Comparative Study of Active and Passive Cooling Techniques for Concentrated Photovoltaic Systems

CHAPTER

COMPARATIVE STUDY OF ACTIVE AND PASSIVE COOLING TECHNIQUES FOR CONCENTRATED PHOTOVOLTAIC SYSTEMS

2.15

Ali Radwan, Mohamed Emam, Mahmoud Ahmed
EgypteJapan University of Science and Technology (E-JUST), Alexandria, Egypt

1. INTRODUCTION Using concentrated sunlight on photovoltaic (PV) cells and replacing expensive solar cells with lowerpriced concentrating lenses or mirrors significantly lowers the cost of solar electricity. The efficiency of PV cells is 20% less than that of silicon solar cells and approximately 40% less than that of multijunction solar cells [1]. The remaining part of the absorbed solar energy is converted into heat, causing the temperature to rise in PV cells. This generated thermal energy in the PV systems causes junction damage and leads to a major decrease in the cells’ electrical efficiency [1,2]. Therefore, adapting an efficient cooling technique to CPV systems achieves higher electrical efficiency and allows for the design of higheconcentration ratio (CR) systems. Furthermore, the extracted thermal energy could be used for domestic or industrial applications. Major design considerations for the cooling of CPV cells are the cell temperature, the uniformity of temperature, the usability of thermal energy, reliability and simplicity, and consumed power [3]. Because CPV cells are temperature-sensitive devices, an efficient thermal management technology is becoming essential to provide high performance and increase PV cell lifetime. However, oldfashioned thermal management technologies such as large-scale liquid cooling systems have limited use because of the low rate of heat dissipation, complexity, and large consumption of manufacturing material. Therefore, it is essential to develop novel thermal management devices that dissipate large amounts of heat rapidly to keep these systems operating efficiently. Moreover, there are many ways to maintain or improve on the compactness of the design of such devices, using active or passive cooling techniques. In active cooling, external energy is required to cool the solar cells. Accordingly, a fraction of the electrical output power of the PV cell is consumed to circulate flow and overcome friction in the thermal absorber. On the other hand, active cooling is more easily controlled than passive cooling.


On leave from the Mechanical Engineering Department, Assiut University, Assiut 71,516, Egypt.

Exergetic, Energetic and Environmental Dimensions. http://dx.doi.org/10.1016/B978-0-12-813734-5.00027-5 Copyright © 2018 Elsevier Inc. All rights reserved.

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CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

Although active cooling might be cost-effective and less efficient owing to the consumption of a fraction of output energy, the heat dissipated from the PV cell can be used in other thermal applications [4]. Microchannels and impinging jets are promising options for the cooling technology of a CPV plant [5]. These small-scale devices are capable of dissipating a large amount of heat flux from hot surfaces [6]. These devices use effective, advanced technology to limit the temperature of high generated heat flux areas [7]. With regard to the use of a microchannel heat sink (MCHS) as an active cooling technique, several investigations have been carried out to study the use of wide microchannel heat sinks (WMCHS) as a simple design and compact cooling system for electronic device applications. Although WMCHS offer a significant heat transfer augmentation, they are associated with a loss in dramatic pressure. Consequently, alternative configurations have been proposed to decrease the incurred pressure loss and simultaneously increase heat transfer. One of those configurations is the manifold microchannel heat sink (MMCHS) [8]. The MMCHS consists of a manifold system that distributes the cooling fluid via multiple inleteoutlet ports. By reducing the flow length through microchannels, a significant reduction in pressure drop was attained. In addition, a decrease in thermal resistance might be achieved by interrupting the thermal boundary layers’ growth. This design was originally suggested by Harpole and Eninger [9], who confirmed a significant enhancement in the heat transfer coefficient relative to the conventional MCHS at a constant pumping power. Rahimi [10] experimentally studied the performance of the combination of microchannels and a PV module as a hybrid PV/thermal (T) system using water as a coolant. In their experiments, the microchannel hydraulic diameter was 0.667 mm and the Reynolds number (Re) varied up to 70. They reported that an approximately 30% increase in the output power compared with uncooled conditions. Based on numerical simulation, Reddy et al. [11] concluded that the optimum dimensions of the microchannel were 0.5 mm in width and an aspect ratio of 8. Moreover, the pressure drop was low in straight flow channels. Bladimir et al. [12] numerically calculated the pressure loss and temperature uniformity of the heated walls of different proposed microchannel configurations. They suggested a new design to achieve a smaller pressure drop and a better flow and temperature uniformity. They recommended using microchannel distributors to cool the CPV cells, fuel cells, and electronics. A two-dimensional (2D) model for CPV systems with an MCHS was developed by Radwan et al. [13,14]. Their study compared the conventional cooling technique and the MCHS technique using CPV systems operating up to CR ¼ 40. They concluded that using a microchannel cooling technique attained the ultimate possible reduction of solar cell temperature owing to the high heat transfer coefficient associated with microscale thermal absorbers. Another promising approach to regulate CPV systems thermally is to use a phase change material (PCM) as a cooling medium. Numerous studies were carried out to integrate PCMs within PV systems for thermal management [15]. The PCM absorbs a significant amount of thermal energy as latent heat during the solideliquid phase transition at a constant phase change temperature. Thus, the electric conversion efficiency increases by preventing overheating of CPV cells during the daytime and releasing it during the night. Browne et al. [16] presented a comprehensive review of PV thermal regulation using PCM as a heat sink. They indicated that although different configurations of PV-PCM systems were investigated, novel designed systems are still needed to overcome complications and enhance efficiency. In addition, Park et al. [17] compared the performance of a PV-PCM module installed on a vertical wall surface with that of a reference PV module without PCM under real outdoor climatic conditions. They concluded that the optimal melting temperature was 25 C regardless of the direction of installation,

