Thermal management of concentrator photovoltaic systems using microchannel heat sink with nanofluids

Solar Energy 171 (2018) 229–246

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Thermal management of concentrator photovoltaic systems using microchannel heat sink with nanofluids Ali Radwana,b, Mahmoud Ahmeda, a b

T

⁎,1

Department of Energy Resources Engineering, Egypt-Japan University of Science and Technology (E-JUST), Alexandria 21934, Egypt Department of Mechanical Power Engineering, Mansoura University, El-Mansoura 35516, Egypt

A R T I C LE I N FO

A B S T R A C T

Keywords: Nanofluid Eulerian-Eulerian Microchannel Concentrator photovoltaic Uniformity

A new cooling method for concentrator photovoltaic system is proposed using wide microchannel heat sink with nanofluids. A comprehensive three-dimensional model is developed. The model couples the two-phase (EulerianEulerian) multiphase model for the conjugate heat transfer of nanofluid flow in a wide microchannel heat sink with the thermal model of the concentrator photovoltaic systems. The model is numerically simulated and validated with the available experimental and numerical data. The influences of nanoparticle types, volume fractions, and coolant flow Reynolds number on the solar cell performance parameters are investigated. Results indicate that using SiC-water nanofluids attains lower cell temperature compared with Al2O3-water nanofluids. The increase of nanoparticles volume fraction ratio remarkably reduces the solar cell temperature and enhances the cell temperature uniformity and electrical efficiency. Furthermore, increasing the flow Reynolds number to a specific value significantly enhances the net electrical power. Further increase of the Reynolds number results in a significant reduction in the cell net gained power. By using 4% SiC-water nanofluid, the reduction in maximum local solar cell temperature is ranged between 8 °C and 3 °C compared with pure water with changing the flow Reynolds number from 12.5 to 250 at solar concentration ratio of 20.

1. Introduction Thermal management of concentrator photovoltaic (CPV) systems is an essential issue in low and high concentration ratio (CR) systems (Royne et al., 2005). In such systems, the overall performance of the solar cells is strongly affected by the working temperature (Sathe and Dhoble, 2017). Recently, the highest confirmed polycrystalline solar cell efficiencies are presented and summarized by (Martin et al., 2017). Based on their review, the maximum obtained electrical efficiency of polycrystalline silicon solar cells is 22.3 ± 0.4% at AM1.5 spectrum (1000 W/m2), and 25 °C. However, when the temperature of the cell is above the standard operating temperature, the solar cell electrical efficiency is expected to decrease by nearly 0.4–0.65% per one degree rise of cell temperature (Ma et al., 2015). The remaining part of the incident solar irradiance is absorbed in the cell causing a significant rise in the cell temperature (Agrawal et al., 2011; Emam et al., 2017; Radwan et al., 2018a). In addition, temperature non-uniformity significantly reduces the CPV system performance due to a loss in the cell output power and induces thermal fatigue due to a large amount of thermal stresses. This might cause irreversible damage to the silicon wafer

⁎

1

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

https://doi.org/10.1016/j.solener.2018.06.083 Received 23 March 2018; Received in revised form 4 June 2018; Accepted 21 June 2018 0038-092X/ © 2018 Elsevier Ltd. All rights reserved.

because of the excess localized heating or hot spots (Al-Amri and Mallick, 2014). In linear Fresnel lens solar concentrators, solar irradiance is concentrated on series connected cells. These series connection exhibit higher damage as the current directly varies with light intensity, so the gained current will be restricted by the cell with the maximum temperature. This failure is defined as the current matching problem (Ahmed and Radwan, 2017; Bahaidarah, 2016; Radwan et al., 2018b). This problem can be avoided by keeping a uniform temperature across the solar cell. Therefore, the better overall performance of the CPV systems can be attained by optimizing the use of solar energy with uniform and low average temperature of the silicon wafer to avoid hotspot and current mismatching problem. Thus, thermal regulation of CPV systems is of great importance. Utilizing hybrid micro-channel photovoltaic thermal systems was comprehensively investigated by Agrawal and Tiwari (2011), Agrawal et al. (2015), and Rajoria et al. (2015). In these works, comprehensive thermal models including exergy, energy, and enviro-economic analysis were developed. However, pure water was examined in several researches to cool the PV system and results showed a temperature variation along the surface of CPV string especially for simple conventional

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δ ε ρ σ τ

Nomenclature A C Dh G H k L ṁ P Re T u V Vw W

solar cell area [m2] specific heat of cooling fluid [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 vector [m/s] wind velocity [m/s] width of the channel and width of the solar cell [m]

Subscripts a ch conv, g-a el Fric. g in int l net p rad, g-s ref s sc th

Greek symbols η µ α β

thickness [m] emissivity fluid density [kg/m3] Stephan-Boltzmann constant 5.67 * 10−8 [W/(m2·K4)] transmissivity

solar cell electrical efficiency and CPV/T system thermal efficiency fluid viscosity [Pa·s] absorptivity cell temperature coefficient [1/K]

ambient channel convection loss from glass to ambient electrical friction glass inlet interval part of EVA liquid phase net solid (particle) phase radiation loss from glass to sky temperature reference condition, G = 1000 w/m2, T = 25 °C solid phase and sky silicon layer thermal

concluded that using nanofluids is not an efficient coolant for the concentrated multi-junction solar cell/thermal systems. Recently, Rejeb et al.(2016) developed a two-dimensional thermal modeling of the PV/ T system using Al2O3-water and Cu-water nanofluids as coolants with nanoparticle loading ranges from 0% up to 0.4% wt. dispersed in different base fluids such as water, and ethylene glycol. They recommended using water rather than ethylene glycol for the thermal management of the PV systems. In addition, they reported that using Cu-water nanofluid attains a higher electrical and thermal efficiency in comparison with Al2O3-water nanofluid at the same nanoparticles loading ratio. It is known that the two-dimensional thermal model correctly predicts the thermal behavior of conventional thermal absorbers when the change in the third dimension could be insignificant (Siddiqui and Arif, 2013). However, in irregular configurations where the temperature variation in the third dimension is a major, the twodimensional modeling cannot be used to predict the precise behavior of the PVT systems (Zondag et al., 2002). To overcome the limitations associated with one- and two-dimensional models of the PV/T systems, it was reported that the three-dimensional model is more flexible and can be easily adapted 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 (Zondag et al., 2002). One of the essential parameters that can be extracted using three-dimensional model is the solar cell temperature uniformity. It was found that the cell efficiency declines because of the cell non-uniform temperature distribution that causes a reverse saturation current (Domenech-Garret, 2011) and current mismatching problems (Bahaidarah, 2016). 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 (Royne et al., 2005). Therefore, the three-dimensional model will greatly assist in predicting the temperature distribution, and consequently, the temperature uniformity of a solar cell can be accurately estimated. Khanjari et al.(2016) numerically investigated the use of pure water and two different types of nanofluids Alumina-water and Ag-water nanofluids with volume fraction up to 12%. They found that increasing the inlet coolant velocity enhances the rate of heat dissipation from the PV panel and the heat transfer rate

