The influence of microchannel heat sink configurations on the performance of low concentrator photovoltaic systems

Applied Energy 206 (2017) 594–611

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

The influence of microchannel heat sink configurations on the performance of low concentrator photovoltaic systems Ali Radwan, Mahmoud Ahmed

MARK

⁎,1

Department of Energy Resources Engineering, Egypt-Japan University of Science and Technology (E-JUST), Egypt

H I G H L I G H T S three-dimensional comprehensive modeling of the CPV/T system is developed. • AParallel single layer heat sink attains the best performance of a CPV/T system. • Counter flow flow single layer heat sink is the least effective cooling technique. •

A R T I C L E I N F O

A B S T R A C T

Keywords: Concentrator photovoltaic systems Three dimensional thermofluid model Microchannel heat sinks Double layer microchannel heat sinks Parallel flows Counter flows

A new cooling technique for concentrator photovoltaic (CPV) systems is developed using various configurations of microchannel heat sinks. Five distinct configurations integrated with a CPV system are investigated, including a wide rectangular microchannel, a single layer parallel- and counter- flow microchannel, and a double layer parallel- and counter- flow microchannel. A comprehensive, three-dimensional thermo-fluid model for photovoltaic layers, integrated with a microchannel heat sink, is developed. The model is numerically simulated and validated using the available experimental and numerical data. Based on the results, the temperature contours on a plane located at the mid-thickness of the silicon layer are presented at different operating conditions and heat sink configurations. Accordingly, the maximum local temperature can be detected and temperature uniformity can be accurately estimated. Furthermore, at a concentration ratio of 20, the CPV system integrated with a single layer parallel- flow microchannel heat sink configuration (B) achieves the highest cell net power, electrical efficiency, and the minimum cell temperature. On the contrary, at the same operating conditions, the use of a single layer counter-flow microchannel heat sink configuration (C) is found to be the least effective cooling technique. The results of this study can guide industrial designers to adopt compact heat sink configurations and simple designs in the manufacturing process of hybrid CPV-thermal systems.

1. Introduction Concentrator photovoltaic (CPV) technologies have attracted much research attention in recent years because of its potential to address the high energy demands of the modern world, due, in part, to rapid population growth and the depletion of fossil fuels. However, the issue of cooling these systems for effective functioning still remains a significant roadblock to their wide-spread use. As sunlight concentration on photovoltaic cells causes a significant increase in the cell temperature, the cells’ system efficiency considerably decreases, while high operating temperatures lead to irreversible decay of the solar cells in the long term. Therefore, the use of efficient cooling techniques for concentrator photovoltaic systems will allow for a higher level of electrical

⁎

1

Corresponding author. E-mail addresses: [email protected], [email protected] (M. Ahmed). On leave from Mechanical Engineering Dept., Assiut University, Assiut 71516, Egypt.

http://dx.doi.org/10.1016/j.apenergy.2017.08.202 Received 6 May 2017; Received in revised form 24 August 2017; Accepted 27 August 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.

efficiency, and will mitigate any potential damage to the cell [1,2]. Many numerical and experimental investigations have been carried out over the past several years to address the issue of cooling photovoltaic cells. It was reported that an appropriate and effective cooling technique must attain a higher cell efficiency, a better cell temperature uniformity, and consume lower levels of pumping power [3]. Thus, this study examines various cooling methods for CPV systems, including passive cooling, active cooling using forced convection [4,5], two phase convective cooling [2], and jet impingement cooling [6,7]. Most recent research only considers a one-dimensional analysis of the thermal model where only the temperature variation with thickness is tested. Tiwari and Sodha [8] developed a one-dimensional thermal model of the photovoltaic thermal (PV/T) system. Based on their model, an

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A. Radwan, M. Ahmed

σ ρ δ λ η

Nomenclature A C Dh G(t) H k L ṁ P Re T u v Vw w W

solar cell area [m2] specific heat of coolant [J/kg K] hydraulic diameter [m] net concentrated solar radiation [W/m2] microchannel height [m] thermal conductivity [W/m K] microchannel length and solar cell length [m] cooling fluid mass flow rate [kg/s] pressure [Pa], electrical, friction and net power [W] Reynolds number temperature [°C] velocity component in x-direction [m/s] velocity component in y-direction [m/s] wind velocity [m/s] velocity component in z-direction [m/s] channel width, thickness of fin between flow channel and neighboring flow channel and width of the solar cell [m]

Subscripts a ambient b back sheet or tedlar ch channel conv, g-a convection loss from glass to ambient el electrical f fluid and fin spacing between the flow channel and the neighboring flow channel Fric. friction g glass in inlet int interval part of EVA net net rad, g-s radiation loss from glass to sky temperature ref reference condition, G = 1000 W/m2, T = 25 °C s sky Sc silicon wafer th thermal w wall

Greek symbols α β ε τ µ

Stephan-Boltzmann constant 5.67 ∗ 10−8 [W/(m2 K4)] fluid density [kg/m3] thickness [m] molecular mean free path [m] solar cell and thermal efficiency

absorptivity solar cell temperature coefficient [1/K] emissivity transmissivity fluid viscosity [Pa s]

non-traditional configurations where the temperature variation in the third dimension is a major, the two-dimensional modeling fails to predict the precise behavior of the PV/T systems. To overcome the limitations associated with one and two-dimensional models of the PV/T systems, a few researchers were developing a three-dimensional model. Siddiqui and Arif [18] developed a three-dimensional hybrid structural, electrical and thermal model of the PV/T system under normal solar radiation and varying climatic conditions. They recommended three-dimensional modeling as an efficient tool to select the most effective heat exchanger in designing the PV/T systems. Subsequently, Zhou et al. [19] developed a three-dimensional thermal model for the uncooled, generic polycrystalline cell using finite element analysis. In their study, the three-dimensional temperature distribution of the cell was simulated under the effects of different metrological conditions. They reported that three-dimensional models are needed to capture temperature uniformity and temperature distribution especially in PV/T systems with complex thermal absorber structure. In addition, three-dimensional models are more flexible and can easily be adopted to investigate the performance of complicated heat sink designs. At the same time, such model can handle the patterns of complex thermal absorber designs with a high level of accuracy [20]. One of the most essential parameters is the solar cell temperature uniformity. It was found that the cell efficiency declines due to the cell non-uniform temperature distribution that causes a reverse saturation current [21]. Moreover, thermal expansion depends on the local cell temperature, and the non-uniformity of cell temperature causes a mechanical stress and reduces the lifetime of solar cells. Therefore, a three-dimensional model greatly assists in predicting the temperature distribution of a solar cell, and consequently, allows the temperature uniformity of a solar cell to be accurately estimated. The originality of the present work is based on two main concepts: first, a new comprehensive three-dimensional thermo-fluid model for photovoltaic layers, integrated with irregular configurations of microchannel heat sinks is developed. This model will predict the temperature contour of the solar cell layer and accordingly predict the existence of potential hotspots. Second, a novel microchannel heat sink with

