Characteristics enhancement of one-section and two-stepwise microchannels for cooling high-concentration multi-junction photovoltaic cells

Energy Conversion and Management 206 (2020) 112488

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Characteristics enhancement of one-section and two-stepwise microchannels for cooling high-concentration multi-junction photovoltaic cells

T

Hosny Abou-Ziyana,b, , Mohammed Ibrahima, Hala Abdel-Hameeda ⁎

a b

Mech. Power Eng. Dept., Faculty of Engineering, Helwan University, Cairo, Egypt Mech. Power Eng. Dept., College of Technological Studies, PAAET, Kuwait

ARTICLE INFO

ABSTRACT

Keywords: High-concentration multi-junction photovoltaic High power integrated circuits Stepwise microchannel cooling Hybrid jet impingement-microchannel cooling Pumping power Net output power

This paper presents the development of simple, effective, and economic microchannel systems for cooling highconcentration multi-junction photovoltaic (HCMJPV) cells. The developed cooling system uses a short cooling fluid path concept with either one or two microchannel sections per the fluid path. The work is conducted using a 3D numerical model that is based on the finite volume method. The effects of design parameters on the thermal characteristics of one and two-section microchannels and output power of the HCMJPV cells are comprehensively investigated. Cooling systems that attained the largest net output power of HCMJPV cells are identified. Developed cooling systems achieved superior characteristics compared to the existing state of the art system. The two-stepwise microchannel cooling system achieves the best temperature uniformity, whereas the constantwidth one-section microchannel cooling system achieves slightly better characteristics than the two-stepwise system. The proposed constant-width one-section cooling system achieves comparable standard deviation and lower surface temperature (35.65 °C), pressure drop (68.41%) and microchannel thermal resistance (49.57%) along with higher generated power (8.27%), net output power (8.44%) and overall heat transfer coefficient (175.8%) than the existed cooling system in literature. The developed cooling system allows the cells to produce an extra 820.5MWh/m2 of cells during their lifetime.

1. Introduction The solar energy becomes one of the most important renewable energy sources. It is the third source of power generation in 2018, after the hydraulic and wind power sources, by installed capacity of 486085 MW [1]. Solar energy has a substantial escalation because of the excessively reduction in the total installed and the Levelized Cost of electricity [1]. Solar energy technologies provide a great role in solving the most pressing problems of conventional energy sources depleting and the increase in energy demand [2]. The solar photovoltaic (PV) cells are considered as the most promising technology of solar energy due to a wide range of applications [3]. The history of PV started by the single-junction cells, but its main weakness is the low conversion efficiency (15–20%). Also, its conversion efficiency decreases by about 0.08% for a 1-degree increase in temperature above 25 °C [4]. Afterward, concentrated photovoltaic (CPV) systems are introduced to enhance the power generation by these low-efficiency solar cells. Nowadays, the most promising PV technology is the multi-junction photovoltaic (MJPV), particularly with concentration (CMJPV) and high concentration (HCMJPV). Those cells

⁎

were usually used in the spaceships and become available for terrestrial applications. Triple junction cells consist of three layers of semiconductors that can absorb a wide range of incident rays (many wavelengths). Thus, its efficiency is higher than the classical photovoltaic cells, which absorb a definite one wavelength of incident rays. Thus, the efficiency of commercial triple-junction PV is 38–43% at a cell temperature of 25 °C [1]. The conversion efficiency of HCMJPV is decreased by 0.05–0.15%/°C increase above 25 °C [1,5]. Therefore, cooling the surface of the PV cells becomes an essential issue to sustain reasonable efficiency of the cells. Different designs of cooling systems of CPV with concentration ratios smaller than 20, which include passive means of cooling such as phase change material, heat pipe, free air, liquid immersion, and evaporation methods. However, HCMJPV technology requires an efficient cooling system [6]. Active methods of cooling HCPV such as forced air and liquids, liquid film or spray, microchannels, jet impingement, and hybrid jet impingement-microchannels can overcome the existing challenges of passive systems [5]. Nižetić et al. [7,8] reviewed and assessed the economic viability of passive and active cooling techniques of PVs. In the last few years, the cooling systems of high densely packed PV

Corresponding author at: Mech. Power Eng. Dept., Faculty of Engineering, Helwan University, Cairo, Egypt. E-mail address: [email protected] (H. Abou-Ziyan).

https://doi.org/10.1016/j.enconman.2020.112488 Received 12 August 2019; Received in revised form 11 December 2019; Accepted 7 January 2020 0196-8904/ © 2020 Elsevier Ltd. All rights reserved.