heat sink designs (Yang and Zuo, 2015). The use of nanofluids as coolant medium has been experimentally and numerically investigated in the applications of photovoltaic thermal (PV/T) systems (Al-Waeli et al., 2017). Most of these studies indicated that using nanomaterials as a dispersed phase in the base fluid could enhance its thermo-physical properties of the coolant and consequently improve the coolant ability for heat removal. It was reported that the energy cost from the PV/T system using silver (Ag) –water nanofluids with volume fraction of 0.5% is 82% less than the domestic price of electricity. Moreover, the PV/T system could prevent the release of 16,974.57 tons of CO2 into the atmosphere (Lari and Sahin, 2017). The techno-economic assessment of grid connected PV/T system using Silver–water nanofluids has been investigated based on theoretical and experimental work existing in (AlWaeli et al., 2018). They concluded that grid connected PV/T system with nanofluid improved the PV technical and economic performance. In the present work, the used nanoparticles such as aluminum oxide (Al2O3) and silicon carbide (SiC) are cheaper than Silver. Accordingly, the used nanofluid is more economical compared with the previous work. Some of the recent nanofluid modeling techniques used one-dimensional, two-dimensional, and three-dimensional thermal model. In one-dimensional model, the photovoltaic module temperature changes only with thickness and the cell temperature uniformity cannot be predicted. One further step toward developing a more accurate thermal model for the PV/T system was conducted by developing two-dimensional analysis. Xu and Kleinstreuer (2014a, 2014b) developed a twodimensional thermal model for concentrated photovoltaic thermal (CPV/T) systems for crystalline silicon at CR of 200 Suns. In their model, the turbulent single-phase model is developed to investigate the performance of Al2O3-water nanofluid as a coolant with channel height ranges from 2 mm to 14 mm. At Re of 3000 and channel height of 10 mm, they concluded that the solar cell electrical efficiency improved with the increase in the nanoparticle volume fraction. It was found that the cell electrical efficiency increases from 16.83% to 17.12% for pure water and 4% Al2O3-water nanofluid, respectively. The same group used the same two-dimensional thermal model to compare the performance of the generic polycrystalline silicon solar cell with the multijunction solar cell (Xu and Kleinstreuer, 2014a, 2014b). They 230

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model of the CPV cell. The developed model takes into consideration all the relevant parameters such as nanoparticle size, shape, volume fraction, thermophysical properties, particle–fluid interaction forces, and operating and metrological conditions. The effects of nanoparticles types, nanoparticles volume fraction, and coolant flow Reynolds number on the temperature distribution of silicon wafer and the overall performance of the CPV/T system are investigated.

increases with the increase of the nanoparticle volume fraction. The same research group developed a three-dimensional modeling based on single phase flow modeling of Al2O3-water nanofluid as cooling for the PV cells in (Khanjari et al., 2017). Their results showed that using nanofluid achieves 10% enhancement in the heat transfer coefficient compared with using pure water. Sathe and Dhoble (2017) concluded that using more accurate modeling technique that effectively predicts the nanofluids behavior with sensitivity to the particle size, shape, and concentration is needed in estimating the performance of the PV/T systems. Yazdanifard et al. (2017) stated that using two-phase approach for nanofluid flow modeling can enhance the understanding of related heat transfer mechanisms. Javadi et al. (2013) concluded that the two-phase flow modeling approach is the need of the current research to cover this phenomenon. Based on the above inclusive survey of the relevant literature, although numerous research works were conducted to investigate the use of nanofluids in the cooling of PV systems, all investigations are adapting a single-phase model for the nanofluid flow in heat sink. However, using two-phase modelling of nanofluids is much more efficient in prediction of heat transfer and friction characteristics (Akbari et al., 2012; Keshavarz Moraveji and Esmaeili, 2012). To the best of authors knowledge, there are no studies using three-dimensional two-phase flow modelling of nanofluid coupled with thermal models of concentrator photovoltaic systems. Therefore, the main objective of the current study is to investigate the perfromance of CPV system at solar concentration ratio of 20 and cooled with microchannel heat sink with different nanofluids. Aluminum Oxide (Al2O3)-water and Silicon Carbide (SiC)-water nanofluids with volume fractions up to 4% are compared with pure water as coolant for CPV system. For accurate modeling, a comprehensive three-dimensional model is developed. This model couples three-dimensional two-phase (Eulerian-Eulerian) model of the nanofluid flow in a wide microchannel heat sink with the thermal

2. Physical model In the current study, the performance of the polycrystalline silicon solar under concentrated illumination with CR of 20 is investigated. Two different water-based nanofluids are used as coolants. Aluminum oxide (Al2O3) and silicon carbide (SiC) nanoparticles with different volume fractions from 0 up to 4%. It is concluded that decreasing the nanoparticle size enhances the heat transfer characteristics (Anoop et al., 2009). In addition, a smaller size of nanoparticles is required to achieve stability compared with a larger size. Therefore, nanoparticle size of 20 nm is used through the whole simulation. The selected nanoparticles proved a stable suspension in water and comprehensively examined in recent experimental work (Al-Waeli et al., 2017; Hajipour and Dehkordi, 2014; Hedayati et al., 2015). Therefore, these two nanofluids have been selected to be simulated using Eulerian-Eulerian multiphase approach. The proposed CPV/T system components including the Fresnel lens, solar cell structure integrated the heat sink are presented in Fig. 1. In this system, a linear Fresnel lens with dual axis tracking is used to concentrate the solar radiation onto the target area of the solar cell. The commercial polycrystalline solar cell composes of a silicon layer with thickness of 0.2 mm and coated with anti-reflective layer. These two layers are embedded in a transparent encapsulation ethylene vinyl acetate (EVA) layer with a thickness of 0.5 mm above and below the

Fig. 1. Schematic diagram for a typical CPV/T uses a linear Fresnel lens solar concentrator and the coordinate system. 231

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silicon layer to fix it and provide both electrical isolation and moisture resistance (Singh et al., 2016; Zhou et al., 2015). Moreover, Tedlar Polyester Tedlar (TPT) polymer layer is a photostable layer of thickness 0.3 mm is used. Finally, a higher transparency tempered glass cover with a thickness of 3 mm is used in this structure. A simple manufactured wide microchannel heat sink (MCHS) of 127.2 mm by 127.2 mm is used as a thermal absorber. The channel height of 100 µm is selected to represent the mid-range of the microchannel size (Kandlikar et al., 2013). The coolant is allowed to enter from the mid of the solar cell and divided into two sides. The heat sink is designed from aluminum as it is economically recommended over the copper for the thermal regulation in CPV systems (Micheli et al., 2016). The MCHS is attached to the backside of the solar cell to remove the excessive heat from the cell. The solar cell dimension is 125 mm by 125 mm in the cell part region, and the EVA interval between each cell and the adjacent cell is 2.2 mm (Zhou et al., 2015). Only one cell is investigated from the series connected strings. Hence, the complete dimension of the computational domain is 127.2 mm by 127.2 mm comprising 1.1 mm EVA interval from all sides. To save the computational time especially for three dimensional with two-phase flow modeling, the solar cell effective area is divided into two equal symmetric domains with dimensions of 127.2 mm by 63.6 mm as showed in Fig. 2.