2. PHYSICAL MODEL

477

whereas the optimal thickness of PCM varied slightly according to the direction in which the PV-PCM module was installed. In addition, electric power generation from the PV-PCM module increased by 1.0%e1.5% compared with that of the reference PV module without a PCM. Hasan et al. [18] investigated five different types of PCMs with a phase transition temperature of 25  4 C and the latent heat range between 140 and 213 kJ/kg. Experiments were carried out using four different cell-size PV-PCM systems at three different values of solar irradiance ranging from 500 to 1000 W/m2, and the ambient temperature was 20  1 C. Their results showed that using calcium chloride PCM in an aluminum-based PV-PCM system maintained a lower PV temperature for a prolonged period at 1000 W/m2, (up to 30 min at 18 C below the reference system and up to 5 h at 10 C below the reference system). Work by Hasan et al. [19] evaluated the PV-PCM system under different outdoor climatic conditions using calcium chloride hexahydrate CaCl2e6H2O or eutectic of cupric-palmitic acid. They concluded that both systems achieved a higher temperature drop and more power savings compared with the reference PV without the PCM. One main obstructions for PCM applications is the low thermal conductivity of such materials. Therefore, different techniques have been used to increase the thermal performance of PCMs in thermal energy storage and thermal management systems. Fan et al. [20] presented a comprehensive review of experimental and computational investigations to improve the thermal conductivity of PCM for latent thermal energy storage. Moreover, Zhang et al. [21] reviewed and explained advances in the investigation, fabrication, and characterization of composite PCMs along with mathematical models describing the phase change heat transfer characteristics. The insertion of metal fins inside PCM containers is the technique most widely adopted for the thermal regulation of PV cells. Huang et al. [22,23] investigated the effect of fin spacing, width, and fin type on PV-PCM system performance. They noticed that the insertion of fins improved the effective thermal conductivity of PCMs and enhanced the thermal performance of the PV-PCM system. Because the fin spacing was reduced, the maximum temperature was decreased and uniformity of temperature of the PV cells was achieved. However, drawbacks were apparent in that the fins constituted barriers to the liquid PCM movement. Thus, the possibility of convective heat transfer in the molten PCM may have been reduced. Enhancement in conduction within a PCM should balance the suppression of natural convection. In addition, period of thermal regulation decreases as the volume of the PCM is replaced by the metal mass of fins. Based on a survey of the literature, it is clear that a comparison of active and passive thermal management techniques for CPV systems has not been sufficiently investigated. Therefore, the objective of the current chapter was to investigate the performance of the CPV system incorporated with MCHS and PCM in a numerical manner. In the MCHS, the conventional design of WMCH was compared with a new MCHS design as an option to reduce the friction power that is consumed. On the other hand, with the PCM cooling technique, insertion of metal fins inside the PCM to improve thermal conductivity is proposed. Accordingly, a comprehensive 2D model of CPV layers integrated with a proposed heat sink was developed and numerically simulated. The model couples a thermal model for CPV layers and the governing equations of cooling mediums. The current results may provide detailed guidance for the industrial field about the limitations and benefits of each cooling technique.

2. PHYSICAL MODEL In the current chapter, a CPV system combined with active and passive cooling techniques was developed. The active cooling technique was accomplished using the MMCHS design and compared

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CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

with the conventional WMCHS design. The passive cooling technique was attained using a PCM heat sink. Moreover, the effect of incorporating fins in the PCM domain was compared with the conventional rectangular cavity containing the PCM. The investigated solar cell was taken to be a generic polycrystalline cell as characterized by Sandia National Laboratory. The solar cell included various layers, depending on the manufacturing technology used. These layers include a glass cover, an antireflective coating (ARC), silicon layer, an ethylene vinyl acetate (EVA) layer, and a tedlar polyester tedlar (TPT) layer. The 3.0-mm glass cover was made of tempered glass with high transparency. An ARC layer with a thickness of 0.0001 mm (100 nm) was used to limit the reflection of incoming radiation. In addition, a silicon wafer 0.2 mm thick was used in these panels, which were responsible for producing electricity [24]. The silicon layer was embedded in the transparent encapsulation EVA layer, with a thickness of 0.5 mm above and below the silicon layer to fix it and provide both electrical isolation and moisture resistance. Moreover, the TPT polymer layer was a photo-stable layer 0.3 mm thick, made of polyvinyl fluoride. That layer provided additional insulation and moisture protection for the silicon layer [25]. The solar cell length was 12.5 cm. In active cooling, a compact MCHS was attached to the back surface of the TPT layer. It was made of high thermal conductive aluminum and was recommended because it was economical compared with the use of copper for the same thermal regulation of CPV systems [26]. Water was used as a coolant because of its effective properties, because it could accomplish a higher thermal performance for PVeT systems compared with air in PVeT systems [27]. However, to ensure better temperature uniformity and lower friction power, the MMCHS design was proposed to replace the conventional WMCHS design in the CPV systems. The manifold distribution system was placed on the bottom of the flat microchannel in a direction transverse to the main direction of flow. The coolant was pumped in through a common inlet header that branched out into parallel manifold inlet channels. Upon entering the microchannel, the fluid underwent a 90-degrees turn and passed through the microchannel midpitch distance (P/2), removing the generated heat from the concentrated solar cell. Subsequently, it flowed through another 90-degree turn and then exited downward through the outlet manifold channels. Another common outlet header was used to collect the outlet flow rate. The complete layers of the CPV system integrated with the proposed MCHS design are presented in Fig. 1A and B for the WMCHS and MMCHS designs, respectively. In the heat sinks, the thermophysical properties the optical properties of the solar cell layers are presented in Tables 1 and 2, respectively. For the passive cooling technique, a schematic diagram of the hybrid CPVePCM system considered in the current work is presented in Fig. 1C. As shown in the figure, the PCM was placed between two aluminum flat plates and then attached to the rear side of the CPV cell. The aluminum front/back walls, which were 3 mm thick, were included to achieve uniform temperature distribution over the front surface of the system. Moreover, they protected the PCM and provided a high rate of heat transfer during both melting and solidification. This was enhanced by a series of aluminum fins 3 mm thick extending into the PCM from the front wall. The interior dimensions of the container were 125 mm in height by 150 mm in depth. The main criterion for selecting a suitable PCM for a particular application was its phase transition temperature, which should be close to the PV standard operating temperature of 25 C. Other relevant parameters included high values of thermal conductivity and latent heat; the stability of the cycling heat process also must be taken into account to reach an appropriate decision [28]. In the current work, the selected PCM was salt hydrate CaCl2$6H2O. The thermophysical properties of both the PCMs and aluminum are shown in Table 3.

2. PHYSICAL MODEL

(A)

479

Net concentrated solar flux Glass Top EVA

δg δEVA

δsc

Silicon layer Lower EVA

δt δw

Channel wall

Inlet

Tedlar

Outlet

H Net concentrated solar flux

(B) δg δEVA

δsc

δt δw P

H

Outlet

Inlet Adiabatic

(C)

3 mm

PCM

H = 125 mm

Net concentrated solar flux

δ = 3 mm

δPCM = 150 mm Glass Top EVA

Silicon

Tedlar

Aluminum

FIGURE 1 Computational domain for (A) wide microchannel heat sinkeconcentrated photovoltaic (CPV) system, (B) manifold microchannel heat sinkeCPV system, and (C) phase change material (PCM)eCPV system. EVA, ethylene vinyl acetate.

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CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

Table 1 PhotovoltaiceThermal Layer Physical Properties [24] Layer Glass (Cover) Antireflective coating Encapsulation (ethylene vinyl acetate) Silicon Tedlar Aluminum channel

Density (kg/m3)

Specific Heat (J/kg K)

Thermal Conductivity (W/m K)

Thickness (mm)

2 32

3 0.01

3000 2400

500 691

960

2090

0.311

0.5

2330 1200 2719

677 1250 871

130 0.15 202.4

0.2 0.3 0.2

Table 2 Optical Properties of Each Layer Material

Reflectivity

Absorptivity (a)

Transmissivity

Emissivity

Glass cover Ethylene vinyl acetate layer Silicon layer Back sheet

0.04 0.02

0.04 0.08

0.92 0.90

0.85

0.08 0.86

0.90 0.128

0.02 0.012

0.9

Table 3 Thermophysical Properties of Selected Phase Change Material (PCMs) and Aluminum Microchannel Walls and PCM Cavity [18] Thermophysical Properties

CaCl2e6H2O (PCM)

Aluminum

Melting point, ( C) Heat of fusion, (kJ/kg) Thermal conductivity Solid (W/m  C) Liquid (W/m  C) Density Solid (kg/m3) Liquid (kg/m3) Specific heat capacity Solid (kJ/kg K) Liquid (kJ/kg K) Thermal expansion coefficient (k1) Thermal cyclic stability Chemical classification

29.8 191

N/A N/A

1.08 0.56

211 N/A

1710 1560

2675 N/A

1.4 2.1 0.0005 Yes [51] Salt hydrate

0.903 N/A N/A e e

N/A, not applicable.

