ΔT=Tsc,max-Tsc,min (oC)

mo(g/min)

Conventional New structure CR=5 CR=20 CR=5 CR=20

50 11.8 48.9 14.1 57.8 101 6.0 25.1 7.3 29.7 203 3.0 12.8 3.7 15.0 304 2.0 8.6 2.5 10.1 507 1.2 5.3 1.5 6.1

1015 0.6 2.9 0.8 3.1

5.5. Comparison of the solar cell electrical efficiency and CPVT-system thermal efficiency. Efficient use of microchannel as an active cooling

technique for CPVT systems can be attained not only by enhancing the output electrical energy but by utilizing the dissipated heat as a source of thermal energy as well. Consequently, this system maintains high electrical efficiency, and the excess heat could be used by residential and heating applications as a CPV/thermal system so that the combined efficiency increases. In Figs.10-a, and 10-b, the variation of electrical and thermal efficiency with the coolant flowrate is presented respectively. For both structures in Fig.10-a, the electrical efficiency increases with ṁ until a specific value of ṁ and then remains constant. In addition, the electric efficiency decreases with the increase in CR returned to the increase in the solar cell temperature at higher CR. Finally it is clear that the new structure attained higher efficiency than the conventional structure at the same ṁ and CR.

On the other hand, in Fig.10-b the thermal efficiency for both structures is compared at various ṁ and CR. It is found that for both structures, increasing CR increases the thermal efficiency due to the higher absorbed solar radiation at higher

CR. Furthermore, the new structure achieves higher thermal efficiency compared with the conventional one. This is due to the lower thermal resistance of the new structure (0.0036 m2.K/W) compared with the conventional (0.00031 m2.K/W).

Fig.10 Variation of the (a) electrical efficiency, and (b) thermal efficiency with ṁ for both proposed structures.

CONCLUSION A novel structure of the polycrystalline silicon solar cell is

presented. To compare the performance of both designs, a comprehensive three-dimensional thermal model is developed. Through the comparison, the traditional and the new proposed

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structures are integrated with MCHS to reduce the silicon temperature under concentrated solar radiation with CR up to 20. The performance of proposed structures is assessed based on the cell temperature, cell temperature uniformity, net gained electric power, and CPVT system electric and thermal efficiency. Through the validated model, it can be concluded that:-

1- The cell structure of EVA-60%BN and replaced TPT with aluminum foil achieve reliable and efficient operation of the solar cell at about 70.5oC and gained the power of 40.3W at CR=20 and m=50g/min while for the conventional structure the solar cell temperature and gained electric power are about 112.2oC and 30.77W respectively. A 30% increase in the acquired electric power is achieved along with 10.9 % decrease in the cell temperature at m=50g/min and CR=20.

2- In addition, at m=1015 g/min, the solar cell temperature at CR=5 were 42oC and 31.6oC while they were 80oC and 36.2oC at CR=20 for the conventional and novel structure respectively.

3- Furthermore, Pnet increases until a critical mass flowrate (m-c) and then decreases a gain. The value of m-c is about 155.4g/min and 404.6g/min at CR=5 and 20 respectively and nearly the same for both structures. The net gained electric power at m-c for the conventional structure is about 11.49W and 37.1W at CR=5 and 20 respectively. While the net gained electric power is about 12.1W and 47W at CR=5 and 20 respectively for the new proposed structure.

4- The conventional structure achieves better temperature uniformity compared with the new structure at the same m and CR

5- Finally it is clear that the new structure attained higher efficiency than the conventional structure at the same m and CR

Nomenclature A Solar cell area [m2] C Specific heat of cooling fluid [J/kg.K] Dh Hydraulic diameter [m] G(t) Net concentrated solar radiation [W/m2] H Microchannel height [m] k Thermal conductivity [W/m.K] L Microchannel length and solar cell length [m] m Cooling fluid mass flow rate [Kg/s] P Electrical, friction and net power [W] T Temperature [oC] V Velocity vector V= ui+vj+wk [m/s] Vw Wind velocity [m/s] W Velocity component in z-direction [m/s] Greek symbols α Absorptivity ε Emissivity τ Transmissivity µ Fluid viscosity [Pa.s]

σ Stephan-Boltzmann constant 5.67*10-8 [W/(m2.K4)] ρ Fluid density [kg/m3] and Reflectivity δ Thickness [m] Solar cell and thermal efficiency Subscripts a Ambient b Back sheet or tedlar ch Channel e1 Upper EVA layer e2 Lower EVA layer el Electrical f Fluid Fric. Friction g Glass in Inlet int Interval part of EVA net Net ref Reference condition, G=1000w/m2,T=25oC s Sky sc Solar cell th Thermal Acknowledgments

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