3. To consider the real situation, the solar energy absorption of all layers in the interval part and cell part are considered. 4. The optical and thermophysical properties of the solar cell layers are assumed to be isotropic and temperature independent. 5. The thermal contact resistances among each layer of the solar cell and microchannel heat sink were neglected. This can be attained by monolithic fabrication of the MCHS along with using electronic grease for the integration of MCHS with the solar cell. 6. The wind speed and ambient temperature are the same on both top and bottom of the solar cell with assumed values of 1 m/s and 30 °C, respectively. The effect of variation of these metrological conditions was investigated in the author earlier work(Radwan and Ahmed, 2017). 7. The model sides are assumed to be adiabatic due to the symmetry and the small thickness of the CPV layers (Zhou et al., 2015). 8. Bus bar connections effect on the calculations is not taken into account. 3.1. PV-module layers As the CPV cell structure contains several layers, the heat conduction equation for these layers can be represented as follows (Siddiqui et al., 2012):

3. Theoretical analysis

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

A comprehensive three-dimensional two-phase flow model of nanofluid flow inside MCHS coupled with a thermal model of the CPV system is developed. The following assumptions are considered in the model:

where: ki represents the thermal conductivity of the layer i, and the term qi denotes the heat generation per unit volume of layer i due to the solar irradiance absorption. In the present solar cell structure, the value of i changes from 1 to 6 for tempered glass, upper EVA, ARC, silicon, lower EVA, and the Tedlar layer respectively. The value of qi is mainly dependent on the net concentrated solar irradiance G; the absorptivity (α) of the layer i and the net transmissivity (τ) of the layers above the layer i can be determined using the following equation as reported in (Siddiqui et al., 2012).

1. The flow in the microchannel heat sink is steady, laminar, and incompressible. 2. The nanoparticle properties are assumed to be temperature independent while the water properties are temperature dependent and can be estimated using the fifth order polynomial equations of (Jayakumar et al., 2008) as shown later.

qi =

(1−ηsc ) G αi τj Ai Vi

Fig. 2. Schematic drawing of the three-dimensional computational domain including the CPV layers combined with the MCHS. 232

(1)

(2)

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where: ηsc is the solar cell electrical efficiency; G, αi, Ai, and Vi are the net concentrated solar irradiance incident on the target area of the cell, the absorptivity, area, and volume of the layer i, respectively; τj is the net transmissivity of the layers above layer i. It is interesting to mention that care is needed while using equation (2). The values of ηsc change to zero when the calculation of qi is performed for glass, top EVA, lower EVA, and TPT layer. However, its value is a function of solar cell temperature and solar irradiance for a silicon wafer. Moreover, the net absorbed solar energy by all layers in the cell part, and the interval part of the computational domain are taken into consideration to simulate the real situation. Dimensions of the CPV/T system layers, optical properties, and CPV/T system are presented in Tables 1, and 2 respectively. As shown in Fig. 2, the computational domain is divided into the cell part and the interval part. In the cell part, the layers under the silicon layer are not directly exposed to the net concentrated solar flux due to the lower transmissivity of the silicon layer. Consequently, the generated heat in the EVA under the silicon layer and Tedlar layer can be neglected. In addition, the reflected solar irradiance absorption by the glass and EVA above the silicon layer is neglected due to the existence of an ARC layer and the low silicon layer reflectivity (Zhou et al., 2015). Therefore, only the absorption of net concentrated solar irradiance by the glass, EVA above the silicon, and the silicon layer are considered. For the interval part, all 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. To manage this problem with different heat generation in specified volumes, the computational domain is divided into multi-zones for each layer in the cell part and interval part. The heat generation per unit volume of the silicon layer depends on its electrical efficiency which can be calculated using the following equation as a function of the solar cell temperature and net concentrated solar radiation (El et al., 2017):

G ⎞⎤ ⎡ ηsc = ηref ⎢1−βref (Tsc−Tref ) + δ ln ⎛⎜ ⎟ ⎥ G ⎝ ref ⎠ ⎦ ⎣

Table 2 CPV/T system dimensions. Factor

Value

Factor

Value

Lsc Hch δw Asc

125 mm 0.1 mm 0.2 mm 125 × 125 mm2

Wsc Wch,flat δch δint

125 mm 126.8 mm 0.5 mm 1.1 mm

approach for the low solid volume fraction dispersed in the base fluid where it is analyzed based on the Eulerian model and the dispersed particle based on the Lagrangian model (Kalteh et al., 2011). However, for large solid particle loading, the Eulerian-Eulerian approach is the appropriate model because it needs less computational time compared with the Lagrangian-Eulerian approach where it needs a high supercomputing ability (Akbari et al., 2012). In the current study, Nano-sized particles with extremely large numbers are dispersed in the base fluid even for a small volume fraction. Thus, the Eulerian-Eulerian approach is the practical approach due to the software ability limitations to model such problem using Eulerian-Lagrangian approach (Akbari et al., 2012). Therefore, the Eulerian-Eulerian model is applied in the current study to model the nanofluid flow inside the MCHS as recommended by (Akbari et al., 2012; Hadad et al., 2013; Kalteh et al., 2012a, 2011; Moraveji and Ardehali, 2013). In the Eulerian-Eulerian multiphase model, the governing continuity, momentum and energy equations for the base liquid and solid particle phases can be written as follows: 3.2.1. Continuity equations For the primary phase (liquid phase): →

∇ · (ρl φl Vl ) = 0

(5)

For the secondary phase (nanoparticles): →

∇ · (ρp φp Vp) = 0

(3)

(6)

where: the subscripts l and p stand for the liquid and solid particles phase, respectively, and φ is the phase volume fraction. The summation of both phases volume fractions equal to unity as follows (ANSYS FLUENT 14.5 Theory Guide):

where: the ηref, βref, and δ are the solar cell efficiency, cell temperature coefficient at a reference temperature of Tref = 25 °C, and solar radiation coefficient, respectively. These values are provided by the manufacturer data sheet for the current study. βref is taken to be 0.0045 K−1 for polycrystalline silicon (Sarhaddi et al., 2010) and δ is taken to be 0.052 (El et al., 2017).

φl + φp = 1

(7)

The volume of the phase q is Vq and can be formulated as follow

Vq =

3.2. Microchannel heat sink

∫ φq dV

(8)

q

For Microchannel heat sink substrate, the general equation of heat conduction in the aluminum microchannel substrate can be written as follows:

where: V is the coolant volume 3.2.2. Momentum equations The momentum equations for the liquid and solid phases can be written as follow (Kalteh et al., 2012a): For liquid:

(4)

∇ · (Ksub ∇Tsub) = 0

where: ksub is the thermal conductivity of microchannel aluminum walls. For nanofluid flow theory, two modeling approaches can accurately predict the solid–liquid mixture. The first approach is the LagrangianEulerian approach. This modeling technique is the most suitable

→→

→

→

∇ · (ρl φl Vl Vl ) = −φl ∇P + ∇ · [φl μl (∇Vl + ∇VlT )] + Fd + Fvm

(9)

For solid nanoparticles:

Table 1 CPV system layer optical properties (Zhou et al., 2015). 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

233

0.9 0.9

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A. Radwan, M. Ahmed →→

→

→

∇ · (ρp φp VpVp) = −φp ∇P + ∇ · [φp μp (∇Vp + ∇VpT )]−Fd−Fvm + Fcol

Table 4 Thermo-physical properties of water as a function of the absolute temperature (Jayakumar et al., 2008).

(10)

where: P, Fvm, Fd, and Fcol are the pressure, virtual mass (added mass), drag, and particle–particle interaction force due to the nanoparticle collision. The expressions of drag force, virtual mass force, and collision forces are presented in Appendix A (Hejazian et al., 2014) Since in the Eulerian-Eulerian multiphase model, the solid particle phase is considered as a continuum, its viscosity µp has to be identified. Kalteh et al. (2011) used a solution technique to distinguish the effect of this parameter on the attained heat transfer coefficient. They concluded that the solid phase viscosity is independent of Reynolds number. In addition, they concluded that changing the solid viscosity (from 0.01 to 0.00001) does not affect the first digit of the decimal of the predicted Nusselt number. So, based on their results, the particle viscosity value of 1.38 × 10−3 Pa·s is used in the current study as they recommended Kalteh et al. (2011). It was recommended by several researchers (Kalteh et al., 2012b, 2011) that including the drag force has a noticeable effect on the predicted average Nusselt number. Consequently, the drag force between the two phases is also taken into account based on Schiller and Naumann model as reported in (Kalteh et al., 2012a). The thermophoresis effect is neglected due to its insignificance as reported by the author previous work using Lattice Boltzmann Method (LBM) (Ahmed and Eslamian, 2015).