3. MATHEMATICAL MODEL

481

3. MATHEMATICAL MODEL A 2D solidefluid conjugate heat transfer model, including different layers of the PV cell, was developed to estimate the electrical and thermal performance of the CPV/T system. The overall CPV/T system involved multiple solid domains and fluid domains. In the currently developed solidefluid conjugate heat transfer model, the following assumptions were adopted: 1. Solar cell optical and physical properties were isotropic and temperature was independent. 2. Thermal contact resistances among each layer of the solar cell and heat sinks were negligible. 3. The flow in the MCHS was laminar, incompressible, and steady-state. However, in the PCM liquid phase it was assumed to be incompressible, Newtonian, and unsteady. 4. The water’s thermophysical properties were temperature dependent.

3.1 PHOTOVOLTAIC MODULE LAYERS The heat conduction equation in the Cartesian coordinates system for each solid layer can be represented as [29]:

 v vT v vT (1) k þ k þ qi ¼ 0 and i ¼ 1; 2; .6 vx vx vy vy where the variable ki represents the thermal conductivity of the layer i and the term qi characterizes the heat generation in the layer i owing to the absorption of solar radiation. In this work, the value of i changed from 1 to 6 for glass, upper EVA, ARC, silicon, lower EVA, and tedlar layers, respectively. The heat generation per unit volume of the layer caused by solar irradiance absorption of the CPV cell layers can be determined using the equation as reported in Zhou et al [30]: qi ¼

ð1  hsc ÞGai sj Ai Vi

(2)

where qi is the heat generation per unit volume in layer i; hsc is the solar cell electric efficiency, whose value changes to 0 when the internal heat generation of other layers is calculated; ai, Ai, and Vi are the absorptivity, area, and volume of layer i, respectively; and sj is the net transmissivity of layers above layer i. Solar energy absorbed by all layers was taken into consideration to simulate the actual situation. In addition, solar irradiance absorption of layers located in the interval between each cell and neighboring cells was taken into account. The silicon layer efficiency was calculated using the equation [1,31]: hsc ¼ href ð1  bref ðTsc  Tref ÞÞ

(3)

where href and bref are the solar cell efficiency and temperature coefficient at a reference temperature of Tref ¼ 25 C, respectively. These values are provided by the manufacturer data sheet for most solar cells. bref is taken to be 0.0045K1 for polycrystalline silicon [32].

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CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

3.2 MICROCHANNEL HEAT SINK DOMAIN For a microchannel substrate, the heat conduction equation in a Cartesian coordinate system without heat generation can be written as:

  v vTch v vTch kch kch þ ¼0 (4) vx vy vx vy For MCHS, the continuity, momentum and energy equations of laminar, incompressible, and steady flow can be written in a Cartesian coordinates system as [33]: For the continuity equation: vðruÞ vðrvÞ þ ¼0 vx vy

(5)

For the momentum equations:



 vðruÞ vðruÞ vP v vu v vu þv ¼ þ m þ m vx vy vx vx vx vy vy

 vðrvÞ vðrvÞ vP v vv v vv þv ¼ þ m þ m u vx vy vy vx vx vy vy

u

(6) (7)

For the energy equation:



 vðrCuTÞ vðrCvTÞ v vT v vT þ ¼ Kl þ Kl vx vy vx vx vy vy

(8)

where u, v, p, m, r, Cf, kf, and Tf are the velocity components in the x and y directions, pressure, fluid viscosity, density, specific heat, thermal conductivity, and temperature, respectively. Because of substantial changes in water properties inside the microchannel, especially at higher CR values, the variation in water’s thermophysical properties with changes in temperature is considered using higherordered polynomial equations presented in Jayakumar et al. [34].

3.3 PHASE CHANGE MATERIAL HEAT SINK DOMAIN The enthalpy-porosity technique is used to model the PCM. In this technique, the liquidesolid interface is not explicitly tracked. Instead, the presence of the solid or liquid phase is monitored using a quantity known as a liquid fraction (l). The liquid phase of PCM is assumed to be incompressible, Newtonian, and unsteady. The liquid PCM density variation in the buoyancy term is modeled by the Boussinesq approximation to involve thermal buoyancy. Accordingly, the governing equations for the 2D transient analysis of PCM during melting, including buoyancy-driven convection, are written as [35,36]: For the continuity equation: vðruÞ vðrvÞ þ ¼0 vx vy

(9)

For the momentum equations:
2  vu vu vu vP v u v2 u r þ ru þ rv ¼  þ m þ þ Sx vt vx vy vx vx2 vy2

(10)

3. MATHEMATICAL MODEL


2  vv vv vv vP v v v2 v ! r þ ru þ rv ¼  þ m þ þ FB þ Sy vt vx vy vy vx2 vy2

483

(11)

where r is the density; u and v are the velocities of the liquid PCM in the x and y directions, respectively; P is the pressure; m is the dynamic viscosity; and FB is a buoyancy force given by the Boussinesq approximation as presented in Appendix A. The energy equation for melt is:
2  vH vH vH v T v2 T þ rl u þ rl v ¼ kl rl þ (12) vt vx vy vx2 vy2 The energy equation for solid is:
2  vH v T v2 T ¼ ks þ rs vt vx2 vy2

(13)

The enthalpy of the material, H, is computed as the sum of the sensible enthalpy, h, and the latent heat, as presented in Appendix A.

3.4 BOUNDARY CONDITIONS To solve the governing equations, the boundary conditions must be identified. First, for the PV layers, the thermal boundary condition for the upper wall of the glass layer is that it is subjected to convection and radiation heat loss. In this case, the convective heat transfer coefficient, ambient temperature, surface external emissivity, and external radiation temperature should be applied accurately, whereas 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 [30]. The side walls of the computational domain are assumed to be adiabatic owing to their symmetry. Second, for the CPV with MCHS, 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. The fluid inlet velocity component normal to the inlet section is identified and assumed to be uniform. In the meantime, the 0-gauge pressure is identified as boundary conditions at the MCHS outlet section. No-slip and no-temperature jump boundary conditions are considered at the interface between the solidefluid domains because the Knudsen number falls in the no-slip regime (Kn < 0.001) [37]. Furthermore, the maximum channel flow Re is estimated to be within the laminar flow regime (i.e., Rein < 2200) [38]. The channel inlet temperature is assumed to be uniform at 30 C. Third, for the CPV with PCM heat sink (initially t ¼ 0), the system contains a solid PCM maintained at a temperature (Tini) lower than the melting temperature (Tm) of the employed PCMs and equal to 25 C. Furthermore, no-slip boundary conditions are taken at the solidefluid interfaces. However, for all existing solidesolid interfaces, a thermally coupled boundary condition is applied. In addition, the adiabatic boundary condition is applied on the upper and lower ends of the CPVePCM system, as presented in Fig. 1C. For the front surface of the CPV cell, the thermal boundary condition is combined with convection and radiation loss. The exterior back boundary is subjected to a convective heat loss for the CPVePCM system, and convection and radiation loss for the CPV system without PCM. The convective heat transfer coefficient from the glass cover to the atmosphere, from the exterior back to the ambient, and from radiation from the top glass to the sky are presented in Appendix A.