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H. Abou-Ziyan, et al.

Nomenclature A cp k L p P Pw q qg Q R T U V Δ ηc(Ta) ρ

σ a av g in m mw net p s t CFD CMJPV CPV CR DNI HCMJPV HCPV IC MJPV PV UDF TIM

Area, m2 Specific heat, J/kgK Thermal conductivity, W/mK Layer thickness, m Pressure, Pa Power, W Wetted perimeter, m Heat flux, W/m2 Generated electrical power per unit area of HCPV cell, W/ m2 Volume flow rate of water, m3/s Thermal resistance, m2K/W Temperature, °C Overall heat transfer coefficient, W/m2K Inlet water velocity, m/s Relative temperature coefficient of HCMJPV cell = 0.0531, %/°C difference Temperature dependence convergent coefficient of HCMJPV cell Density, kg/m3

and high power integrated circuits have incredible advancements and improvements. The main aims are providing low thermal resistance of heat transfer to maintain the temperature of cells at proper operating temperature and improving the temperature uniformity to maintain the reliability and efficiency of cells [9,10]. On the other hand, the compromise between the consumed pumping power of the cooling system and power increased due to cooling must be considered. The most critical cooling is for densely packed cells, which must be cooled actively, and the thermal resistance has to be less than 10−4m2K/W [11]. “The densely packed cells are those where each cell is surrounded by other cells on each side, excluding the cells placed on the edges of the assembly [11,15]”. Such a small thermal resistance can be achieved only by impinging jets and microchannels. The microchannel system is considered as one of the most powerful technologies in liquid cooling. Microchannels can be integrated as liquid cold plates (heat sink) or itched in the surface of HCMJPV and integrated circuits. Microchannels are defined by their channel dimensions, which are typically 10–200 μm or up to 1–3 mm in some cases. Microchannels provide high heat transfer rates due to high heat transfer coefficients and high heat transfer area per unit volume. However, pressure drops are also enlarged for microchannels [12]. Tuckerman et al. [13] were the first who used microchannels for cooling integrated circuits. The results indicated that heat transfer is decreased gradually along the path of water, which leads to very poor temperature uniformity. Lee et al. [14] replaced the continuous fins of microchannels by sectional oblique fins cut at about 27° to improve the temperature uniformity. The authors reported an enhanced heat transfer by 30%, with a slight increase in pressure drop compared to the conventional microchannel cooling system. Micheli et al. [15] showed that the maximum temperature of the cooled surface was 78.8 °C for flat plate and 70.4 °C for the finned plate. Reddy et al. [16] investigated the effects of microchannels width (0.2–0.4 mm), aspect ratio (0.2–0.5 mm), and Reynolds number (500–1500) on the thermal and electrical performance of the cooling system. They concluded that microchannels of 0.5 mm width, 4 mm depth, and 12 mm length provided a minimum pressure drop. However, the temperature of the cooled surface was high, even at high flow rates. Some studies investigated the performance of microchannels with different cross-sectional shapes such as hexagonal, circular, and rhombus cross-sectional microchannels [17] or circle, square, trapezium, two

The standard deviation of HCMJPV surface temperature, °C area-weighted average of HCMJPV surface average generated inlet microchannel middle width of cooling system (plan at y = 5 mm) net output pumping surface total Computational Fluid Dynamics Concentrated Multi-Junction Photovoltaic Concentrated Photovoltaic Concentration Ratio Direct Normal Irradiance High-Concentration Multi-Junction Photovoltaic High Concentrated Photovoltaic Integrated Circuits Multi-Junction Photovoltaic Photovoltaic User Defined Function Thermal Interface Material