Property = A + B × T + C × T2 + D × T3 + E × T4, (T in absolute value) Coefficient

ρ(kg/m3)

Cp (J/kg·K)

µ (Pa·s)

K(W/m·K)

A B C D E

1277.8 −3.0726 0.01178 −1.53e−5 0

4631.9 −1.478 −0.003108 1.111e−5 0

0.3316 −0.003753 1.6028e−5 −3.06e−8 2.19e−11

−1.0294 0.010879 −2.261e−5 1.536e−8 0

assumed to be isolated. Moreover, the lower wall of the microchannel heat sink is taken to be adiabatic to accomplish the utmost conceivable thermal energy gain. For microchannel heat sink, both solid and liquid phases are assumed to enter the MCHS with a uniform temperature and velocity normal to the inlet boundary. The value of the inlet velocity component changes according to the selected Reynolds number. In the meantime, pressure outlet boundary condition is identified at the outlet section with zero gage pressure. As the water Knudsen number falls in the no-slip regime (Kn < 0.001) (Dehghan et al., 2015), no-slip and no temperature jump boundary conditions are considered at the interface between the walls–fluid domains. The boundary conditions for the half of the CPV cell integrated with the heat sink are presented as follows:

3.2.3. Energy equation The energy equation for the fluid and particle phase can be written as follows (Kalteh et al., 2011):

3.3.1. The CPV layer For the upper side of glass cover:

→

∇ ·(ρl φl Cpl Tl Vl ) = ∇ ·(φl K eff , l ∇Tl )−h v (Tl−Tp)

(11)

At 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and z = (δch + δT + 2δEVA + δARC + δsc + δg)

→

∇ ·(ρp φp C pp Tp Vp) = ∇ ·(φp K eff , p ∇Tp) + h v (Tl−Tp)

(12)

where: Cp, Keff, T, and hv are the phase-specific heat, effective thermal conductivity, temperature, and volumetric heat transfer coefficient between the two phases. The volumetric heat transfer coefficient is calculated using equations that detailed presented in Appendix A (Syamlal and Gidaspow, 1985). In the current work, the thermophysical properties of CPV layers along with the Al2O3, and SiC nanoparticles are listed in Table 3, while thermophysical properties of water are estimated using the fifth order polynomial function of the absolute temperature as shown in Table 4.

−k g

∂T ∂y

= qrad, g − s + qconv, g − a

(13)

z

where: the qrad,g-s, and qconv,g-a are the radiative and convective heat flux from the glass cover to the sky temperature and ambient temperature respectively as presented in Appendix A (Xu and Kleinstreuer, 2014a, 2014b). Mixed boundary condition has to be applied with convective heat transfer coefficient, free stream temperature, glass external emissivity, and external radiation temperature. Complete details about the calculation of convective heat transfer coefficient caused by wind and external radiation temperature available in Appendix A. For glass cover, EVA, ARC, silicon, and tedlar sides:

3.3. Boundary conditions First, the glass cover including the interval part and the cell part is subjected to combined convection and radiation heat loss as a thermal boundary condition. At the upper surface, ambient temperature, convective heat transfer coefficient caused by the wind, external radiation temperature and glass emissivity are defined. Due to the symmetry and very small thickness, the sides of the computational domain are

−ks

∂T =0 ∂z

where: Ks is the material thermal conductivity. For the interfaces between all connected layers, the thermally coupled boundary condition is implemented (ANSYS FLUENT 14.5

Table 3 Thermophysical properties and thicknesses of PV/T layers, nanoparticles, and MCHS material (Singh et al., 2016; Zhou et al., 2015; Jayakumar et al., 2008). Layer

Density (kg/m3)

Specific heat (J/kg·K)

Thermal conductivity (W/m·K)

Thickness (mm)

Glass (Cover) ARC Encapsulation (EVA) Silicon Tedlar (PVF) Al2O3-nano-particles SiC-nano-particles MCHS substrate, aluminum

3000 2400 960 2330 1200 3960 3370 2719

500 691 2090 677 1250 773 1340 871

2 32 0.311 130 0.15 40 150 202.4

3 0.01 0.5 0.2 0.3 dp = 20 nm dp = 20 nm 0.4

234

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momentum and energy equations are accomplished. Meanwhile, the new silicon layer temperature is obtained. Then, the electrical efficiency is calculated using Eq. (3). The iteration procedure is repeated until achieving two convergence criteria. The first one is the maximum residuals in the solution of the two-phase conjugate heat transfer equations is less than 10−6 and the second is the relative error between the two consequent silicon layer temperatures less than 10−3. Therefore, parallel computing is implemented using Dell Precision T7500 workstation with Intel Xeon® processor of 3.75GH, 48-core, and 64-MB installed memory.

Theory Guide). For the solid–solid interfaces located at: 0 ≤ x ≤ (Wsc + 2δint), (Lsc/2 + δint) ≤ y ≤ (Lsc + 2δint), and the zcoordinate changes as follows: At the interface between the glass cover and top EVA layer, z = (δch + δT + 2δEVA + δARC + δsc) kEVA ∇TEVA = k g ∇Tg and Tg = TEVA At the interface between the top EVA and the ARC layer, z = (δch + δT + δEVA + δARC + δsc) kEVA ∇TEVA = kARC ∇TARC and TARC = TEVA At the interface between the ARC and the silicon layer, z = (δch + δT + δEVA) ksc ∇Tsc = kARC ∇TARC and TARC = Tsc At the interface between the silicon layer and the bottom EVA layer, z = (δch + δT + δEVA) kEVA ∇TEVA = ksc ∇Tsc and Tsc = TEVA At the interface between the bottom EVA and the tedlar layer, z = (δch + δT) kT ∇TT = kEVA ∇TEVA and TAl = TT At the interface between the tedlar and aluminum channel, z = δch kAl ∇TAl = kT ∇TT and TAl = TT

3.5. Numerical method In single phase modeling approach, the nanofluid equivalent thermophysical properties such as thermal conductivity, density, specific heat capacity, and viscosity have to be defined in the model. All of the equations used to estimate the equivalent thermophysical properties are dependent on nanoparticle volume fraction, nanoparticle properties, and base fluid properties and some of them include the nanoparticle size, and shape effect and some not. Therefore, it can be concluded that single phase simulation model justify the nanofluid as a new coolant with new properties. In this study, a double precision solution is adopted to ensure the accurate transfer of the boundary information as recommended (ANSYS FLUENT 14.5 Theory guide). In ANSYS 17.2 commercial software, the solution steps start with Eulerian-multiphase model selection with two phases and implicit formulation of each phase volume fraction. In twophase flow modeling, liquid and solid particle thermophysical properties such as density, specific heat capacity, and thermal conductivity are defined as presented in Table 3. Water is considered as primary phase while the nanoparticles with a specific volume fraction are considered as a secondary phase. The granular option has to be selected to define the secondary phase as a solid phase with size of 20 nm and granular viscosity of 1.38 × 10−3 Pa·s (Kalteh et al., 2011). The energy equations for all phases should be enabled and then the interaction between the primary and the secondary phase is well-defined. The heat transfer effect between both phases is also considered as mentioned in the energy equation. The inlet and outlet boundary conditions are defined for each phase separately and the nanoparticle volume fraction is identified at the inlet of the secondary phase.