analytical expression for the cell temperature, water outlet temperature, and thermal efficiency as a function of metrological conditions was derived. In their work, both air and water were used as coolant fluids for their suggested designs. They found that using water achieves a higher daily efficiency compared to air, for all studied designs except the design of glazed PV without tedlar. Their work was extended to include the electrical model of the PV module as reported by Sarhaddi et al. [9]. They concluded that the results obtained from the combined thermal and electrical models were more precise than those obtained from the thermal model only. Several researchers [10–13] applied the same model to predict PV/T system performance. A further step toward a more accurate thermal model for the PV/T system was the development of the two-dimensional analysis. Xu and Kleinstreuer [14] developed a two-dimensional thermal model for concentrator photovoltaic thermal (CPV/T) systems for both a generic crystalline silicon and multi-junction solar cells. In their model, they used Al2O3-water nanofluid as a coolant with channel heights ranging from 2 mm to 14 mm. They proposed to solve the Navier Stokes equations along with the fluid energy equation to predict the exact behavior of the thermal absorber rather than using an empirical correlation. Rejeb et al. [15] developed a two-dimensional model for the PV/T system. They reported that the increase in the heat conduction coefficient between the back side of the photovoltaic module and the absorber plate enhances the electrical and thermal efficiency of the PV/ T systems. Recently, a two-dimensional model for concentrator photovoltaic systems with a microchannel heat sink was developed by Radwan et al. [16,17]. In their study, a comparison between the conventional cooling technique and the microchannel heat sink technique was conducted using CPV systems operating up to concentration ratio (CR) of 40. They concluded that using a microchannel cooling technique attained the ultimate possible reduction of solar cell temperature due to the high heat transfer coefficient associated with micro-scale thermal absorbers. The study concluded that the two-dimensional thermal model correctly predicts the thermal behavior of conventional thermal absorbers while the change in the third dimension could be insignificant. However, in 595

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sink are assessed, and the best configuration is recommended for practical applications.

different designs is proposed to be integrated with a concentrated photovoltaic system that includes a polycrystalline silicon solar cell and a solar concentrator with varying CR up to 20. Both single and double layer heat sink configurations are investigated under parallel and counter flow conditions. For each configuration of heat sinks, the effects of different operating parameters such as concentration ratio CR, coolant mass flowrate on temperature uniformity, solar cell power, and the electrical and thermal efficiency of the CPV system, are investigated. Accordingly, all suggested designs of the micro-channel heat

(a)

2. Physical model The concentrator photovoltaic system integrated with various configurations of microchannel heat sink is shown in Fig. 1. The entire system consists of a linear Fresnel lens concentrator, a solar cell, and a microchannel heat sink. The concentrator dimensions Llens, Wlens, and

Linear Fresnel lens

Incident Solar Flux

Flat mirrors H

W lens

(b)

Concentrated Solar flux Solar cell

Glass cover EVA- Encapsulation Silicon layer, ARC- layer EVA- Interval EVA- Encapsulation Tedlar

MCHS

Channel outlet

MCHS-2 Inlet

z y

MCHS-1

x Outlet

(c)

y

A įg įARC+2įEVA+įsc z įT

įint z

ARC EVA

2į

in

t

įint

A

sc +

įEVA

Glass cover

įg įARC+2įEVA+įsc

L

TPT

Silicon Layer

įsc+įARC x

įT y Interval part

Wsc+2įint

Cell part

Interval part

Cross-sectional view at A-A

Polycrystalline silicon solar cell structure

Fig. 1. (a) A neat schematic sketch of the proposed linear Fresnel lens concentrator photovoltaic/thermal system, (b) Assembly of the proposed PV/T system layers, (c) uncooled solar cell structure geometry and cross-sectional view.

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the solar cell is subjected to combined radiation and convective heat loss. The excess absorbed energy in the solar cell is extracted by the heat sink underneath the solar cell. The concentrated solar irradiance is focused onto a row of the photovoltaic/thermal units electrically connected in a series formation as schematically presented in Fig. 1a. The investigated solar cell is taken to be a generic polycrystalline cell as characterized by Sandia National Laboratory [22]. The solar cell

Hconcentrator vary according to the required CR. The Fresnel lens is supported from the sides with a steel frame that holds the reflective mirror. The ends of the concentrator are open to facilitate the periodic maintenance and to allow for the air flow over the solar cell, acting as an auto-designed air duct. To take into account the effect of heat removal from the top surface, a wind speed of 1 m/s is assumed to be at the top surface of the CPV/T systems. Consequently, the top surface of

įg

Concentrated solar radiation

įARC+2įEVA+įsc įT įch įint

įint

ARC įsc

/2

sc

L

Hch įw Inlet įint +Wsc

t

+į

in

z

sc

L

/2

y

(a) Configuration (A)

x

Concentrated solar radiation

Concentrated solar radiation įg

įg

įARC+2įEVA+įsc įT

įT

įch

įch įint

ARC

t

į

in

įi

nt

įint

įARC+2įEVA+įsc

ARC įsc

Hch

įw

N Wf Wch

Hch

Inlet

/2

sc

L

L

sc / 2

įsc

įw

N Wch

įw

Inlet

įw

(c) Configuration (C)

(b) Configuration (B) 2įint +Wsc

2įint +Wsc

Concentrated solar radiation

įg

Concentrated solar radiation

įg

įARC+2įEVA+įsc

įARC+2įEVA+įsc

įT

įT

2įch

ARC

į int

įsc

2įch

ARC

į int

Hch

N

Inlet

L

L

sc / 2

sc / 2

įsc Hch

N

Outlet Inlet

Inlet

(e) Configuration (E)

(d) Configuration (D)

Fig. 2. Schematic diagram of the computational domains of PV integrated with diiferent microchannel heat sinks such as: (a) wide rectangular microchannel (Configuration A) (b) single layer parallel-flow (Configuration B), (c) single layer counter-flow (Configuration C), (d) double layer parallel-flow (Configuration D), and (e) double layer counter-flow (Configuration E).

597

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on the solar cell is taken to be 20 kW/m2. The entire cell area is considered in numerical calculations because the heat generation for each layer is not uniform along the cell domain. By referring to the cross–sectional view A–A as shown in Fig. 1(c), it was found that the heat generation in the interval part is completely different than that in the cell part [19].