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CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

3.5 SOLUTION METHODS AND CONVERGENCE CRITERIA The developed comprehensive thermal model for PV layers, coupled with the heat sinks either using MCHS or PCM, was numerically simulated to determine the solar cell temperature and consequently the performance parameters. The solution steps commenced by estimating an initial value of electrical efficiency (href ¼ 0.2). Then the corresponding internal heat generation for the silicon layer was determined using Eq. (2) and the heat generation for other PV layers in the cell part and the interval part were also calculated. The model governing equations were solved and the new solar cell temperature was obtained. The iteration procedure was repeated until the error between the two consequent solar cell temperatures reached 103 and the maximum residuals in the solution of conjugate heat transfer equations was less than 106. Therefore, parallel computing was implemented using a Dell Precision T7500 workstation with a 3.75-GH Intel Xeon processor, 48 core, and 64-MB installed memory. The SIMPLE algorithm was used to solve pressureevelocity coupling equations. The second-order upwind scheme was used to solve momentum and energy equations. For the PCM domain, the PREssure STaggering Option scheme was adopted for the pressure correction equation. Furthermore, for every heat sink design, a grid independence test was conducted using several mesh sizes to ensure that results did not change with a further increase in the number of elements. In addition, the model was validated by comparison with available experimental and numerical data.

3.6 NUMERICAL RESULTS VALIDATION The current model was validated using different sets of available experimental and numerical results. The first set was used to validate the uncooled solar cell model with available experimental results [18] and numerical results presented in Zhou et al. [30]. In this part, the iterative technique for Eqs. (1)e(3) was applied for all layers of the solar cell. The second set of results was used to validate heat transfer characteristics in MCHSs for both WMCHS and MMCHS configurations with the available experiments [6] and numerical results using Lattice Boltzmann method (LBM) [28] for WMCHS and using the experimental results of Choue et al. [39] and the numerical results of Zhou et al. [40] for MMCHS at different values of Reynolds numbers. The final set of results were used to validate the PCM domain by comparing the average predicted and measured temperatures on the front surface of the system versus the time available in Huang et al. [23], and with the numerical computations of Huan et al. [41]. Finally, the PVePCM system was validated by comparison with the average predicted PV cell temperature versus time with the measured results of Hasan et al. [18].

3.6.1 Uncooled Concentrated Photovoltaic System Validation Firstly, the uncooled CPV model was validated by comparing the average predicted solar cell temperature versus time with the measurements of Hasan et al. [18] in Fig. 2A. Moreover, the predicted difference between the maximum solar cell temperature and the ambient temperature (DT) was compared with the numerically calculated difference in Zhou et al. [30] at various operating conditions, as presented in Fig. 2B. The solar radiation changed from 300 to 1000 W/m2 and the ambient temperature varied from 10 to 40 C with a wind speed of 1.0 m/s, as shown in Fig. 2. Excellent agreement was found between the current predicted results and those available in Hasan et al. [18] and Zhou et al. [30].

3. MATHEMATICAL MODEL

485

FIGURE 2 Uncooled photovoltaic (PV) model validation with (A) the experimental results of Hasan et al. [18], and (B) the numerical results [30]. EVA, ethylene vinyl acetate.

3.6.2 Microchannel Heat Sink Validation To validate the current results with the experimental results, Fig. 3 compares the predicted values (current study) and experimental values of the Nusselt number published in Kalteh et al. [6]. The same dimensions, boundary conditions, and fluid properties were applied for fair comparison. In their study, a wide microchannel with a length of 94.3 mm, width of 28.1 mm, and height of 0.580 mm was studied. The microchannel heat sink was heated from the bottom at constant heat flux (20.5 kW/m2), where the Re varied from 70 to 300. Comparison between measured and predicted values showed good agreement with a maximum relative error of about 4.4%. This value of error may be attributed to experimental data uncertainties and the absence of details about the measured values. To validate the predicted results further, the current CFD results were compared with the numerical results using the LBM [42] in Fig. 3A. To validate the fluid flow characteristics in WMCHS, the friction factor was validated with the analytical results of the fully developed laminar flow friction characteristics presented in Rohsenow and Hartnett [43] in the case of the wide microchannel. Excellent agreement was obtained between the predicted friction factor and the analytical results. Furthermore, the heat transfer characteristics in MMCHS were validated with the available numerical results of Manca et al. [40] in Fig. 3B. Excellent agreement was obtained. Consequently, the current CFD solution methodology was able to predict the heat transfer and friction characteristics of the investigated MCHS designs.

3.6.3 Phase Change Material Heat Sink Validation For the transient simulation of PCM model validation, the predicted results were validated with the available experimental data of Huang et al. [23] by comparing the average predicted and measured temperatures on the front surface of the system versus time, as shown in Fig. 4A. The incident solar

486

CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

FIGURE 3 Comparison of predicted results with (A) measured results of [6] and numerical using Lattice Boltzmann method (LBM) [42]. (B) Numerical results of Manca et al. [40] and experimental results [39]. Nu, Nusselt number; Re, Reynolds number.

FIGURE 4 Comparison between predicted average temperature on front surface with (A) measured results of Huang et al. [23] and (B) numerical results of Huang et al. [41]. PCM, phase change material.

4. RESULTS AND DISCUSSION

487

irradiance and ambient temperature used were 750 W/m2 and 19 C, respectively. The top, bottom, and back surfaces were assumed to be adiabatic. Comparison indicated that good agreement was obtained between the current computational results and the experiments, with a maximum difference of about 2 C. Moreover, the computational results were compared with the available numerical results of Huang et al. [41], as shown in Fig. 4B for an ambient temperature of 20 C, and an incident solar irradiance of 1000 W/m2. Good agreement was shown between the predicted and the numerical results, with a maximum difference of about 4 C.

4. RESULTS AND DISCUSSION This section is divided into three subsections. The first one the performance of a CPV cell cooled with the investigated MCHS designs. The second subsection demonstrates the performance of the CPV system cooled with a PCM heat sink. Finally, the third subsection compares the active and passive cooling techniques. The comparison is based on the average solar cell temperature, temperature uniformity, electric efficiency, solar cell net gained electric power, and the CPV system’s thermal efficiency.

4.1 ACTIVE COOLING TECHNIQUE USING MICROCHANNEL HEAT SINK In the current section, the effect of jet pitch (P) in the MMCHS was investigated to determine the most efficient pitch value for the field of CPV systems. Then the appropriate pitch value was selected for comparison with the conventional WMCHS design at different operation parameters such as coolant flow rate and solar concentration ratio. The comparison was implemented by calculating the average solar cell temperature, temperature uniformity, and net gained electrical power.