3.3.2. For microchannel heat sink At the inlet: δw ≤ x ≤ (Wsc + 2δint − δw), y = (Lsc/2 + δint), and δw ≤ z ≤ (δw + Hch) Vl = 0 i + (vin) j + 0 k, and Tl = 30 °C Vp = 0 i + (vin) j + 0 k, and Tp = 30 °C, and φp varies from 0 to 4% At the outlet: δw ≤ x ≤ (Wsc + 2δint. − δw), y = (Lsc + 2δint), and δw ≤ z ≤ (δw + Hch) Pgage,l = 0, and the back flow temperature of 30 °C. Pgage,p = 0, flow temperature of 30 °C and backflow volume fraction of zero is defined. For microchannel walls: Side walls at: (x = 0 and x = Wsc + 2δint), 0 ≤ y ≤ (Lsc + 2δint), and 0 ≤ z ≤ (2δw + Hch)

−kAl

3.5.1. Grid sensitivity test Grid independence test is accomplished by computing the solar cell temperature at different numbers of grids. The test is performed for the CPV cell layers combined with the investigated MCHS. Uniform meshing with element size in the fluid zone is much smaller than in the solid regions is used with total number of quadrilaterals elements of 9,450,752. This value was selected after testing of several mesh sizes while no changes in cell temperature with a further increase in the number of elements is observed.

∂T =0 ∂x

Lower wall at: 0 ≤ x ≤ (Wsc + 2δint), 0 ≤ y ≤ (Lsc/2+ δint), and z = 0:

−kAl

∂T ∂y

=0 z

For solid–fluid interface, no slip and thermally coupled boundary conditions are applied as follows:

3.6. Model validation The present model is validated using two different sets of experimental data. First, the two-phase flow model using Eulerian-Eulerian approach is compared with available experiments in (Kalteh et al., 2012a) and numerical results published in (Ahmed and Eslamian, 2015). Second, the whole model of the PV/T system including the thermal absorber is validated with the experimental results of (Kasaeian et al., 2017), and (Joshi et al., 2009).

Vp (x,y,z) = up i + vp j + wp k = 0, Tp = Twall (x,y,z) Vl (x,y,z) = ul i + vl j + wl k = 0, Tl = Twall (x,y,z) 3.4. Solution method The applied solution technique is started by estimating an initial value of cell electrical efficiency (ηref = 0.2). Then, the corresponding internal heat generation per unit volume of the silicon wafer is determined using Eq. (2), and the heat generation for other PV layers in the interval part and the cell part is also calculated. After that, the PV governing equations coupled with the Eulerian-Eulerian multiphase model are solved until the convergence criteria in continuity,

3.6.1. Eulerian-Eulerian multiphase model validation The governing equations for the nanofluid domain are solved to validate the current predicted results of Al2O3-water nanofluid flow inside a wide microchannel heat sink with the experiments of (Kalteh et al., 2012a). In this step, a wide microchannel heat sink with channel 235

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6

1000

G 4

800

2 0

600

Vw 8

9

10

11

12

13

14

15

16

17

400 18

Daytime (hr)

(b) 70 Temperature (oC)

G, (W/m2)

Wind speed, Vw, (m/s)

(a)

Tsc, Exp. Kasaeian et al., 2017 Tsc, Present model

60

Tin Ta

50 40 30

8

9

10

11

12

13

14

15

16

17

18

Daytime (hr) Fig. 5. PV/T model validation with the experimental results available in (Kasaeian et al., 2017), (a) hourly variation of wind speed and solar irradiance, and (b) hourly variation of inlet coolant, ambient, measured solar cell temperature, and present model predicted temperatures.

Fig. 3. Comparison between the variation of predicted Nusselt number (Nu) versus Reynolds number and those obtained experimentally by (Kalteh et al., 2012a) and numerically using LBM (Ahmed and Eslamian, 2015).

height of 0.58 mm, channel length of 94.3 mm, and channel width of 28.1 mm is examined. During this validation step, the two-phase Eulerian-Eulerian model is adopted with secondary phase volume fraction of 0.002 and Al2O3-water nanofluid. Meanwhile, the predicted Nusselt number of the present model is compared with the results of using multi-phase Lattice Boltzmann Method (LBM) developed by (Ahmed and Eslamian, 2015). In Fig. 3, the present predicted Nusselt number are compared with the experimental (Kalteh et al., 2012a), and numerical results of (Ahmed and Eslamian, 2015) at various Reynolds number ranges from 50 up to 350 for the 2% Al2O3-water nanofluid. It is found that the current predicted results are in agreement the

experimental and numerical results.

3.6.2. Photovoltaic/thermal model verification In the current subsection, the numerical results obtained via present numerical simulation are compared using two sets of experimental data published in (Baloch et al., 2015). The first set includes two groups of local cell temperature measurements at two different days where incident solar radiation was 300 and 980 W/m2 respectively. The second set is comprised of the average cell temperature measurements at various hours where the metallurgical properties and incident solar

Fig. 4. (a) Comparison between the predicted local cell temperature and both measured and numerical values at 10:00, (b) comparison between the predicted average cell temperature with the experimental results at time from 10:00 to 14:00 (Baloch et al., 2015). 236

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on local, average and maximum silicon layer temperature, and temperature uniformity will be investigated.

radiation varied hourly. Fig. 4a shows the comparison between the local computed solar cell temperature and both measured and predicted values at two different incident solar radiations. Based on the figure, at an incident solar radiation of 300 W/m2, a very good agreement is found between the computed temperatures at those measurements, where the maximum deviation is about 2%. In addition, at an incident solar radiation of 800 W/m2, a slight difference between computed temperature and measured values is noted, with a maximum deviation of about 5%. Fig. 4b presents a comparison between the hourly calculated solar cell temperature and those measured and predicted at two different seasons where the solar radiation, wind speed, and ambient temperature are different. Excellent agreement between the computed temperature and those measured and predicted is shown. Further validation step is conducted with the experimental results of (Kasaeian et al., 2017) as shown in Fig. 5. In this experiment, air is used as a coolant in a wide thermal absorber with channel height of 5 cm and air flowrate of 0.06 kg/s and zero nanoparticle volume fraction. In Fig. 5a, the hourly variations of the wind speed and solar irradiance are displayed. In Fig. 5b, the hourly variations of the ambient, and coolant inlet temperature along with the experimental results for the top PV module surface temperature in (Kasaeian et al., 2017) and the corresponding predicted values are shown . It is obvious that the current predicted results match the experimental results with a maximum relative error of 6.8% at 14:30 of the test day. Furthermore, the predicted results are compared with the experimental of (Joshi et al., 2009). It is noticeable that the same meteorological conditions of these studies are applied as operating and boundary conditions in the current numerical model. In Table 5, the predicted results are compared with the experimental of (Joshi et al., 2009) to verify the solar cell temperature, coolant outlet temperature, and solar cell electrical power. Based on validation results, it is noticeable that the current model accurately predicts the PV/T system performance parameters with maximum relative errors of 3.3%, 1.5%, and 2.4% in the solar cell temperature, outlet temperature, gained power, respectively.