includes various layers depending on the manufacturing technology used. These layers include the glass cover, an anti-reflective coating (ARC), a silicon layer, an ethylene vinyl acetate (EVA) layer, and a tedlar polyester tedlar (TPT) layer as presented in Fig. 1b. A glass cover with a thickness of 3.0 mm is made of tempered glass with higher transparency. An anti-reflective coating layer with a thickness of 0.0001 mm (100 nm) is used to limit the reflection of the incoming radiation. In addition, a silicon wafer of 0.2 mm thickness is used in these panels, which are responsible for electricity production [23]. The silicon layer is embedded in the transparent encapsulation ethylene vinyl acetate (EVA) layer with a thickness of 0.5 mm above and below the silicon layer to keep it fixed and provide both electrical isolation and moisture resistance. Moreover, the TPT polymer layer is a photo stable layer of thickness 0.3 mm and is made of polyvinyl fluoride (PVF). The final layer provides additional insulation and moisture protection for the silicon layer [24]. In order to cool the solar cell, a compact microchannel heat sink is attached to the back TPT layer. It is made of a high thermal conductive aluminum, and it is economically recommended over the use of copper for the thermal regulation of the CPV systems [25]. Water is used as a coolant for its effective properties as it can generate a higher thermal performance of PVT systems compared to the use of air [26]. The complete structure of the uncooled solar cell is presented in Fig. 1c. In the current work, five different configurations are studied as shown in Fig. 2. The first configuration includes a single layer wide microchannel heat sink (configuration A). The second design consists of a single layer microchannel heat sink with parallel flow channels (configuration B), and the third uses the same design as configuration B with additional counter flow-channels (configuration C). The fourth configuration includes a double layer with parallel flow design (configuration D), and the last configuration is the same as the previous one, with a counter-flow design (configuration E). For all investigated configurations, the wall thickness, and channel height, are selected to be the same for fair comparisons. For the last four configurations, the channel aspect ratio (defined as the ratio of the width to the height), the material, the wetted area ratio, and the coolant mass flowrate are also selected to be the same. The microchannel height is selected to be 100 μm [17]. Furthermore, the aspect ratio of the cooling channel is carefully chosen to be 8 to achieve the maximum heat transfer coefficient in the rectangular ducts as recommended by [27]. The typical dimensions of the commercial silicon wafer are 125 mm by 125 mm, and the EVA interval between adjacent cells is 2.2 mm. In the current study, only one cell is investigated including half of a EVA interval part from each side. The total dimension of the computational domain is 127.2 mm by 127.2 mm, including a 125-mm silicon wafer and a 1.1 mm half EVA interval from all sides. The effective area of the photovoltaic cell is divided into two equal parts of 127.2 mm by 63.6 mm. Consequently, two microchannel heat sinks of 127.2 × 63.6 mm2 are used for a single solar cell unit to ensure better temperature uniformity and lower friction power loss in the heat sink. Consequently, each cooling unit is composed of 106 microchannels per layer. The numbers of microchannels are obtained by dividing the total width of a 127.2 mm heat sink into equal channel widths of 800 μm. The thickness of each channel wall is 400 μm except for the channel end walls where half of the thickness is considered as shown in Fig. 2(b) and (c). Accordingly, the total number of channels (Nch) are 106, based on the following relationship: Nch ∗ Wch + (Nch − 1) ∗ Wf + 2δw = 127.2 mm, where: Wch = 0.8 mm, Wf = 0.4 mm, and δw = 0.2 mm as reported in Table 1. The PV layers rest on the designed microchannel heat sink, and water is used as a cooling medium to maintain a high efficiency and avoid excessive cell temperatures. The term CR is taken as the average net solar irradiance of the concentrated beam incident on the target, relative to some reference value, usually the “one-sun” value 1000 W/m2 [28]. Consequently, the net received solar flux on the solar cell area increases with the increase in CR. For example, in the case of CR = 20, the net incident solar flux

3. Theoretical analysis The investigated CPV/T system includes different layers of the PV cell and a microchannel heat sink as shown in Fig. 2. In the currently developed three-dimensional solid–fluid conjugate heat transfer model, the following assumptions are adopted [18]: 1. Solar cell materials are isotropic, and temperature independent. 2. The thermal contact resistances between each layer of the solar cell and microchannel heat sink are neglected. 3. The fluid flow in the microchannel heat sink is steady, laminar, and incompressible. 4. The fluid properties are temperature dependent. The current comprehensive model is developed to predict the threedimensional temperature distribution of the CPV/T system. For heat transfer in the PV layers, the temperature distribution is governed by the energy equation. To model the fluid flow and heat transfer in microchannel heat sinks, the continuity, momentum, and energy equations are used. 3.1. PV-module layers The heat conduction equation in a Cartesian coordinates system for each solid layer can be represented as follow [18]:

∇ . (ki ∇Ti ) + qi = 0 and i = 1,2,…,6

(1)

where the variable ki represents the thermal conductivity of the layer i, and the term qi indicates the heat generation per unit volume of the layer i due to the absorption of the solar radiation. In this work, the value of i changes from 1 to 6 for glass, upper EVA, ARC, silicon, lower EVA, and the tedlar layer, respectively. The heat generation per unit volume of the layer due to the solar irradiance absorption can be determined using the following equation as reported in [19].

qi =

(1−ηsc ) G αi τj Ai (2)

Vi

where ηsc is the solar cell electrical efficiency; αi, Ai, and Vi are the absorptivity, area, and volume of the layer i, respectively; and finally, τj is the net transmissivity of layers above layer i. The CPV system contains several layers. The heat generated in each layer is due to the absorbed solar radiation where it is a function of layer absorptivity. For each layer, the absorbed solar radiation converts into heat, while for the silicon wafer layer, the net absorbed solar irradiance is converted into electricity and heat. The electricity generated depends on the cell’s electrical efficiency while the remainder [(1 − ηsc) ∗ Qnet,abs,sc] is converted into heat. To calculate the heat Table 1 Dimensions of microchannel heat sink.

598

Factor

Value

Factor

Value

Lsc Hch Wch δw Wf

125 mm 0.1 mm 0.8 mm 0.2 mm 0.4 mm

Wsc Wch,flat N δch δint

125 mm 126.8 mm 106 0.5 mm 1.1 mm

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generation of each layer, Eq. (2) is used. This equation applies very well to the silicon wafer layer, contrary to other layers, where the electrical generation is zero and therefore is substituted with ηsc which equals to zero. The optical properties of the CPV layers and the thermophysical properties with thicknesses of the CPV/T layers are presented in Tables 2 and 3 respectively. The silicon layer efficiency is calculated using the following equation [14,29]:

ηsc = ηref (1−βref (Tsc−Tref ))

Table 3 Thermophysical properties and thicknesses of CPV/T layers [19,23]

(3)

where ηref and βref are the solar cell efficiency and temperature coefficient at a reference temperature of Tref = 25 °C, respectively. These values are provided by the manufacturer data sheet for most solar cells, and βref is taken to be 0.0045 K−1 for polycrystalline silicon solar cell [9].

(4)

For microchannel heat sink, the fluid flow and energy equations of laminar, incompressible, and steady flow can be written in vector form as follows: Mass conservation equation:

Thickness (mm)

Glass (Cover) ARC Encapsulation (EVA) Silicon Tedlar Microchannel (Aluminum)

3000 2400 960

500 691 2090

2 32 0.311

3 0.0001 0.5

2330 1200 2719

677 1250 871

130 0.15 202.4

0.2 0.3 0.2

(9)

To solve the governing equations, boundary conditions must be identified. First, for the PV layers, the thermal boundary condition for the upper wall of the glass layer is a combination of convection and radiation heat loss. The radiation heat loss is the heat lost between the cell glass cover and the atmosphere. The side walls of the computational domain are assumed to be adiabatic due to symmetry. In addition, the lower wall of the computational domain is assumed to be adiabatic for the CPV/T system to achieve the highest possible gain of thermal energy. Second, for the microchannel heat sink, the inlet fluid velocity component (v) in the y-direction is identified and assumed to be uniform. The value of v-velocity component is varied according to the coolant mass flowrate. The x and z components of the velocity are zero at the inlet section. Meanwhile, the outlet flow boundary conditions are identified at the coolant outlet section. No-slip and no temperature jump boundary conditions are considered at the interface between the solid–fluid domains, as the Knudsen number (the ratio of the molecular mean free path length to the flow characteristic dimension as defined in the Appendix A) falls in the no-slip regime (Kn < 0.001) [33]. Furthermore, the maximum channel flow Reynolds number is estimated to be within the laminar flow regime (i.e. Re < 2200). The channel inlet temperature is assumed to be uniform. For the uncooled solar cell, the same boundary conditions, and operating conditions are used as the same as applied in [19]. The upper glass surface is subjected to combined convective and radiation heat loss, while the lower TPT surface is subjected to the same type of boundary condition with a different convection heat transfer coefficient that equals half the value applied at the top, as concluded by Zhou [19]. The back side convective heat transfer coefficient is smaller than that at the top. Several empirical correlations were used to estimate the back side heat transfer coefficient and it was found to be approximately half of the heat transfer coefficient of the top surface as reported in [19,34].