concave surfaces, and two convex surfaces [18]. However, these designs are very complicated and very expensive to manufacture. T-shaped microchannels cooling systems with different configurations were investigated [19]. Also, T-shaped microchannels itched on the surface of the PV base with five sequential steps were considered [20]. The effects of the width of microchannels, the number of manifolds, and the water flow rate on the performance of the manifold (multi-layered) microchannel cooling system were investigated [21,22]. The results showed that the best model had channels of 0.025 × 0.3 mm. However, this design is complicated to manufacture, and it needs a high flow rate, which causes a very highpressure drop. Nanofluids were used to enhance the heat transfer coefficient without increasing the flow rate in a trial to decrease the highpressure drop in the manifold microchannels [23,24]. Other models were designed to enhance the convection coefficient by increasing the turbulence in the flow path such as wavy [25–26], U [27], and microscale ribs and grooves [28] microchannels. All those models enhance the heat transfer but increase the consumed pumping power and become more challenging to manufacture, especially for microscale applications. On the other hand, as the jet impingement can achieve a high local heat transfer coefficient, it was used for cooling high-performance ICs and densely packed PVs. The effects of the jets number and the nozzle pitch on industrial CPVs are investigated where the system offers low-pressure drop, but gives a high temperature of the cooled surface with bad temperature uniformity, even under low heat flux [10]. The effects of jet-to-jet spacing, nozzle-to-plate distance, and flow rate on the performance of a cooling system of a flat plate with three air jets impingement were investigated [29]. The results indicated that the optimum jet-to-jet spacing was four times the jet diameter as it maximizes Nusselt number and minimizes the negative effect of interaction between jets. Hybrid jet impingement-microchannel is the most appropriate cooling system to achieve low thermal resistance [11]. Naphon et al. [30] showed that for the hybrid fixed nozzle-microchannel system (single pass), the heat transfer coefficient increases, but the pressure drop increases by decreasing the jet diameter. Dede [31] optimized a new model of hybrid multi-pass branching microchannel-jet impingement cooling system. This model provided a low-pressure drop but with bad cooling performance. Lamini et al. [32] investigated models of fixed and moving nozzles, where the results provided that the mean temperature was dropped by 5 °C by using the moving nozzle. This model had excellent thermal performance but provided bad 2

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temperature uniformity. Han et al. [33] proposed a new design to eliminate the problem of the negative cross-flow effect between the adjacent nozzles. The results provided that the heat transfer coefficient was enhanced due to the impingement of jets array over the small cooled surface. Ming et al. [34] suggested combining dimples with hybrid microchannels-jet impingement. Their results indicated that by increasing the radius of dimples, the heat transfer enhanced, and the temperature uniformity improved, but the maximum temperature increased. Barrau et al. [35] proposed a milliscale model of the hybrid cooling system with three stepwise channels per fluid path; their widths were 3.5, 1.5, and 0.5 mm. In this model, the heat transfer coefficient increased gradually through the steps of microchannels due to the enhancement of velocity to compensate for the increase in temperature of the water. Then, Barrau et al. [36] compared their hybrid cooling system for densely packed PV with other microchannels cooling systems reported in [37]. The results showed that the hybrid cooling system provided lower standard deviation and minimum thermal resistance, but had lower net output power for concentration ratio 1905. Also, the temperature uniformity was improved by increasing the flow rate and decreasing the heat flux [38]. This hybrid system operated under high flow rates to enhance the rate of heat transfer and achieved a minimum thermal resistance of 2.18 × 10−5 m2K/W. Moreover, for HCMJPV and high power IC chips, five stepwise microchannel cooling system with variable widths 1.53–0.14 mm (Fig. 1) was experimentally investigated by Riera et al. [9,39]. This system has one jet inlet and two outlets and includes thermal interface material (TIM) between the copper layer and the heat sink device (silicon wafer microchannel). This TIM had a low thermal conductivity of 0.82 W/mK to improve the smoothness of temperature uniformity. The model achieved a high heat transfer rate and a more uniform temperature distribution, under a lower water flow rate and higher inlet water temperature. Also, the system achieved a lower microchannel thermal resistance of 2.35 × 10−5 m2K/W. The TIM affects the temperature distribution by its soothing effect, and the temperature uniformity improved by decreasing the smoothing resistance [40]. Finally, Vilarrubi et al. [41] replaced the ordinary stepwise microchannels by variable density micro-pin-fins that provided the same trend of total thermal resistance as ordinary microchannels. They showed that the pressure drop generated at jet impingement/pin fins is higher than that generated at the jet impingement/microchannel cooling system. This design improves the temperature uniformity over the cooled surface due to good mixing of the fluid at high flow rates. The above literature review indicated that the state of the art cooling system for HCMJPV cells is based on five stepwise microchannel sections with widths of 0.14–1.53 mm [9]. In this system, the cooling fluid loses considerable pressure drop as it passes through the five micro-scale sections. Thus, considerable pumping power is needed to operate the system. Although the system is adequate, it is complicated and expensive to manufacture, operate, and maintain. On the other hand, the effects of design parameters on the thermal and electrical characteristics of the HCMJPV cells were not studied for a hybrid jet impingement-microchannel cooling system yet. In addition, most of