4.1.1. Average and maximum silicon layer temperature Fig. 6a and b shows the effect of using Al2O3 and SiC nanoparticles with volume fraction up to 4% on the average and maximum silicon layer temperature at Re of 12.5, 25, 50 and 250. As seen in Fig. 6a, increasing the nanoparticle loading remarkably reduces the average silicon layer temperature at the same value of Re. At 4%-Al2O3–water nanofluid, the reduction in temperature is about 3.1 °C, 2.1 °C, 1.1 °C, and 0.5 °C at Re of 12.5, 25, 50, and 250, respectively. Similarly, the reduction of temperature is about 5.8 °C, 4.1 °C, 2.5 °C, 1.7 °C when using 4%-SiC-water nanofluid and Re of 12.5, 25, 50, and 250, respectively. The reason for the reduction of cell temperature is most likely due to that inclusion of nanoparticles in the base fluid enhances the fluid overall thermal conductivity which in return increases the rate of heat dissipation from the silicon wafer as supported by the recent studies (Xu and Kleinstreuer, 2014a, 2014b; Yazdanifard et al., 2017). Another point of view indicated that the fluid flow became heterogeneous with the inclusion of the dispersed nanoparticles and this leads to a better mixing which enhances the heat dissipation to the coolant through the boundary layer disturbance (Ahmed and Eslamian, 2015, 2014). Moreover, increasing Re leads to a reduction in cell temperature at the same nanoparticle volume fraction. This is mainly returned to that increasing Re number increases the heat transfer coefficient inside the microchannel heat sink. As shown in Fig. 6, increasing the Re from 12.5 to 50 leads to decrease the cell temperature from 97.7 °C to 84.9 °C for pure liquid. Further increase of Re from 50 to 250 leads to a slight reduction in the cell average temperature from 84.9 °C to 81.7 °C. This observation is supported by several researches (Bahaidarah, 2016; Baloch et al., 2015). The reason for this trend is explained by the author earlier work. It is noted that using SiC-water nanofluid attains lower cell temperature compared with using Al2O3-water nanofluid over the studied range of Re number. For instance, at nanoparticle volume fraction of 4%, the average silicon layer temperature decreases from 97.8 °C to 94.6 °C using Al2O3-water nanofluids and from 97.8 °C to 91.9 °C using SiC-water nanofluid at Re of 12.5. That’s mainly returned to the higher thermal conductivity of the SiC particles compared with Al2O3. Furthermore, the variation of maximum solar cell temperature with the nanoparticle volume fraction at different values of Re number is presented in Fig. 6b. Generally, it is apparent that increasing the nanoparticle loading along with the Re number significantly reduces the maximum solar cell temperature. At Re of 12.5, increasing the nanoparticle volume fraction up to 4% results in reducing the maximum cell temperature from 107 °C to 102 °C using Al2O3-water nanofluid and from 107 °C to 98.8 °C using SiC-water nanofluid. At higher Re of 250, by increasing the nanoparticles volume fraction up to 4% for Al2O3water and SiC-water nanofluids, the maximum cell temperature reduces from 82.1 °C to 81.5 °C and to 80.3 °C respectively. It was reported that

4. Results and discussion The solar cell thermal parameters such as the local silicon layer temperature, maximum silicon layer temperature, and cell temperature uniformity are essential parameters that influence the performance of the CPV/T systems (Royne et al., 2005). Therefore, the effect of operational conditions such as nanoparticle volume fraction (φ), and coolant flow Reynolds number (Re) on the CPV/T system performance is investigated. 4.1. Effect of nanoparticle volume fraction and coolant Re number on CPV/T system temperatures The effect of nanoparticle volume fraction (φ) and coolant flowrate

Table 5 Verification of the predicted results with the experimental data of (Joshi et al., 2009). Solar cell temperature (°C)

Coolant outlet temperature (°C)

Module electrical power (W)

Time

Exp. (Joshi et al., 2009)

Current predicted

% error

Exp. (Joshi et al., 2009)

Current predicted

% error

Exp. (Joshi et al., 2009)

Current predicted

% error

8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

37.6 41.5 48.0 50.4 54.9 54.7 52.9 50.6 47.3 42.3

37.2 40.7 46.4 50.0 55.3 55.7 54.4 51.2 46.5 41.8

1.1 1.9 3.3 0.8 0.7 1.8 2.8 1.2 1.7 1.2

32.5 34.1 36.5 39.0 44.5 45.6 44.4 43.1 41.5 39.2

32.9 34.4 37.1 38.7 44.6 46.1 44.4 43.6 42.0 39.8

1.2 0.9 1.6 0.8 0.2 1.1 0.0 1.2 1.2 1.5

38.9 49.8 62.5 72.4 73.4 66.2 62.5 47.6 29.8 12.4

38.4 48.6 61.5 71.4 72.5 65.2 62.0 46.7 29.8 12.7

1.3 2.4 1.6 1.4 1.2 1.5 0.8 1.9 0.0 2.4

237

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Fig. 6. Variation of (a) the average silicon layer temperature, and (b) maximum silicon layer temperature with the nanoparticle volume fraction at different Re numbers.

4.1.2. Silicon layer temperature uniformity The temperature distribution across the silicon layer is an important parameter to estimate the thermal stresses resulted from a the temperature gradient. Temperature uniformity is a parameter defined by the maximum cell temperature difference (ΔT = Tsc,max − Tsc,min) (Yang and Zuo, 2015). Therefore, it is essential for CPV cells to operate

the maximum operating temperature limit of the silicon-based cells is around 85 °C (Agrawal and Tiwari, 2015). Therefore, increasing the nanoparticle loading in the base fluid above 1.8%-SiC or 2.5%-Al2O3 keeps the solar cell temperature below the maximum limit of 85 °C at Re of 50.

Fig. 7. Variation of the cell temperature uniformity with the Re numbers at (a) φp = 1%, (b) φp = 2%, (c) φp = 3%, and (d) φp = 4%. 238

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under lower values of ΔT to avoid the potential current mismatching problems as stated by (Bahaidarah, 2016; Royne and Dey, 2007). In Fig. 7, the maximum cell temperature differences, ΔT, is presented at different nanoparticle volume fractions, types, and Re numbers. Generally, it is observed that ΔT significantly decreases with Re number due to the increase in the heat transfer coefficient inside the heat sink with Re as discussed earlier. Further, at lower Re number of Re = 12.5 and higherφp of 4%, the significance of using nanofluid is observed over the use of pure water. For instance, using 4%-Al2O3 and SiC nanoparticle dispersed in water enhances the cell temperature uniformity to 17 °C and 15.9 °C, respectively compared with 19.8 °C for pure water. With further increase in the Re up to 250, slight effects of the nanoparticle types and volume fractions on the cell temperature uniformity are noticed. It may be attributed to the heat transfer rate from the cell layer reaching a saturation limit at higher Re as previously discussed and concluded by (Baloch et al., 2015).

y

1% nanoparticle volume fraction

4% nanoparticle volume fraction

Re=12.5

y

4.1.3. Local silicon layer temperature The local temperature distribution over the silicon layer is another important parameter especially for complex heat sink designs in order to allocate the hot spots. This parameter cannot be predicted in one or two-dimensional modeling. Therefore, it can be considered as a very essential outcome of this work. Therefore, the local solar cell temperature on a plane located at the mid-thickness of the silicon wafer is shown in Fig. 8. The local cell temperature is presented at Re of 12.5, 25, 50, and 250 for pure water, Al2O3-water and SiC-water nanofluids with nanoparticle volume fraction of 1% and 4%. Based on Fig. 8, it is remarked that increasing the nanoparticle loading from 0% to 1% and to 4% reduces the local cell temperature. This enhancement is considerable at lower Re and higher nanoparticle volume fraction. For instance, at Re of 12.5 and nanoparticle of 1%, the silicon layer temperature varies from 88 °C to 104 °C, from 87 °C to 103 °C, and from 86.6 °C to 100 °C in the case of using pure water, 1%

x

x y

Re=25

y

x

x

Fig. 8. Local cell temperature on a plane located at the mid-thickness of the silicon wafer where Re = 12.5, Re = 25, Re = 50, and Re = 250 and nanoparticle volume fraction of 1% and 4%. [pure water (continuous black line), Al2O3-water (blue dash line), and SiC-water nanofluid (dash-dot red line)]. 239