Momentum equations: (6)

Energy equation:

→ V . ∇ (ρ Cf Tf ) = ∇ . (kf ∇Tf )

(7) → where the subscript f represents the fluid; V , p, µ, ρ, Cf, kf, and Tf are the velocity vector, pressure, fluid viscosity, density, specific heat, thermal conductivity, and temperature. The variation of the water’s thermophysical properties with temperature is considered using the higher ordered polynomial equations presented in [30] due to the substantial changes that occur inside the microchannel, especially at higher CR values. 3.3. PV characterizations Several parameters are commonly used to characterize the performance of CPV/T systems. First, the electrical power produced by the CPV/T system, Pel is expressed by the following equation [31]:

Pel = ηsc τg βsc G (t ) wsc . lsc

Thermal conductivity (W/ m K)

3.4. Boundary conditions

(5)

→ → → V . ∇ (ρ V ) = −∇P + ∇ . (μ∇ V )

Specific heat (J/ kg K)

where Pth, Cf,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 microchannel heat sink, respectively. Other performance parameters such as thermal efficiency (ηth), friction power (Pfric), the net gained power (Pnet), are presented in Appendix A [16,17].

For a microchannel substrate, the heat conduction equation in the vector form without heat generation could be written as follow [18]:

→ ∇ . (ρV ) = 0

Density (kg/m3)

Pth = mf. Cf ,in (Tf ,out −Tf ,in )

3.2. Microchannel heat sink

∇ . (kch ∇Tch) = 0

Layer

(8)

where ηsc, τg, G(t), wsc, lsc are the solar cell efficiency, glass transmissivity, the net concentrated solar radiation incident on the solar cell surface regardless of the concentrator’s optical losses, and the width and length of the solar cell, respectively. Second, the rate of thermal energy gained is calculated using the following equation [32]: Table 2 Optical properties of CPV system layer [19]. Material

Reflectivity

Absorptivity (α)

Transmissivity (τ)

Emissivity (ε)

Glass cover EVA layer Silicon Layer Back sheet Aluminum

0.04 0.02 0.08 0.86 –

0.04 0.08 0.90 0.128 –

0.92 0.90 0.02 0.012 –

0.85

599

0.9 0.9

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A. Radwan, M. Ahmed

Finally, the sides of the solar cell are taken to be adiabatic. In addition, the boundary conditions for the cooled CPV system integrated with the microchannel heat sink configuration (A) are presented here in detail, as an example. To save computational time, half of the solar cell is modeled and the results are reflected onto the other half. The current boundary conditions are presented for the half solar cell integrated with its own microchannel heat sink.

At the channel inlet δw ≤ x ≤ (Wsc + 2δint. − δw), y = (Lsc/2 + δint), and δw ≤ z ≤ (δw + Hch) Then: V = 0 i + (vin) j + (0) k, Tin =30 °C At the channel outlet δw ≤ x ≤ (Wsc + 2δint. − δw), y = (Lsc + 2δint), and δw ≤ z ≤ (δw + Hch)

3.4.1. The PV layers For upper side of glass cover [18]: 0 ≤ x ≤ (Wsc+ 2δint), (Lsc/2+ δint) ≤ y ≤ (Lsc+ 2δint), and z= (δch+ δT+ 2δEVA+ δARC+δsc+δg)

∂T Pout = 0 ⎜⎛gage⎟⎞ and kf =0 ∂z ⎝ ⎠

kg

∂T = hrad,g − s (Tg−Ts ) + hconv,g − a (Tg−Ta) ∂z

For microchannel heat sink material sides (x = 0 and x = Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and 0 ≤ z ≤ (2δw + Hch)

ks

(10)

where the equivalent radiative and convective heat transfer coefficients are calculated using the correlations presented in Appendix A [14]: For glass cover, EVA, ARC, silicon, and tedlar sides, at the two planes parallel to the yz and located at x = 0, x = 2δint + Wsc and y = Lsc/2 + δint to y = Lsc + 2δint an adiabatic boundary condition is applied due to the symmetry as.

ki

∂T =0 ∂x

∂T =0 ∂y

−kAl

(11)

(12)

(13)

(14)

(15)

(16)

For the investigated microchannel heat sinks, the grid independence test is performed for all investigated configurations integrated with the CPV layers. The first test is established for CPV cell layers combined with configuration (D). A total number of 1,286,208, 2,552,318, 5,128,704, 12,115,800, and 13,256,800 cells are tested. It is found that at 12115800 cells, there is no significant change in cell temperature with a further increase in the number of cells. Accordingly, the cell numbers of 12,115,800 are selected for the simulation of CPV cells cooled with heat sink configurations D and E. Similarly, the cell numbers of 8,884,920 are selected for configurations B and C, and 4,489,000 are selected for configuration A. Finally, a total number of 2,559,150 cells are applied for uncooled CPV cells. The mesh independence test for the uncooled CPV and the CPV system coupled with the microchannel heat sink design D is presented in Fig. 3

(17)

At tedlar-aluminum channel interface: 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and z = δch

kAl ∇TAl = kT ∇TT

(22)

4.1. Mesh independence test

At EVA- tedlar layer interface: 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and z = (δch + δT),

kT ∇TT = kEVA ∇TEVA

(21)

The developed comprehensive thermal model for photovoltaic layers coupled with the thermo-fluid model for a microchannel heat sink is numerically simulated to determine the solar cell temperature, and consequently, the other performance parameters. In the current work, computational fluid dynamics (CFD) commercial package ANSYS FLUENT 17.2 code was used to numerically simulate both the developed thermal model for the uncooled PV system and the thermo-fluid model for the cooled PV/T system. The governing partial differential equations are discretized using the finite volume method. The discretized equations are solved using a fully implicit scheme with second order upwind spatial differences. This is implemented by following the SIMPLE algorithm for the coupling of pressure and velocities. As the silicon layer absorbed solar irradiance is a function of the solar cell electrical efficiency, an iterative technique is adopted as described in previous works [16,17]. Parallel computing is implemented using a Dell Precision T7500 workstation with an Intel Xeon® processor of 3.75GH, 48-core, and 64-MB installed memory. 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 as presented in the following subsections.