the other cooling systems were suffering a high-pressure drop, high surface temperature, or bad temperature uniformity. Therefore, the purpose of the present work is to create a simpler, more efficient, and less expensive cooling system for HCMJPV cells. This system is based on the idea of using a short cooling fluid path with one-section or two-stepwise microchannel sections instead of the five stepwise sections. Thus, the system becomes simple and consumes less pumping power to operate. A comprehensive investigation of the effects of the system design parameters on the thermal characteristics of the cooling system and the output power of the HCMJPV cells is conducted. The design parameters include inlet jet impingement width, outlet slot width, microchannels width, length, and depth. Also, two more conductive thermal interface materials are exercised with the new system, as this will make the system more efficient. In addition, the developed designs are compared with the state of the art cooling system. 2. Numerical modeling and simulation This section describes the modeling and simulation of water flow and heat transfer in the cooling system of HCMJPV cells. Three-dimensional models that are based on CFD code (FLUENT 18.2) integrated with three user-defined functions (UDFs) were used to simulate the cooling system. The program is based on a finite control volume approach that uses an unstructured mesh to obtain a high resolution of nodes. The equations for conservation of mass (Eq. (1)), conservation of momentum (Eq. (2)), and conservation of energy (Eq. (3)) were solved in each cell.

t

t

t

+

xi

( ui ) +

( T) +

( ui ) = 0

xj

xi

(1)

p + µ xi xj

( ui uj ) =

( ui T ) =

xi

k T cp x i

uj ui + xj xi

+ ST

+ gi

(2)

(3)

where is the density of the fluid, t is time, ui is the velocity vector components (u, v, and w), xi is the Cartesian coordinate axis (x, y, and z), p is the pressure, µ is the dynamic viscosity, and g i is the body force in the x, y, and z directions, T is the temperature, k is the thermal conductivity of the material, c p is the specific heat, and ST is the source term. Turbulence was considered using the Reynolds Averaged NavierStokes (RANS) equations by time-averaging Eqs. (1)–(3), and a twoequation turbulence model was chosen to account for the additional terms generated for this method. The appropriate turbulence model for the present cooling system is RANS Realizable k-ε model because the studied cooling system has a low level of turbulence without strong vorticity. Also, the required initial layer of water mesh inflation is not very fine and allowed the value of Y+ > 30. This reduces the required number of cells and required computational time and cost. In addition, this model has been widely validated for a wide range of flows,

Fig. 1. Schematic diagram of the state of the art five stepwise microchannel cooling system [9]. 3

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including jets and mixing flows, channel, and boundary layer flows and separated flows.

Fig. 2 shows that both cooling systems are symmetric in the XZ plane and YZ plane. Therefore, a quarter of the cooling system is representative of the full cooling system. Thus, the simulation is conducted on a quarter of the cooling system that is depicted in Fig. 3. It can be seen that the water jets are introduced through the inlet slot, in the middle at x = 12.5 mm, where each jet cools half the HCMJPV surface and discharged through two outlet slots at the ends of the cooled sections, at x = 0 and x = 25 mm.

2.1. Computational domains: The cooling system needs to be able to cool a PV module that is consisting of 5 HCMJPV cells, where each cell is 1 × 1 cm. Thus, the cooling system size is 5 cm long by 1 cm wide and 2.2 mm high. Fig. 2 shows the two cooling systems that were proposed and examined, in this work, for HCMJPV cells. Each system contains four similar microchannel stages (i.e., four cooling water paths) with two water inlets and three outlets, as shown in Fig. 2a that presents the elevation of either cooling systems. Fig. 2b shows the plan of the constant-width one-section microchannel cooling system and Fig. 2c shows the plan of the two-stepwise microchannel cooling system. The first system has constant-width microchannels, and the second system has two-stepwise microchannels sections of different width in each of the four stages (four fluid paths).