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y

Re=50

y

x

x y

Re=250

y

x

x

Fig. 8. (continued)

4.2. Effect of nanoparticles and coolant flow rates on the CPV/T-system performance

Al2O3-water, and SiC-water nanofluids, respectively. By increasing the nanoparticle volume fraction up to 4% at the same Re, the silicon layer temperature varies from 88 °C to 104 °C, from 84 °C to 100 °C, and from 83.7 °C to 96 °C using pure water, 4% Al2O3-water, and 4% SiC-water nanofluids, respectively. Increasing the Re up to 250 leads to insignificant enhancement in local cell temperature due to the use of nanofluids. The cell temperature varies from 81 °C to 82 °C, from 80.9 °C to 81.5 °C, and from 79.5 °C to 80.25 °C using pure water, 4% Al2O3-water, and 4% SiC-water nanofluids, respectively. This is most likely attributed to the effect of nanofluids is considerable at lower Re where the heat transfer is small (Ahmed and Eslamian, 2015). Consequently, the use of SiC-water nanofluid achieves a better cell operating temperature range compared with Al2O3-water nanofluid at the same Re and nanoparticle volume fraction.

In this section, the influences of the nanoparticle volume fraction, type, and flow Re number on the performance parameters such as solar cell power, CPV/T system net power, friction power, and electrical efficiency, system thermal efficiency are presented. 4.2.1. CPV/T system power variation Fig. 9 displays the variation of the CPV/T system friction power, cell electrical power and the net gained electric power with the flow Re number for pure water and 4% Al2O3-water and 4% SiC-water nanofluids. In Fig. 9a, the friction power increases with the increase of Re which leads to a significant increase in the pumping power. By increasing the nanoparticle volume fraction, the friction power increases, especially at higher Re. For instance, at Re = 50, the friction power reaches 0.104, 0.147, and 0.153 W for pure water, 4%Al2O3-water, and 240

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(a)

8

48

Psc 6

46 45

4%-SiC-Water 4%-Al2O3-Water

44

Pure water

4

43

2

42 41

Friction power, PFriction , (W)

Solar cell elelctical power, Psc , (W)

47

PFriction 0

50

100

150

200

250

0

300

Reynolds number, Re Fig. 9. Variation of (a) friction power and solar cell electrical power and (b) net gained electric power with the flow Re number for pure water and 4%Al2O3-water and 4%SiC-water nanofluid.

values of 12.5, 25, and 50, the net gained electric power increases with the increase in Re and the nanoparticle volume fraction. At Re = 12.5, the net gained power increased from 42 W to 42.9 W and 43.7 W for pure water, 4% Al2O3-water, and 4% SiC-water nanofluids, respectively. With further increase of Re to 50, the corresponding values of net gained electrical power are 45.5, 45.8, and 46.2 respectively. Second, at Re of 250, a slight difference between all coolant effects while the net power slightly increases with nanoparticle volume fraction of 1% and after that a decline in the net gained power is accomplished. To elucidate the reason for this trend, Table 6 shows the variation of friction power, solar cell power, and net gained the electrical power of the solar cell at Re of 250 with different nanoparticle volume fractions. Based on Table 6, at Re = 250, it is noticed that the friction power is much pronounced even with the use of pure water as a coolant medium. In addition, it is found that the solar cell power, Psc, increases by 0.2 W

4%SiC-water nanofluids respectively. By increasing the Re up to 250, the corresponding friction power reaches 2.79 W, 3.91, and 4.09 respectively. The increase of power with increasing nanoparticles volume fraction is due to the increase in the nanofluid viscosity and density with the nanoparticle inclusion. Further, the solar cell gained electric power is also affected by the variation of Re, nanoparticle loading, and nanoparticle type. At lower range of Re number from 12.5 up to 125, a significant increase in the cell electrical power with the increase in Re is found. With further increase in the Re from 125 to 250, a slight variation of the cell electrical power is observed. That is because the increase in Re is associated with significant reduction in the cell temperature up to the certain limit until the saturation cooling is attained. Therefore, increasing Re number increases the cell electrical power and the friction power. To evaluate the enhancement of using nanofluid with MCHS as a cooling technique for CPV systems, the net cell gained power is calculated and presented in Fig. 9b. The net gained electrical power is defined as the difference between the solar cell electric power and the friction power. Based on Fig. 9b, the net gained electric power increases up to a maximum value and then sharply decreases again. The value of Re at which the net gained electric power is maximum is defined as the critical Re number, Re-C, and it changes with the coolant type. The value of Re-C is about 80, 65, and 60 and the corresponding net gained cell electrical power are 45.7, 45.9, and 46.28 W for pure water, 4%Al2O3water and 4%SiC-water nanofluid, respectively. In addition, the results reveal that two different trends were found. Increasing the Re from 12.5 to Re-C leads to enhance the net gained power due to the large enhancement in the cell electrical power and small effect of the friction power. However, increasing the Re, from Re-C to 250, a substantial increase in the friction power associated with a slight increase in the electrical power is noticed where it causes a sharp decrease in the net gained power. Moreover, SiC-water nanofluid applications in CPV/T system proved a better performance compared with an Al2O3-water nanofluid and pure water over the investigated range of Re. On the lights of Fig. 9b, defining the operating point for the cooling system is essential which depends on the coolant type, Re, and CR as discussed in the author earlier work (Radwan et al., 2016; Radwan and Ahmed, 2017). The effect of Re, nanoparticle volume fraction and nanoparticle type on the net gained electric power is presented in Fig. 10. Two different trends are observed based on the figure. First, at lower Re number

Fig. 10. Variation of the net gained electric power with the nanoparticle volume fraction at different Re number. 241

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nanoparticle loading increases the cell electrical efficiency at the same Re. Moreover, SiC-water nanofluid is still preferred over Al2O3-water and pure water. The higher solar cell electrical efficiency is attained at the highest Re and maximum particle loading. For instance, at Re of 12.5, the cell electrical efficiency reaches a 13.4%, 13.7%, and 14% for pure water, 4%Al2O3-water, and 4%SiC-water nanofluids, respectively. Increasing the Re to Re-C values attains a maximum solar cell electric efficiency of 14.6%, 14.75% and 14.85% for pure water, 4%Al2O3water, and 4%SiC-water nanofluids, respectively. In the CPV/T system, the maximum achievement of the solar energy can be attained not only by enhancing the solar cell electrical efficiency but by using the dissipated heat as a low grade of thermal energy as well. Therefore, Fig. 13a, and b, displays the variation of CPV/T thermal efficiency with Re for 1% and 4% nanoparticle loading, respectively. Based on the Figs, increasing Re slightly enhances the thermal efficiency due to the high heat transfer rate associated with higher flowrate and low heat transfer loss from the top surface of the solar cell with higher Re. In addition, the use of nanofluid reduces the thermal efficiency in comparison with pure water. The reason is that the total net absorbed solar energy is converted to electrical energy, thermal gained energy, and energy lost from the solar cell surfaces. With using nanofluids, the electrical energy is higher than that of using water. Assuming a smaller amount of heat loss from the top of the solar cell results in a reduction of thermal efficiency with the use of nanofluid. This can be observed at lower Re of 12.5. At such value of Re, the solar cell electrical efficiency is significantly enhanced by the use of nanofluid. Therefore, a reduction in the thermal efficiency is attained by using nanofluids.