At silicon layer – bottom EVA interface: 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and z= (δch + δT + δEVA)

kEVA ∇TEVA = ksc ∇Tsc

=0 y

4. Numerical solution

At ARC-silicon layer interface: 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and z= (δch+ δT+ δEVA+δsc)

ksc ∇Tsc = kARC ∇TARC

∂T ∂y

kf ∇Tf = kch ∇Tch,Tf = Tch and u = v= w= 0

At top EVA layer- ARC layer interface: 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and z= (δch + δT + δEVA + δARC + δsc)

kEVA ∇TEVA = kARC ∇TARC

(20)

For the fluid-solid interface, a no slip, and thermally coupled no slip boundary condition is applied

For solid-solid interfaces, a thermally coupled boundary condition is applied: at glass cover-top EVA layer interface: 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and z= (δch+ δT+ 2δEVA+ δARC +δsc).

kEVA ∇TEVA = k g ∇Tg

∂T =0 ∂z

For lower wall at: 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc/ 2 + δint), and z = 0, an adiabatic boundary condition is applied [35].

where Ki is the material thermal conductivity of layer i and its value varies for: glass cover, EVA, silicon, ARC, tedlar, and aluminum material. Similarly, at the planes parallel to the xz plane and located at y = Lsc/2 + δint and y = Lsc + 2δint except the coolant inlet and outlet regions, an adiabatic boundary condition is assumed due to the symmetry.

ki

(19)

(18)

3.4.2. For microchannel heat sink design Fluid domain 600

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resulted due to the use of a one-dimensional energy balance model. 5. Results and discussion This section is organized into three subsections. The first subsection demonstrates the performance of the uncooled CPV system under concentrated illumination. In this subsection, the optimal permissible CR for an uncooled polycrystalline silicon solar cell under various climatic conditions is presented. The second subsection presents the performance of the CPV system when cooled using the proposed microchannel designs. In addition, the impact of various operational conditions such as the coolant mass flowrate, the solar concentration ratio, and the microchannel heat sink design, on the local solar cell temperature and uniformity, solar cell power, solar cell electrical efficiency, and system thermal efficiency are presented in detail. In the final subsection, the performance assessment of different CPV/T systems is evaluated for each design of the heat sink. 5.1. Uncooled CPV system performance The operation of the uncooled polycrystalline silicon solar cell under concentrated illumination is restricted by the operating temperature range. Additionally, increasing the cell temperature will significantly reduce its electrical efficiency. The maximum allowable operating temperature is 85 °C and any further increase of the temperature beyond this limit can cause potential damage to the cell. Consequently, it is essential to identify the optimum CR at which the maximum operating temperature can be reached. Fig. 7 presents the temperature distribution on a plane located in the middle of the silicon layer at an ambient temperature of 30 °C and a wind speed of 1.0 m/s. By increasing the value of CR, the cell temperature rises from about 57.8 °C at a CR of 1.0, to about 83.3 at a CR of 2.0. Thus, the maximum acceptable CR for the reliable and efficient operation of such solar cells under the given climate conditions is about 2.13, where the cell temperature reaches 85 °C. The location where the maximum solar cell temperature is found is at the center of the cell. This is mainly caused by the existence of EVA in the interval region between the investigated cell and the neighbor cells. The existence of such low thermal conductive encapsulating material between the cells causes a slight heat transfer from the cell to its neighboring cell. Additionally, the lower thermal

Fig. 3. Mesh independence test for uncooled CPV system and CPV system integrated with microchannel heat sink design D.

4.2. Model validation The current model is validated using different sets of the available experimental, and numerical results. The first set of results is used to validate the uncooled solar cell model with the available experiments [22] and the numerical results presented in [11,19]. The last set of results is used to compare the comprehensive thermal model results with the corresponding available experimental and numerical results of [4] and the numerical results of Royne et al. [3]. 4.2.1. Photovoltaic (PV) model validation Several sets of data are used to validate the uncooled photovoltaic panel. The predicted solar cell temperature of the photovoltaic system is compared with estimated values using the empirical correlation developed by Sandia National Laboratories for the generic polycrystalline silicon solar cell [22], as shown in Fig. 4. The comparison indicates that a good agreement is found between the currently predicted values and those of the correlation. In addition, the comparison between the present predicted results and those predicted by [11] is carried out. A good agreement is obtained with a maximum deviation of about 3%. Thirdly, the solar cell temperature of the PV cell is compared with the numerically predicted values in [19] at various climatic conditions. The solar radiation changes from 300 W/m2 to 1000 W/m2 and the ambient temperature varies from −10 °C to 40 °C with a wind speed of 1.0 m/s, as shown in Fig. 5. An excellent agreement is found between the currently predicted results and those obtained by the published work in [19]. 4.2.2. Photovoltaic–Thermal (PV/T) model validation The comprehensive PV/T system model is validated using two sets of experimental data. Fig. 6a compares the hourly calculated average cell temperature, both measured and predicted by [4] for two different days of December, 16th and June, 23rd, while the metrological conditions are used as stated in [4]. Furthermore, a slight difference was found in the comparison between the current predicted results and those numerically obtained [4]. The difference is most likely due to using a 3-d analysis in the present work, while other results [4] were obtained using a 2-d analysis. To further validate the current model at a CR up to 20, Fig. 6b, indicated that the predicted solar cell temperature is in a good agreement with the results of Royne et al. [3] with a maximum relative error of 9% and 6% at back side heat transfer coefficient of 10 W/m2 K and 100 W/m2 K respectively. This error may be

Fig. 4. Uncooled model validation with the empirical correlation [22] and numerical results available in [11].

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60

(a)

Time: 10:00 - 14:00

June, 23rd Exp. [4] Num. [4] Present Model

Average cell temperature (oC)

55 50

Dec., 16th Exp. [4] Num. [4] Present Model

45 40 35 30 25 20 10

11

12

13

14

Time (hr) 250

Fig. 5. Uncooled photovoltaic model validation with the published results of [19] at various solar irradiance and ambient temperature and Vw = 1 m/s.

(b) Silicon layer temperature (oC)

energy absorption of the EVA layer makes its temperature lower than the silicon layer. A similar trend is observed in [18]. Interestingly, the temperature uniformity of the cell is found to be very good at the concentration ratios used; the local cell temperature showed almost constant values with a variation within the 0.15 °C range at CR = 1, and up to 0.25 °C at CR = 2. This trend is attributed to the uncooled CPV cell being subjected to a uniform heat loss from the upper and lower surfaces by both convection and radiation. Moreover, increasing the wind speed leads to a decrease in the solar cell temperature at the same CR. This reduction of cell temperature is attributed to the increase in the wind speed, which is accompanied with an increase in the convection heat transfer coefficient from the TPT and the front glass. It is noteworthy to mention that the maximum allowable CR without possibly damaging the solar cell increases with the increase in the wind speed. The uncooled CPV system can still operate without possible damage to its component as long as the CR does not exceeded the values of 2.13, 3, 3.9, and 4.8 at wind speeds of 1, 3, 5, and 7 m/s, respectively, while the ambient temperature is maintained at 30 °C. It should be emphasized that although the performance of the uncooled polycrystalline silicon solar cell was previously investigated, the optimal permissible CR and the cell temperature uniformity are probed here for the first time.