2.2. Model solver description: The cooling system is constructed of four layers, as shown in Fig. 2d. These are the copper base, thermal interface material (TIM), silicon wafer microchannels as a heat sink (cooling device), and water as a cooling liquid. Tetrahedral cells are used for water and silicon microchannels domains and hexahedral cells for the thermal interface material and copper layers. In addition, some modifications are performed to improve the quality of the grid, which is evaluated by the aspect

(a) Elevation of either constant section or stepwise microchannels.

(b) Plan of constant section microchannel cooling system.

(c) Plane of two stepwise microchannels cooling system.

(d) Details of cooling system layers (zone d in the elevation). Fig. 2. Schematic diagram of the cooling system of HCMJPV. 4

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(a) Elevation of quarter the cooling system.

(b) Plan of quarter the constant section microchannels cooling system.

(c) Plan of quarter the two stepwise microchannel sections cooling system. Fig. 3. Schematic diagram of quarter the cooling system of HCMJPV.

momentum were less than 10−5. Program inputs are water flow rate, inlet water temperature, and heat flux, in addition to the geometry of the cooling system. On the other hand, the outputs from the program are HCMJPV surface temperature, a standard deviation of temperature, and inlet and outlet pressure.

ratio, skewness, and orthogonal quality. Specifically, the edge sizing is used for edges of microchannels and water domains and creates inflation layers on the walls of the liquid domain. Navier-Stokes equations are solved in the fluid domain with turbulent flow under the range of investigated parameters of inlet water temperature, velocity, and heat flux. The steady, pressure-based coupled algorithm method was used to solve the problem as it obtains more robust and efficient single-phase implementation for steady-state flows. Least Squares Cell-Based is used for gradient, second-order upwind discretization is used for energy and momentum and second order is used for pressure to control the spatial discretization of the convection terms in the equations. The pseudo transient helps to stabilize the case and at the same time, gives faster convergence. The direct normal solar irradiance DNI is incident on the double stage Fresnel lens. Then, the surface of HCMJPV receives this concentrated solar energy; part of it is converted to generate power, and the rest is transferred to the body of HCMJPV as heat. This heat is conducted through the copper base, thermal interface materials, and silicon anisotropic microchannels layers, and then transferred by convection to the cooling liquid. The correct simulation of the cooling system depends on the appropriate specifications of the boundary conditions. Each simulation was assumed to converge when the residuals for the energy equation were less than 10−8, and those for the equations of continuity and

2.3. Model validation The described numerical model is validated against experimental data reported in [9], where the HCMJPV cooling system is made up of two stages (fluid paths) each stage comprised five stepwise microchannel sections per the fluid path as described in Section 1 (Fig. 1). Minor changes were implemented in the numerical model to accommodate the various conditions of the experiment in [9] including the flow type and the boundary conditions. The material and fluid properties were taken as reported in [9] or through private communication with the authors. Only the properties of the anisotropic silicon wafer used in their work were not available; thus, these properties are not definite in the model. 2.3.1. Mesh independent study: Accurate numerical predictions require a mesh that is sufficiently refined to obtain results that are independent of the mesh used. The mesh independent study was conducted for three sizes, namely 10.5 5

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3. Analysis of output power and cooling of HCMJPV The implementation of an idea or a new concept to the cooling process of HCMJPV cells targets to decrease the thermal resistance while maintaining the temperature uniformity of the cooled HCMJPV surface. The accomplishment of this target depends on the successful design that optimizes the use of suitable materials and flow conditions. The total thermal resistance (Rt), microchannel global thermal resistance (Rm), and the overall heat transfer coefficient (U) can be evaluated using Eqs. (4)–(6).

Rt =

Ta

Tin

Rm = Rt (a) Effect of grid size on the temperature distribution

U=

(4)

q ''

L cu k cu

L TIM kTIM

(5)

1 Rt

(6)

where Ta is the average surface temperature of HCMJPV base, Tin is the inlet water temperature, q'' is the heat flux,Lcu and kcu are thickness and thermal conductivity of copper layer, and LTIM and kTIM are thickness and thermal conductivity of thermal interface layer. The inlet water velocity (Vin) is calculated to define the inlet boundary condition of numerical simulation using Eq. (7) in which Q is the volume flow rate of water, and Ain is the area of the inlet slot jet.