4.1.1 Effect of Manifold Pitch Different values of the manifold pitch (P) are investigated. In case A, the distance between the two consecutive inlet ports was 1.25 mm and the computational domain length was 125 mm. Thus a total of 100 inlet ports for one solar cell was designed in this case. Similarly, in the case of B, and C, the pitch values were 2.5 and 5 mm, which gives 50 and 25 total inlet ports, respectively, for one cell. The same total mass flow rate was used for each case and the CR was selected to be 20 where the maximum temperature occurred. The comparison between the investigated pitches was implemented based on the average solar cell temperature, coolant outlet temperature, and consumed pumping power. The variations in the average solar cell temperature influenced by the cooling fluid mass flow rate at the investigated different pitch values is presented in Table 4. Generally, increasing the cooling mass flow rate led to a reduction in the solar cell temperature. This trend was observed by several researchers [44e46]. There are different hypotheses to interpret this trend. It is reported that at a lower Re, the heat transfer mechanism between the upper wall and the cooling fluid was dominated by convection, whereas at a higher Re, the heat transfer mechanism was dominated by conduction within the thin layer of the laminar wall region [46]. Another point of view relates this trend to the reduction of contact time between the fluid and the upper wall owing to the higher velocity associated with a higher flow rate [44]. The last interpretation is that at a high Re, the heat extracted by the cooling water reached the saturated level, and therefore the cell temperature slightly increased [45]. Furthermore, decreasing the

488

CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

_ at Different Pitch Values Table 4 Variations in Average Solar Cell Temperature With m Pitch (mm)

m_ [ 50 g=min

m_ [ 100 g=min

m_ [ 200 g=min

m_ [ 400 g=min

m_ [ 800 g=min

m_ [ 1000 g=min

m_ [ 2020 g=min

(A) P ¼ 1.25 (B) P ¼ 2.5 (C) P ¼ 5

111.01 125.49 136.05

103.6 109.07 110.53

95.1 95.88 95.7

88.44 88.39 88.18

84.75 84.67 84.54

84.04 83.97 83.86

82.72 82.67 82.62

pitch reduced the solar cell temperature, especially at lower flow rates. This may be attributed to the reduction in the fluid pass under the heated CPV cell. Consequently, the flow might have been in the entrance region. The heat transfer in the entrance region was significantly higher than that in the fully developed regime. This might have caused a greater reduction in the solar cell temperature, as shown in the case of the lowest pitch (A). The solar cell temperature dropped from 136 to 111 C with a decrease in the pitch from 5 to 1.25 mm at the same lowest total cooling mass flow rate of 50 g/min and a solar concentration ratio of 20. In addition, a further increase in the mass flow rate beyond 800 g/min led to no significant effect of pitch value on the solar cell temperature. The reason for this lack of effect _ the heat transfer coefficient reached a sufficient value for it to be essential for was that at a higher m, heat removal from the back side of the solar cell regardless of the configuration. The maximum permissible solar cell temperature was 85 C; consequently, all investigated pitches attained the same maximum allowable temperature at the same coolant flow rate close to 800 g/min. Hence it is recommended that the higher pitch value be selected, because it is also the simplest and easiest to manufacture.

4.1.2 Average Solar Cell Temperature Comparison Conventional WMCHS was compared with MMCHS with P ¼ 5 mm. Fig. 5A and B shows the variations in the average solar cell temperature versus the cooling fluid mass flow rate for WMCHS and MMCH, respectively. Generally, increasing the cooling fluid mass flow rate led to an enhancement of the average solar cell temperature up to a certain limit. A further increase in the mass flow rate beyond this limit attained only a slight enhancement in the solar cell temperature. In addition, increasing the solar concentration ratio led to a significant increase in the solar cell temperature caused by a rise in the absorbed solar irradiance. In a comparison of Fig. 5A and B, it is apparent that MMCHS with P ¼ 5 mm achieved a higher average solar cell temperature, especially at lower mass flow rates; however, by increasing the mass flow rates, both configurations achieved a relatively equal solar cell temperature. The reason for this trend is that at a lower mass flow rate, the heat transfer coefficient for MMCHS was smaller than that of WMCHS. The heat transfer coefficient in the MMCHS was small enough to dissipate the required heat. However, at a higher mass flow rate, the heat transfer coefficient for both configurations exceeded the optimal necessary value to limit the cell temperature below the optimum operating temperature. Therefore, at CR ¼ 15 and 20, it is recommended to use the WMCH with m_ > 60 and m_ > 350 g=min, respectively, to limit the CPV system temperature without causing possible damage to its components. CPV systems can safely operate when they are combined with MMCHS, with m_ > 120 and m_ > 550 g=min at CR ¼ 15 and 20, respectively.

4. RESULTS AND DISCUSSION

489

FIGURE 5 Variations in average solar cell temperature with the cooling mass flow rate at various concentrations ratios (CR) for (A) wide microchannel heat sink (WMCHS) and (B) manifold microchannel heat sink (MMCHS) with P ¼ 5 mm.

4.1.3 Local Solar Cell Temperature Comparison Because the main purpose of this study was to provide a reliable and efficient cooling system, calculation of solar cell temperature uniformity is vitally important. However, the effect of temperature uniformity on CPV cells’ durability and efficiency was examined in few studies. These studies concluded that cell efficiency declined as a result of the cell’s nonuniform temperature distribution. It was found that cell temperature nonuniformity caused a reverse saturation current [47]. Moreover, thermal expansion depended on the local cell temperature. Consequently, CPV cells’ temperature nonuniformity implies mechanical stress and reduces the lifetime of the solar cell. A comparison of solar cell temperature uniformity is presented in Fig. 6AeC at mass flow rates of 50, 800, and 2020 g/min, respectively, and CRs of both 5 and 20. Generally, the local solar cell temperature increased with the axial distance for WMCHS, whereas for the MMCHS, the local solar cell temperature was nearly constant along the solar cell length. For instance, at m_ ¼ 50 g=min, the difference between the maximum local solar cell temperature and the lower local solar cell temperature for the WMCHS was about 11.3 and 46.8 C at CR ¼ 5 and 20, respectively. However, in the case of MMCHS, the maximum local solar cell temperature difference was about 1.1 C and 4.02 C at CR ¼ 5 and 20, respectively, at the same total coolant flow rate of 50 g/min. In Table 5, the difference between the maximum and minimum local silicon layer temperature (DT ¼ Tsc,max  Tsc,min) is presented at CR ¼ 5 and CR ¼ 20 and various values of m. Generally, increasing m decreased the temperature degradation in the silicon layer, and it was much smaller in the MMCHS compared with the conventional WMCHS. For example, at CR ¼ 20, where the temperature uniformity was crucial, the MMCHS attained a temperature uniformity of 4.02, 0.365, and 0.125 C at m_ of 50, 800, and 2020 g/min, respectively. However, the WMCHS achieved a maximum temperature difference of 46.8, 3.13, and 1.44 C at these total coolant mass flow rates.