Royne et al [3] Current Predicted

200

hback=10W/m2.K 150

hback=100W/m2.K

100

50

0

4

8

12

16

20

Concentration ratio (CR) Fig. 6. (a) comparison between the predicted average cell temperature and experimental results of [4] at time from 10:00 to 14:00, (b) Comparison between the predicted silicon layer temperature and the numerical results in [3] at different backside heat transfer coefficient and CR up to 20.

whereas the local temperature at a specific location can be much higher. This situation will lead to potential hotspots and thermal stresses associated with temperature non-uniformity which eventually causes solar cell damage. With this in mind, the present work draws attention to the local temperature distribution on a plane located at the mid-thickness of the silicon layer, where the temperature is at its maximum. Figs. 8 and 9 present the local temperature distribution at different coolant flow rates of 100, 800, and 2020 g/min, with a CR of 5, and 20 respectively. Based on Fig. 8, it is clear that at the lowest coolant flow rate of 100 g/min, the maximum temperature ranges between 47.5 °C for heat sink D and 56 °C for heat sink C. Thus, the solar cell temperatures of all configurations of the heat sink are far below the maximum allowable operating temperature. Increasing the coolant flow rate causes a minor reduction in the cell temperature. Fig. 9 shows the temperature distributions for all configurations of the heat sink at a CR of 20. At a lower coolant flow rate of 100 g/min, the temperature

5.2. The CPV/T system performance The performance of the CPV/T system under varying concentration ratios, coolant mass flowrates and microchannel heat sink designs is investigated at a constant value of 30 °C for both the ambient temperature and the inlet water temperature, and at a wind speed of 1.0 m/ s. The performance parameters include local solar cell temperature distribution, cell temperature uniformity, microchannel pumping power or friction power, net output power, and thermal and electrical efficiency. 5.2.1. Local temperature distribution and uniformity Most of previous studies have focused on estimating the average cell temperature to assess the performance of CPV/T systems without considering local temperature distributions. However, the average provides misleading information on the actual temperature distribution, as it might be much less than the maximum permissible temperature 602

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Fig. 7. Uncooled solar cell temperature contours at a plane located at the mid of the silicon layer.

counter flow designs, especially at lower coolant mass rate values where a significant difference in maximum temperature for each design is recorded. However, increasing the coolant mass rate leads to a reduction in the temperature difference shown in the contours and accordingly the contour shapes become approximately similar. It is generally observed based on the temperature contours that the solar cell temperature at the entrance of the heat sink is the same as the other side of the solar cell with the highest temperature in the middle of the cell. The reason is due to the existence of another entrance fluid into the heat sink on the other side of the cell. Evidently, based on the temperature contours of the silicon layer, the development of potential hotspots can be detected and consequently, any possible damage to the solar cell can be avoided. Such results cannot be obtained using the previous conventional one- or twodimensional models of the CPV/T system. To avoid the non-uniform temperature distribution on the solar cell surface, temperature uniformity of the solar cell surface is investigated for each heat sink design at different operating conditions. In the present work, the temperature uniformity can be expressed using the maximum temperature difference on the upper surface of the silicon layer. Figs. 10a, and b present the difference between the maximum and minimum local silicon layer temperature (ΔT = Tsc,max − Tsc, min) at a CR of 5, and 20, and a coolant flow rate of 100, 800, and 2020 g/min. At CR = 5, it is found that increasing the coolant mass flow rate dramatically decreases the temperature difference on the solar cell surface. At the lowest cooling mass rate, the double-layer configurations E and D achieve better temperature uniformity where the temperature difference (ΔT) is 3.75 °C, and 4.5 °C, respectively, as show in Fig. 10a. Additional increase of the coolant mass flow rate leads to a significant reduction in ΔT, and all the configurations achieve a relatively equal temperature uniformity ranging from 0.6 °C up to 0.8 °C. Similarly, Fig. 10b shows the variation of temperature difference for all heat sink configurations at coolant flow rates of 100, 800, and 2020 g/min, and CR = 20. At the lowest coolant flow rate, the temperature difference ranges between 17 °C and 27 °C, with the highest value found for heat sink C. Increasing the coolant mass flow rate up to 800 g/min significantly reduces the temperature difference, where it ranges between 3 °C and 7 °C. Further increase in the coolant mass flow rate up to 2020 g/min, moderately reduces the temperate difference for all configurations of heat sinks except configuration C, where a slight reduction in temperature uniformity is observed. This is most likely due to the saturated level of heat extracted from the solar cell achieved at higher coolant mass rates, as explained by Du et al. [36]. The value of ΔT decreases with the increase of the coolant mass rate, due to an increase in the coolant convective heat transfer coefficient. Notably, the accurate estimation of temperature uniformity is not possible using previous models’ due to its inability to determine temperature contours of the solar cell layer.

distributions range between 90 °C and 140 °C, where these values are much higher than the maximum allowable temperature. Further increase of the coolant flow rate, up to 800 g/min, reduces the temperature for all heat sinks. For configurations B, A, and D, the maximum temperatures are 82.5 °C, 84 °C, and 84 °C, respectively, which are slightly lower than the maximum permissible solar cell temperature. On the other hand, temperatures higher than the maximum acceptable solar cell temperature are obtained for configurations C and E, where the maximum temperatures are 92 °C, and 89 °C, respectively. An additional increase of coolant flow rate up to 2020 g/min, results in the reduction of the maximum solar cell temperature below the maximum permissible value for all configurations of heat sinks; the exception is configuration C, where the temperature is still higher than the maximum value. Furthermore, in this case, the temperature distribution is almost uniform in the middle region of the computational domain, when compared with the use of a coolant flow rate of 800 g/min. As seen in Fig. 9, increasing the coolant flowrate significantly decreases cell temperature. A significant reduction in the cell temperature is observed when increasing the coolant mass rate from 100 to 800 g/min. However, further increase of the coolant rate from 800 to 2020 g/min results in a slight decrease of solar cell temperature for all investigated configurations. This trend also observed by several researchers [28,4], and [36] and explained in [16,17]. The counter flow configurations C and E achieves higher solar cell temperatures at the same CR and coolant mass rate when compared with the parallel flow configurations A, D, and B at CR = 5 and CR = 20. The main reason for this trend is that the overall thermal resistance for counterflow designs is higher than that for parallel flow designs. This effect is less significant as the flow rate increases. For higher flow rates, the overall thermal resistances for both counter and parallel flow are very small and close to each other, especially for lesser wall thickness and higher heat transfer coefficients in the microchannel. To acquire a deeper understanding of how the thermal resistance affects the solar cell temperature necessitates an investigation of the variation of thermal resistance versus the coolant mass flow rates as shown in Table 4. The thermal resistance is defined as follows [37,38]. Tmax,MCHS − Tf ,in Rth,MCHS = , where Tmax, MCHS and qw are the maximum qw temperature on heated surface of the microchannel and the surface heat flux in W/m2 respectively. Based on Table 4, as the coolant mass flowrate increases from 100 g/min to 800 g/min., a significant decrease in the microchannel heat sink thermal resistance is observed for all investigated designs. With further increase of flow rates up to 2020 g/ min, there is a minor reduction in the thermal resistance of microchannel heat sinks. In addition, heat sinks A, B, and D have a lower thermal resistance compared to other configurations such as C, and D, and therefore attain a lower solar cell temperature. The temperature contours are different in value for parallel and 603

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A

ী=100g/min

ী=800g/min

ী=2020g/min

B

C

D

E

Fig. 8. Variation of temperature contours on a plane located at the mid of the silicon layer at CR = 5.