Table 6 Variation of Psc, Pfriction, and Pnet with φp and nanoparticle type at Re of 250. Fluid

φp

Psc

Pfriction

Pnet

Pure water

0%

46.540

2.796

43.744

Al2O3-water

1% 2% 3% 4%

46.618 46.655 46.692 46.707

2.857 2.966 3.396 3.913

43.761 43.528 43.296 42.793

SiC-water

1% 2% 3% 4%

46.710 46.686 46.746 47.046

2.894 3.121 3.517 4.092

43.816 43.565 43.229 42.954

and 0.3 W while increasing the nanoparticle loading from 0% to 4% for Al2O3 and SiC nanoparticles respectively. Increasing the nanoparticle loading by the same value increases the friction power by 0.6 W and 1.3 W for Al2O3 and SiC nanoparticles, respectively. In Fig. 11a, and b, the ratio of net gained electric power in the case of using nanofluid with specified volume fraction to the net gained electric power in the case of using pure water is shown for Al2O3-water and SiC-water nanofluid, respectively. Based on Fig. 11, SiC-water nanofluid attains a higher net power ratio compared to Al2O3-water nanofluid. In addition, it is noticed that at lower Re of 12.5, 25, and 50 the use of nanofluids enhances this ratio. However, increasing Re to 250 increases the friction factor and consequently reduces this ratio as discussed earlier in Table 6. For instance, at Re of 12.5, the net gained power ratio increases to 1.021 and 1.038 in the case of 4% Al2O3-water and 4%SiC-water nanofluids, respectively. However, increasing the Re to 250, and using nanofluid results in a negative effect on the net gained power ratio which reduces to 0.978 and 0.981 for 4%Al2O3-water and 4%SiC-water nanofluid respectively. This is attributed to the high friction power with using 4% nanoparticle loading at Re of 250 as presented in Table 6.

5. Conclusion A wide microchannel heat sink with nanofluids as coolant medium is proposed to cool the concentrator photovoltaic system. The influences of nanoparticle types, volume fractions, and coolant flow Reynolds numbers on the solar cell performance are investigated. Therefore, a comprehensive three-dimensional model that couples the two-phase (Eulerian-Eulerian) model of nanofluid flow in microchannel with the thermal model of the concentrator photovoltaic system is developed. In the light of the current results, some important findings can be stated.

4.2.2. CPV/T system efficiencies The variations of solar cell electrical efficiency versus Re number at 1% and 4% nanoparticle volume fractions are shown in Fig. 12a and b, respectively. As seen in the figures, increasing the Re number enhances the cell electrical efficiency due to the decrease in the cell temperature at the same incident solar irradiance. In addition, increasing the

Fig. 11. Variation of the net gained electric power ratio with the nanoparticle volume fraction at different Re number for (a) Al2O3-water and (b) SiC-water nanofluid. 242

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Fig. 12. Variation of CPV/T system electrical efficiency with Re at (a) φp = 1% and (b) φp = 4%.

Fig. 13. Variation of CPV/T system thermal efficiency with Re (a) φp = 1% and (b) φp = 4%.

• Using SiC-water nanofluids achieves a better cooling effect compared with Al O -water nanofluids. • Increasing of nanoparticles, volume fraction ratio remarkably aug2

• •

3

•

ments the thermal conductivity of the coolant and consequently reduces the solar cell temperature and enhances temperature uniformity and electrical efficiency. As the coolant flow Reynolds number increases up to a specific value, the net electrical power increases. With further increase of the Reynolds number, a reduction in the cell net gained power is observed due to the increase of friction effect. By using nanofluids, the reduction in maximum local solar cell

temperature is highly significant compared with water at low coolant flow Reynolds number. By using SiC-water nanofluids, the net gained solar cell electrical power is higher than that using Al2O3-water nanofluid at the same Reynolds number and nanoparticle volume fraction.

Acknowledgment The first author would like to thank the Ministry of Higher Education (MoHE)-Egypt for providing him with a fully funded Ph.D. scholarship to conduct this study.

Appendix A. Auxiliary equations used in the current model The drag force is calculated as follows:→

→

Fd = −β (Vl −Vp) where: β is the friction coefficient and it is calculated using the following correlation (Syamlal and Gidaspow, 1985).

β=

3 φl (1−φl ) → → Cd |Vl −Vp| ρl φl−2.65 4 dp

The drag coefficient Cd is calculated from the following relation (ANSYS FLUENT 14.5 Theory guide). 24

Cd =

0.687 ⎧ Rep (1 + 0.15Rep ) Rep < 1000 ⎨ 0.44 Rep⩾1000 ⎩

where: nanoparticle Reynolds number Rep is calculated from the following relation: →

Rep =

→

φl ρl |Vl −Vp| dp μl

Regarding the virtual mass force (Fvm) effect, it takes place when the nanoparticles accelerate relative to the base fluid (ANSYS FLUENT 14.5 Theory guide), and can be expressed by the following relation (Kalteh et al., 2011): 243

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Fvm = 0.5 φp ρl

D → → (Vl −Vp) Dt

where: D/Dt is the material derivative. The collision forces resulted from the particle-particle interaction is calculated according to the following relation (Kalteh et al., 2011). →

Fcol = ζ (φl ) ∇φl where: the value of ζ represents the particle–particle interaction module developed by (Bouillard et al., 1989) and given by the following correlation:

ζ (φ) = 1.0 exp (−600 [φl−0.376 ] ) 6(1−φl ) hp dp

hv =

where: hp is the fluid-particle heat transfer coefficient and it is calculated using empirical correlations (Kaguei and Wakao, 1983). Different empirical correlations are available to estimate the value of hp. In the present study, the Nusselt number is calculated using the following correlation (Kaguei and Wakao, 1983):

hp dp

Nup =

Kl

0.33 = 2 + 1.1Re0.6 p Prl

where: Prl is the Prandtl number for the base liquid. The effective thermal conductivity of the liquid phase and the particle phase is calculated according to the following relations (Kuipers et al., 1992):

( 1− 1−φl ) Kl

K eff , l =

φl

1−φl (ωA + [1−ω] Γ) Kl

K eff , p =

φp

The variables Г, A, and ω are calculated according to the following relations for spherical particles.

Γ=

⎧

2

(

B 1− A

B (A−1) A (B−1) B + 1 ⎫ ln ⎛ ⎞− − ⎨ A 1− B 2 ⎝ B ⎠ 1− B 2 ⎬ ⎪ A A ⎭ ⎩

) (

(

)

)

10

B = 1.25 ⎜⎛ ⎝ A=

Kp Kl

[1−φl ] ⎞ 9 ⎟ φl ⎠

and ω = 7.26 × 10−3

Some performance parameters such as CPV/T system thermal efficiency, solar CR, MCHS friction power, solar cell net power, MCHS pressure drop, coolant mass flowrate, flow Reynolds number, radiative and convective heat transfer coefficient, and sky temperature are presented here as follows:

ηth =

Pth G (t ) . Asc

CR =

G (t ) , Gref

Gref = 1000 W/m2

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

ΔP = f

lch ρin Vin 2 Dh 2

ṁ = ρin (Hch × Wch) × Vin

Re =

ρin Vin Dh μin

hrad, g − s =

σεg (Tg4−Ts4 ) (Tg−Ts )

hcon, g − a = 5.82 + 4.07 Vw

Ts = 0.0522 Ta1.5

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