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CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

FIGURE 6 Variations in local solar cell temperature with axial distance at cooling fluid mass flow rate of (A) 50 g/min (B) 800 g/min, and (C) 2020 g/min. CR, concentration ratio; MMCHS, manifold microchannel heat sink; WMCHS, wide microchannel heat sink.

4.1.4 Net Gained Electrical Power Comparison Use of an MCHS will significantly increase friction power loss owing to its small size. It is clear that for both configurations that were investigated, the friction power increased with the flow rates whereas the solar cell power increased until it reached a nearly constant value. A further increase in the cooling

4. RESULTS AND DISCUSSION

491

Table 5 Variations in Silicon Layer Temperature Uniformity (DT [ Tsc,min L Tsc,min) at _ for Investigated Configurations CR [ 5 and 20 and Various m CR [ 5

m_ ¼ 50 g=min m_ ¼ 800 g=min m_ ¼ 2020 g=min

CR [ 20

WMCHS

MMCHS

WMCHS

MMCHS

11.3 0.76 0.35

1.1 0.1 0.03

46.8 3.13 1.44

4.02 0.365 0.125

CR, concentration ratio; MMHCS, manifold microchannel heat sink; WMHCS, wide microchannel heat sink.

fluid mass flow rate led to a significant rise in the friction power while maintaining the solar cell power as a constant value. Therefore, the net power, which is defined as the difference between the solar cell electric power and the friction power, will first increase and then decrease again. The same trend was observed in Xu and Kleinstreuer [46] and was explained in detail in earlier studies [13,14]. In comparing the friction characteristics of both configurations, it is interesting that the MMCHS _ This was because consumed a lower friction power compared with the WMCHS at the same CR and m. of the distribution of coolant mass rate over large jets, which decreased the velocity in each channel below the cell; because the friction factor was proportional to the squared fluid velocity, the friction factor decreased dramatically in the MMCHS. The pumping power can be neglected compared with the WMCHS at the same m, as presented in Table 6. Moreover, it can be concluded that increasing CR caused a slight variation in the friction power that was affected by the variation in the cooling fluid thermophysical properties with CR. A comparison of the net gained electric power (Pnet ¼ Pel  Pf) for the CPV systems integrated with the MMCHS and WMCHS is presented in Fig. 7A and B for CR ¼ 5 and 20, respectively. For MMCHS, the net gained power increased with an increase in the cooling fluid mass flow rate and then remained unchanged with the coolant flow rate. This was attributed to the lower pumping power consumed with this configuration along with an increase in the coolant flow rate. However, in the case of WMCHS, the net CPV cells’ output power (Pnet) increased until it reached a maximum value, and _ at CR [ 5 and 20 for Investigated Table 6 Variations in Friction Power With m Configurations Wide Manifold Microchannel Heat Sink

Manifold Microchannel Heat Sink

_ (g/min) m

CR [ 5

CR [ 20

CR [ 5

CR [ 20

50 800 2020

0.0063 1.8443 11.6427

0.0046 1.7885 11.483

2.6E-06 8.6E-04 5.5E-03

1.7E-06 8.2E-04 5.4E-03

CR, concentration ratio.

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CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

FIGURE 7 Variation of the solar cell electric power versus the cooling fluid mass flow rate for MMCHS and WMCHS at (A) CR ¼ 5 and (B) CR ¼ 20.

then it significantly decreased again. This was caused by an increase in the coolant flow rate, which caused a significant increase in the gained solar cell electrical power up to a certain limit. The friction power in WMCHS dramatically increased with an increase in the flow rate. Consequently, the net gained electric power increased up to a certain limit and then significantly decreased again. This trend was in good agreement with the experimental results of Baloch et al. [44] and the numerical results of Xu and Kleinstreuer [46]. By comparing both investigated MCHS configurations, it was found that the solar cell net power integrated with the MMCHS was greater than that for WMCHS, especially at a higher mass flow rate, as shown in Fig. 7. This was because both investigated configurations attained the same cell temperature at higher m, whereas the MMCHS consumed a lower friction power at higher m. Furthermore, the coolant flow rate of 800 g/min was appropriate to achieve the safe operation of the silicon layer below 85 C; hence the MMCHS with P ¼ 5 mm was more appropriate because it achieved a temperature requirement with a higher net power. In more detail, at CR ¼ 20 and m_ ¼ 800 g=min, the net gained electric power for the investigated cell area of 12.5  12.5 cm2 was 39.6 and 41.1 W using WMCHS and MMCHS, respectively.

4.2 PASSIVE COOLING TECHNIQUE USING PHASE CHANGE MATERIAL In the current section, two major sets of numerical simulation tests were carried out. The first set of numerical simulations was performed to study the thermal behavior of the CPVePCM system without fins using salt hydrate CaCl2$6H2O (PCM). The second set of numerical simulations was carried out to examine the effects of the insertion of a different number of aluminum fins on the thermal regulation of the CPVePCM system.

4. RESULTS AND DISCUSSION

493

4.2.1 Thermal Performance of the Concentrated PhotovoltaicePhase Change Material System Without Fins Thermal regulation of the CPVePCM system depends on the thermal behavior of the PCM during melting. The transient variations in the average solar cell temperature of the nonfinned CPVePCM system with 15-mm thick PCM and CR ¼ 5 are presented in Fig. 8. The same figure presents the temperature variations with elapsed time along the height at the center of the nonfinned CPVePCM system (location points A, B, and C) (Fig. 8) as well as the time evolution of the liquidesolid interface of the PCM during the melting process. Based on the figure, using PCM salt hydrate CaCl2$6H2O with a melting point of 29.8 C, the CPVePCM without fins could maintain the solar cell at an average temperature of 70 C for 390 min whereas the temperature at the complete melting point of PCM was around 88 C. Based on the figure, generally three stages of temperature variation for solar cells are associated with the phase change process of the cooling material. First, a steep increase in the average solar cell temperature is observed, followed by a gradual increase with time. This variation most likely results from sensible heating of the PCM by conduction heat transfer through the aluminum front plate. Subsequently, phase transition of the PCM adjacent to the aluminum front plate causes a thin melting layer on the PCM. During this period, the PCM acts as an insulation material for the CPV cell, whereas heat transfer is dominated by conduction, raising the CPV temperature. Second, as time passes there is a decrease in the average cell temperature after which it remains almost constant for a period. This stage indicates the start of the convective heat transfer that balances conductive heat transfer. During

FIGURE 8 Average predicted solar cell temperature and temperature variations with time in center vertical line of concentrated photovoltaicephase change material (CPV-PCM) system with the time evolution of solideliquid interface of CPV-PCM system at ambient temperature of 30 C and 1 m/s wind velocity. CR, concentration ratio.