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ী=100g/min

ী=800g/min

ী=2020g/min

A

B

C

D

E

Fig. 9. Variation of temperature contours on a plane located at the mid of the silicon layer at CR = 20.

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that the friction power increases with the increase in coolant mass flow rate for all configurations. Furthermore, the consumed pumping power for both configurations B and C is approximately the same, and is higher than that of configuration A; meanwhile, the consumed pumping power for the double-layer configurations D and E, is less than that of configuration A. The main reason for this trend is that the fluid velocity in configurations B and C are much higher than in configuration A, followed by configurations D and E. The channel pressure drop is directly proportional to the velocity squared. Therefore, at the same coolant mass rate, the pressure drop in configurations B and C is higher than in configuration A, and a lower friction power is found in configurations D and E. Furthermore, it is found that varying the concentration ratio between 5 and 20 has a slight effect on the friction power, decreasing the friction power consumption in all heat sink configrations. This is most likely due to the fact that increasing the fluid

Table 4 Thermal resistance variation for all investigated microchannel heat sink designs with the coolant flowrate, [Rth, MCHS × 105], °C/(W/m2). ṁ (g/min)

A

B

C

D

E

100 800 2020

36.76 6.95 4.81

36.66 6.71 4.71

40.51 6.45 4.25

36.13 6.01 3.57

41.79 10.12 6.19

5.2.2. Solar cell power It is widely known that using a microchannel heat sink significantly increases the consumed pumping power due to the micro-scale of channel height. Accordingly, the power loss due to friction versus the coolant flowrates at CR = 20, is presented for all investigated configurations as shown in Fig. 11. As demonstrated in the figure, it is found

(a) CR=5

(b) CR=20 Fig. 10. Variation of the silicon layer temperature uniformity for all investigated configurations at various values of coolant mass and (a) CR = 5 and (b) CR = 20.

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5.2.3. Solar cell thermal and electrical efficiency Efficient use of microchannels as an active cooling technique for CPV systems can be achieved not only by enhancing the output electrical energy, but also by utilizing the dissipated heat as a source of thermal energy. The variations of thermal and electrical efficiency for all suggested designs of heat sinks versus the concentration ratio at different values of coolant mass flowrates of 100, and 800 g/min are presented in Figs. 13 and 14. The variation of thermal efficiency with the CR for all investigated configurations is presented in Figs. 13a and b for coolant mass flow rates of 100, and 800 g/min respectively. In general, increasing the CR leads to a rise in the thermal efficiency for all investigated configurations and coolant mass flow rates. In addition, increasing the coolant mass flow rate from 100 to 800 g/min considerably enhances the thermal efficiency. Further increase of the coolant mass flow rate slightly increases the thermal efficiency. This is because increasing the coolant mass flow rate from 100 to 800 g/min considerably reduces the cell temperature, and further increase of the coolant mass flow rate beyond 800 g/min has only a slight effect on the cell temperature variation, as shown earlier in Figs. 8 and 9. At a coolant mass flow rate of 100 g/min, the thermal efficiency using configurations C, and E, is lower than with the other configurations; meanwhile, at coolant mass flow rates of 800 g/min, the thermal efficiency with design C is higher than with any other configurations at a CR greater than 8. At coolant ̇ mass rate of 100 g/min, the thermal efficiency of the CPV/T system using configurations C and E is the lowest among the studied designs; this confirms that designs C and E have the highest thermal resistance of all investigated configurations at the same CR. Additionally, the higher solar cell temperature causes an increase in the thermal loss from the front surface of the CPV cell which reduces the gained thermal energy of configurations C and E. It is worth mentioning that all the investigated configurations achieve nearly the same thermal efficiency at higher flowrates. This is because at higher coolant mass flow rates, the thermal resistances of all configurations are nearly equal as reported in previous subsection. Moreover, there is a slight change in their electrical performance as supported by the experimental results of [37], which compare the heat transfer behavior of configuration D and E for application in the cooling of integrated circuits. The variation of solar cell electrical efficiency versus CR for all the investigated configurations is presented in Fig. 14a and b for coolant mass flow rates of 100, and 800 g/min, respectively. As shown in these

Fig. 11. Variation of the consumed friction power with coolant mass flowrate for all investigated configurations.

temperature reduces the fluid density and viscosity, which consequently reduces the friction pumping power. As shown in Fig. 12, increasing the coolant mass flow rate significantly raises the friction power where the frictional pressure drop is determined based on the simulation results, and the friction power is estimated using the equation of Pfrict. as reported in the Appendix A. In addition, the gained solar cell electrical power increases with the increase in the coolant mass flowrate up to certain limit and then remains nearly constant. Consequently, the net gained electrical power, which is the difference between the gained solar cell electrical power and the friction power, increases up to a certain limit, and then decreases. This trend is in good agreement with the experimental results of [4] and the numerical results of [16,28]. Fig. 12 shows an example of the variation of the output electrical power, the power loss due to friction, and the net gained electric power versus the coolant mass flowrate at two different values of CR, 5, and 20 for configuration A. As shown in the figure, the solar cell gained power increases dramatically with the increase in the CR. For the coolant mass flow rate of 2020 g/min, the solar cell power is about 14.4 W and 46 W at CR = 5 and 20, respectively. Furthermore, the power loss increases with the increase in coolant flowrate, and the solar cell power also increases to a certain limit and then remain nearly constant. Further increase in the flowrate causes an increase in the net gained electrical power, up to a certain limit, after which it decreases again. The optimum coolant mass flowrate at which the net gained power will start to decrease again is defined as the critical mass flowrate (MC). The value of the MC is dependent on the CR and the microchannel heat sink configurations. For configuration A, the values of MC are about 265.2 g/min and 694.4 g/ min at CR = 5 and CR = 20, respectively. Thus, the friction powers are 0.055 W and 0.45 W, which account for 0.32% and 0.7% of the solar cell electric power. A similar trend is seen in all studied configurations, and the values of MC and the net electric power for different heat sink configurations at a CR = 5, and 20 are shown in Table 5. The low values of the consumed friction power confirm that the microchannel heat sink is a suitable choice for the cooling of CPV, especially at higher CRs, where the cooling is a crucial aspect; the microchannel heat sink allows for optimal cooling while retaining a compact design, compared to the other conventional, large-scale thermal absorbers.

5

50

PSC

Power (W)

40

Pnet

4

CR=20

PFric.

30

3

2 20

CR=5

Operating point

10

1 PSC Pnet

0

400

800

Friction power (W)

Operating point

1200

m.(g/min)

1600

2000

0

2400

Fig. 12. Variation of Psc, Pfric, and Pnet with the coolant mass flowrate at CR = 5 and 20 for CPV system combined with heat sink configuration A.

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Table 5 Critical coolant mass flowrates, (MC), and corresponding maximum net powers for all investigated configurations. Configuration CR = 5 CR = 20

MC, (g/min) Pnet@ MC, (W) MC, (g/min) Pnet@ MC, (W)

A

B

C

D

E

265.2 14.2 694.4 45.7

266 14.2 687.6 45.6

414 14 920 44.3

264 14.3 600 45.9

600 14 1240 45

Fig. 14. Solar cell electric efficiency variation of the cooled CPV system at (a) ṁ = 100 g/min, and (b) ṁ = 800 g/min.

14.5%, as the CR increases from 5 to 20. Furthermore, there is no noticeable difference in cell electrical efficiency using different configurations of the heat sink. This is because the thermal resistance of all the investigated microchannel heat sinks reaches the same value at higher coolant mass rates, as reported in [37]. Fig. 13. Thermal efficiency variation of the CPVT system at (a) ṁ = 100 g/min, and (b) ṁ = 800 g/min.

5.3. Performance assessment of CPV/T systems The variation of the performance parameters of CPV units integrated with different configurations of heat sink designs at various values of coolant mass flowrates and solar concentrations are investigated. The performance parameters include maximum local solar cell temperature, temperature uniformity, cell net power, and electrical and thermal efficiency. It was found that at a low CR value of 5, the maximum local cell temperature was much lower than the maximum permissible solar cell temperature at all studied values of coolant mass flow rate. At a coolant mass rate of 800 g/min., the maximum cell net power is 14.01 W with a thermal efficiency of 67% for a CPV integrated

figures, the electrical efficiency reduces as the CR increases from 5 to 20 for the investigated configurations and coolant mass flow rates. This is mainly due to the rise in solar cell temperature with the increase in CR. At the lowest coolant mass rate, the electrical efficiency reduces from approximately 18% to 13.5% when using configurations, A, B, and D. When using configurations C and E, the cell electrical efficiency reduces from approximately 17.5% to 10%. An additional increase of coolant mass flow rates up to 800 g/min leads to an enhancement of the electrical efficiency, where it varies between approximately 18.5% and 608

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efficiency of 69.1% are obtained using a CPV system with heat sink configuration B. At a coolant mass rate of 2020 g/min., using heat sink configuration D attains the maximum cell power of 44.4 W, the maximum local cell temperature of 81.6 °C, and a thermal efficiency of 69.2%. Thus, for a CR of 20, the CPV system integrated with a parallel flow single layer microchannel heat sink, configuration B, is recommended where the maximum cell net power and thermal efficiency can be achieved using a coolant mass flow rate of 800 g/min. Comparison with the previous work indicated that the suggested

with configuration D of the heat sink. With a higher CR of 20, as presented in Fig. 15, using a low coolant mass flow rate of 100 g/min, results in local cell temperatures higher than the maximum allowable cell temperature for all investigated designs of the CPV/T systems. However, further increase of coolant mass flow rates up to 800 g/min, significantly reduces the local cell temperature and enhances the net cell power, thermal efficiency, and temperature uniformity. Based on the figure, the maximum cell temperature of 83 °C, the highest cell net power of 45.8 W, and a thermal

(a)

=100g/min

(b)

=800g/min

(c)

=2020g/min

Fig. 15. Variation of maximum local solar cell temperature, solar cell electric efficiency, net gained power, thermal efficiency and solar cell temperature efficiency for all investigated configurations at CR = 20 when (a) ṁ = 100 g/min, (b) ṁ = 800 g/min, and (c) ṁ = 2020 g/min.

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maximum local solar cell temperature and avoid the development of potential hotspots. In addition, the temperature uniformity can be accurately estimated to overcome the stress associated with the nonuniformity of cell temperature, and accordingly increase the solar cell’s lifetime. For concentration ratios up to 20, using a microchannel cooling technique with different configurations is an effective method. The CPV system integrated with a parallel flow microchannel heat sink achieves the highest cell net power, electrical efficiency, and the minimum cell temperature. On the other hand, the counter-flow microchannel heat sink is the least effective cooling technique due to high thermal resistance associated with the counter flow.

new microchannel design attained the highest net output power of the CPV/T system. The net output power of previous studies was 2.38 kW/ m2 at a CR of 28 [39], while this study has achieved a net output power of 2.7 kW/m2 at a CR of 20. Furthermore, the thermal and electrical efficiency in the current design is much higher than those previously reported by [36,40–42]. The findings in the present work provided a crucial step toward reaching the optimal cooling design technique for CPV systems. 6. Conclusion In light of the present study, some important findings can be derived. The operation of the uncooled polycrystalline silicon solar cell under concentrated illumination is restricted by the operating range of temperature, and so, the cell efficiency. The maximum acceptable CR for the efficient operation of solar cells under climatic conditions of a 1.0 m/s wind speed, and an ambient temperature of 30 °C, is 2.13. Using three-dimensional models of CPV/T systems to determine the temperature contour of the solar cell surface is essential to capture the

Acknowledgement The authors would like to thank the Egyptian Ministry of Higher Education as well as the Egypt-Japan University of Science and Technology, for offering the financial support and computational tools to conduct this research.

Appendix A. Auxiliary equations in the current study The CPV/T system thermal efficiency is calculated based on the following equations:

ηth =

Pth G (t ). Asc

CR =

G (t ) ,Gref = 1000 W/m2 Gref

Pfrict . = ΔP. ṁ / ρin Pnet = Pel−Pfrict. ΔP = f

2 lch ρin Vin Dh 2

ṁ = ρin (Hch × Wch) × Vin × N × n

Kn =

λ Dh

Re =

ρin Vin Dh μin

Dh =

2(Hch × Wch) (Hch + Wch)

Where: n is the number of microchannel heat sink layers. It equals to one for designs A, B and C and two for designs D and E. The radiation heat transfer coefficient from the glass surface to the ambient is calculated based on the following:

hrad,g -s =

σεg (Tg4−Ts4 ) (Tg−Ts )

Ts = 0.0522Ta1.5 hcon,g -a = 5.82 + 4.07Vw

Cells 2005;86:451–83. http://dx.doi.org/10.1016/j.solmat.2004.09.003. [4] Baloch AaB, Bahaidarah HMS, Gandhidasan P, Al-sulaiman Fa. Experimental and numerical performance analysis of a converging channel heat exchanger for PV cooling. Energy Convers Manage 2015;103:14–27. http://dx.doi.org/10.1016/j. enconman. 2015.06.018. [5] Ali AHH, Ahmed M, Youssef MS. Characteristics of heat transfer and fluid flow in a channel with single-row plates array oblique to flow direction for photovoltaic/ thermal system. Energy 2010;35:3524–34. http://dx.doi.org/10.1016/j.energy. 2010.03. 045. [6] Royne A, Dey CJ. Design of a jet impingement cooling device for densely packed PV cells under high concentration. Sol Energy 2007;81:1014–24. http://dx.doi.org/10. 1016/j. solener. 2006.11.015.

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