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this period, the natural convection current becomes more significant in the liquid PCM as the melting fraction increases [48,49]. Finally, as time passes, the cell temperature gradually begins to increase until the PCM reaches the complete melting point. This variation is observed when the hot molten liquid touches the aluminum rear plate. Furthermore, the solid PCM, which acts as the cold source that drives the natural convection currents, starts to disappear from the upper part of the system. During this period, natural convection currents are weakened in this region. In addition, the temperature of the liquid PCM at the upper part of the system increases, which results in less heat transfer from the hot wall to the liquid PCM. With the lapse of time, the region of weak convection currents extends from up to down while raising the cell temperature gradually until it reaches a fully liquid phase. In addition, along the height at the center of the CPVePCM system at points A, B, and C, heat transfer is initially dominated by conduction, with an increase in linear temperature over time. After 100 min, the melting interface reaches point A, where heat transfer is dominated by convection. This causes the temperature to increase sharply toward the solar cell temperature whereas the temperatures in the solid phase locations (B and C) maintain a slow conduction-dominated increase. This behavior is observed at points B and C after 200 and 300 min, respectively.

4.2.2 Thermal Performance Comparison for Concentrated PhotovoltaicePhase Change Material Systems With a Different Number of Fins In the current work, a detailed analysis is presented of the effect of inserting various numbers of aluminum fins on the thermal regulation of the CPV-PCM system. Fig. 9AeC presents the transient variations of the average solar cell temperature of the CPV-PCM system with different numbers of fins (each fin is 100 mm in length) and no fins, at CRs of 5, 10, and 20, respectively. At CR ¼ 5, increasing the number of fins led to a significant reduction in the average solar cell temperature, where it was reduced from 70 C to 52 C as the number of fins increased from zero to four. This can be explained by the fact that metal fins increased heat transfer inside the PCM by increasing the surface area over which the heat transfer to or from the PCM occurred. By increasing the CR to 10 and 20, a similar trend was observed in Fig. 9B and C, as when the number of fins increased from zero to four fins. At CR ¼ 10, the average solar cell temperature was reduced from 106 C to 76.5 C, whereas at CR ¼ 20 min, the average solar cell temperature was reduced from 155 C to 115 C. Moreover increasing the value of CR led to a significant increase in the melting rate. This was because as the value of CR increased, the amount of solar irradiance received by the CPVePCM system also increased. Hence, the amount of the front wall heat flux transferred to the PCM increased, which indicated a higher melting rate. Predicted temperature distributions during the PCM melt process within the CPV-PCM system with four fins at CR ¼ 5 are presented in Fig. 10. As seen in the figure, when aluminum fins were added to the system, the formation of a deep cavity in the upper part of the CPV-PCM system was reduced and divided into several smaller, shallower cavities between the fins, which reduced the thermal stratification within the system. After 170 min, a natural convection flow of hot molten PCM passed through the gap at the end of the fins into the upper part of the system; it then turned to flow downward through the gap, near the liquidesolid interface into the lower section. After 235 min, the molten PCM reached the aluminum rear plate and its temperature rose, causing an increase in the heat transfer rate from the side to the PCM adjacent to it. Then the melting velocity increased and the CPVePCM temperature began to rise quickly. This flow pattern was maintained until the PCM was fully molten. Once the PCM in the uppermost section was fully molten (after 260 min), the temperature of the CPVePCM system increased rapidly.

4. RESULTS AND DISCUSSION

495

FIGURE 9 Average predicted solar cell temperature of concentrated photovoltaicephase change material concentrated photovoltaicephase change material system with different number of fins and no fins at (A) concentration ratio (CR) ¼ 5, (B) CR ¼ 10, and (C) 20, an ambient temperature of 30 C and 1 m/s wind velocity.

To demonstrate the effect of using fins on the temperature uniformity of the CPVePCM system, Fig. 11 presents the local solar cell temperature for the CPVePCM with a different number of fins at 00 min. This figure shows that the temperature difference between the top and base of the solar cell (125 mm in height) for the nonfinned CPVePCM system equals 13.5 C. The use of aluminum fins provided improved thermal control whereas the temperature difference was reduced to 7 C for the CPVePCM system with two fins. Increasing the number of fins to four was able to decrease the temperature difference to 4.5 C and reduce the solar cell temperature.

496

CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

t = 80 min

t = 120 min

t = 170 min

t = 235 min

t = 260 min

t = 300 min

FIGURE 10 Predicted isotherms of concentrated photovoltaicephase change material system with four fins at concentration ratio ¼ 5 at different times.

4.3 COMPARISON BETWEEN THE PROPOSED ACTIVE AND PASSIVE COOLING TECHNIQUES The current section compares the investigated MCHS designs and the proposed PCM configurations implemented based on the predicted average solar cell temperature, solar cell efficiency, net power, and thermal efficiency. Because the PCM model is an unsteady model, the average solar cell

4. RESULTS AND DISCUSSION

497

FIGURE 11 Variations in local solar cell temperatures of concentrated photovoltaicephase change material system without fins and with two and four fins after 100 min at concentration ratio (CR) ¼ 10.

temperature changes with time instantaneously. In the current section, the average solar cell temperature and stored thermal energy over the period from the initial time (ti) to the complete melting time (tm) was calculated to be straightforwardly compared with the steady-state solution of the MCHS domain. The average solar cell temperature, stored thermal energy, and thermal efficiency of the CPePCM system are calculated based on the equations: T sc;avgPCM Qth;avgPCM

1 ¼ tm  ti 1 ¼ tm  ti

hth;PCM ¼

Z Z

t¼tm

Tsc ðtÞdt

(14)

Qth ðtÞdt

(15)

t¼ti t¼tm

t¼ti

Qth;avgPCM  mPCM G  Asc  ðtm  ti Þ

(16)

Fig. 12A and B present the most essential parameters that affected the selection of the appropriate CPV cooling technique at CR ¼ 5 and 20, respectively. The heat sink designs that were compared were the WMCHS and MMCHS, with P ¼ 5 mm as an example for the active cooling technique, and the conventional cavity of PCM without fins and with four fins as examples for the passive cooling technique. In Fig. 12A, at CR ¼ 5, the MCHS designs operated at m_ ¼ 100 g=min, which was capable of achieving a lower cell temperature; a further increase in the m increased the friction

498

CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

FIGURE 12 Variations in average solar cell temperature, solar cell electrical efficiency, net gained electrical power, and concentrated photovoltaicethermal system thermal efficiency with different active and passive cooling techniques at (A) concentration ratio (CR) ¼ 5 and (B) CR ¼ 20. MMCHS, manifold microchannel heat sink; WMCHS, wide microchannel heat sink.

power whereas the cell temperature remained unchanged, as discussed earlier. However, in the CPVePCM system, the parameters were calculated from the initial time only to the complete melting time. The CPVeWMCHS system attained the lowest average cell temperature, followed by the CPVeMMCHS system. Moreover, including the fins significantly reduced the cell temperature from an average value of 72 C for no fins to around 58 C for the case of four fins. Although the MCHS consumed a portion of the CPV electrical power, the electrical efficiency and net gained power of the systems using the PCM were smaller than those using the MCHS. These were returned to power enhancement owing to efficient cooling using the MCHS, which was much greater than that consumed to overcome friction. However, regarding thermal efficiency, the CPVeMMCHS system attained the highest thermal efficiency compared with the other configurations. This high thermal

5. CONCLUSION

499

efficiency was attributed to the coolant passing through a shorter distance under the cell and to its being divided into several jets that absorbed heat from the cell at relatively the same value over the cell length. However, in the CPVeWMCHS system, the solar cell temperature at the end of the MCHS was high; consequently, the cell lost a large amount of heat to the atmosphere via combined radiation and convection. In CPVePCM systems, thermal efficiency using four fins was much greater than without the use of fins. The same trend observed at CR ¼ 5 in Fig. 12A was detected as shown in Fig. 12B at CR ¼ 20, except that in the active technique using MCHS, both WMCHS and MMCHS attained relatively equal values for the solar cell temperature and thermal efficiency. This occurred at m_ ¼ 800 g=min, when both configurations attained the same cell temperature. However, the net gained electric power of the CPVeMMCHS was much higher compared with all proposed designs because it has the lowest consumed friction power of the cooling configurations with lower attained cell temperatures.

5. CONCLUSION Active and passive cooling techniques were compared for CPV systems. The active technique using an MCHS was compared using PCM as a passive cooling technique across different designs. A comprehensive 2D model was developed to investigate the effect of various designs and operation conditions on CPVeT system performance parameters. The comparison was implemented based on the average solar cell temperature, solar cell electric efficiency, system net power, and system thermal efficiency. Based on the results, there were several findings: •

•

•

• •

•

In an active cooling technique with MMCHS, the solar cell temperature is reduced from 136 to 111 C with a decrease in pitch from 5 to 1.25 mm at a cooling mass flow rate of 50 g/min and CR of 20. Use of a WMCHS with a minimum coolant mass flow rate of 60 and 350 g/min at CR ¼ 15 and 20, respectively, is recommended. In addition, CPV systems can safely operate when they are combined with MMCHS at a minimum coolant flow rate of 120 and 550 g/min at CR ¼ 15 and 20, respectively. At CR ¼ 20, using an MMCHS attains a solar cell temperature uniformity of 4.02, 0.365, and 0.125 C at coolant mass flow rates of 50, 800, and 2020 g/min, respectively. However, the WMCHS achieves a maximum temperature difference of 46.8, 3.13, and 1.44 C at coolant mass flow rates of 50, 800, and 2020 g/min, respectively. In the passive cooling technique, at CR ¼ 5, including fins significantly reduces the cell temperature from an average value of 72 C without fins to around 58 C with the use of four fins. At CR ¼ 10, the cell temperature uniformity of a nonfinned CPVePCM system equals 13.5 C. The use of aluminum fins enhances thermal control when the temperature difference is reduced to 7 and 4.5 C for a CPVePCM system with two and four fins, respectively. The CPVeWMCHS system attains the lowest average cell temperature, followed by the CPVeMMCHS. Moreover, including fins significantly reduces the cell temperature from an average value of 72 C without fins to around 58 C with the use of four fins. The MCHS consumes a portion of the CPV electrical power, whereas electrical efficiency and the net gained power of the systems using the PCM are smaller than those with the use of the MCHS.

500

CHAPTER 2.15 COMPARATIVE STUDY OF COOLING TECHNIQUES

NOMENCLATURE Amush C g G(t) h H k L m_ N P t T V Vw

Mush zone constant (Kg/m3 s) Specific heat capacity (J/kg$K) Gravitational acceleration (m/s2) Incident solar radiation (W/m2) Heat transfer coefficient (W/m2$K) microchannel height (m), and total specific enthalpy (J/kg) Thermal conductivity (W/m$K) Microchannel length, solar cell length (m), and latent heat (N m) Unit cooling fluid mass flow rate (Kg/s) Number of inlet or outlet ports Pressure (Pa), electrical power (W) Phase change material thickness (m), time (s) Temperature ( C) Velocity vector (m/s) Wind velocity (m/s)

Greek symbols a b bl ε s m s r d l n h

Absorptivity Backing factor and solar cell temperature coefficient (K1) Thermal expansion coefficient (K1) Emissivity Transmittivity Fluid viscosity (Pa s) StephaneBoltzmann constant 5.67  108 (W/m2$K4) Fluid density (kg/m3) Thickness (m) Liquid fraction Kinematic viscosity (m2 s) Solar cell and thermal efficiency

Subscripts

a conv. eff el f g in i m out ref s Sc Sc, x

Ambient Convection Effective Electrical Fluid Glass Inlet Initial Melting Outlet Reference condition, G ¼ 1000 W/m2, T ¼ 25 C Sky and solid Solar cell Local solar cell

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T th w w

501

Tedlar Thermal Wall Water

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APPENDIX A AUXILIARY EQUATIONS USED IN THE CURRENT MODEL The CPV/T system thermal efficiency is identified as: hth ¼

Pth GðtÞ$Asc

whereas the friction power, solar cell electrical power, and net gained electrical power are described as: _ in Pfrict ¼ DP$m=r Pel ¼ hsc sg bsc GðtÞwsc $lsc Pnet ¼ Pel  Pfrict The channel Re and hydraulic diameter are calculated based on the following correlations: Re ¼ Dh ¼

rin Vin Dh min

2ðHch  Wch Þ ðHch þ Wch Þ

The equivalent radiative heat transfer coefficient from the glass cover to the sky and the sky temperature are calculated using the following equations as reported by Rejeb et al. [50]:   sεg Tg4  Ts4 hrad;gs ¼ ðTg  Ts Þ Ts ¼ 0:0522Ta1:5 whereas the convective heat transfer coefficient from the glass cover to the ambient temperature and from the back sheet of the heat sink to the atmosphere are calculated based on the following correlations [30]: hcon;ga ¼ 5:82 þ 4:07Vw hconv;alamb ¼ 2:8 þ 3Vw The buoyancy force used in the PCM model is given by the Boussinesq approximation as: ! F B ¼ ro b1 ! g ðT  To Þ Parameters Sx, and Sy are Darcy’s law damping terms (as the source term), which are added to the momentum equation owing to the phase change effect on convection; they are defined as: ð1  lÞ2 $Amush $u Sx ¼  3 l þg

APPENDIX A

505

ð1  lÞ2 $Amush $v Sy ¼  3 l þg The enthalpy of the PCM material, H, is computed as the sum of the sensible enthalpy, h, and the latent heat, DH: H ¼ h þ DH where: Z h ¼ href þ

T

cp dT Tref

The latent heat content can be written in terms of the latent heat of the material, L: DH ¼ lL where DH may vary from 0 (solid) to L (liquid). Therefore, the liquid fraction, l, can be defined as: 8 DH > > > ¼0 T < Tm > > L > > > < DH T  Tsolidus ¼ Tm < T < Tm þ DTm l¼ L T  Tsolidus > liquidus > > > > > DH > > ¼1 T > Tm þ DTm : L The parameter Tm is the melting temperature of the PCM and DTm is the phase transition range, which is defined as the difference between the liquidus and solidus temperatures as: DTm ¼ Tliquidus  Tsolidus The PCM thermal conductivity, depending on its phase, is defined as: 8 > ks T < Tm > > > < ðks þ kl Þ kpcm ¼ Tm < T < Tm þ DTm > 2 > > > : kl T > Tm þ DTm