Vin =

Q Ain

(7)

On the other hand, the generated power (Pg) and consumed pumping power (Pp) are calculated using Eqs. (8) and (9). Then, the most important performance factor of the HCMJPV, which is the net output power (Pnet), can be evaluated using Eq. (10). Thus, the characteristics of the cooling system control the net output power because the HCMJPV surface temperature influences the generated power, and the pressure drop (Δp) across the cooling system controls the pumping power.

(b) Comparison between numerical and experimental results Fig. 4. Validation of the numerical model.

MCells (2.77 M nodes), 11.9 MCells (3.55 M nodes) and 18.3 MCells (5.01 M nodes). Fig. 4a shows the temperature distribution in the middle width (y = 5 mm) of the copper base at z = −1.25 mm, where the thermocouples are located in the experimental work [9]. Similar results are shown for the three mesh sizes for x > 10 mm (the last three microchannel sections). The difference between the results is noted for the fluid entrance where the inlet jet impinges the surface and first two-stepwise microchannel sections. The large size grid (10.5 MCells) fails to predict accurate results under the conditions in this area. However, the difference between the results of 11.9 and 18.3 MCells is minor, while the difference in computation time is significant. Therefore the mesh size, of 3.55 million nodes and 11.9 million cells, provided accurate results and reasonable computation time and was used throughout the validation and system modeling.

PP = p × Q

(8)

Pg = q g × A s

(9)

Pnet = Pg

(10)

PP

qg is the generated electrical power per unit area of HCMJPV cell, and As is the surface area of the cell. It is calculated using Eq. (11), and the conversion coefficient ηc(Ta) of HCMJPV is estimated using Eq. (12).

qg = (CR × DNI ) × c (Ta )

=

c (25)

c (Ta )

(Ta

(11)

25)

(12)

where CR is the concentration ratio of solar concentrator facility, DNI is the direct normal solar irradiance, ηc(Ta) is temperature dependence convergent coefficient of HCMJPV cell, ηc(25) is the convergent coefficient at the surface temperature of 25 °C and equals 30.0% [38]. The parameter α is the relative temperature coefficient of HCMJPV cell (%/°C). This factor indicates the percentage decreasing into the convergent coefficient by increasing the surface temperature by 1 °C and equals 0.062 [38] for the considered solar cell. It is to be indicated that Ta is dependent strongly on the effectiveness of the cooling system.

2.3.2. Validation results Fig. 4b shows the experimental and numerical distribution of two experimental tests [9] at z = -1.25 mm. The average error along the curve is ± 3.643% (2.94 °C), for test 1 and ± 4.04% (3.19 °C), for test 2. Considering the uncertainty in the experimental results, which is about ± 2.11% (1.6 °C), it reveals that the difference between the experimental and predicted results is between 1.6% for test 1 and 2% for test 2. The small difference between experimental and predicted results may be attributed to the uncertainty in the thermophysical properties of materials that weren't available and the uncertainty in the experimental results. In conclusion, the numerical model predicts the results accurate enough within an average range of 0 to 1.93%.

4. Results and discussion In this section, the comparison between the considered cooling systems are based on surface temperature (Ta or Tmw), temperature uniformity along the HCMJPV base, which is measured by the standard deviation (σa or σmw) of temperature, total (Rt) and microchannels (Rm) thermal resistance and net output power (Pnet). It has to be stated that 6

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the cooling system is 5 cm × 1 cm and is responsible for cooling a module of five HCMJPV cells; each is 1 cm × 1 cm. Thus, a square meter contains 2000 modules or 10,000 HCMJPV cells. Therefore, the design that produces a higher net output power of the module by 0.01 W produces an extra 20 W per square meter of cells that is about 0.16 kWh/day or 58.4 kWh a year and 1.46 MWh during the cell’s lifetime (25 years). Similarly, 1 W difference in the net power produced by the considered module generates an extra 146MWh per square meter of cells, during their lifetime. However, the effects of design parameters on the output power and the cooling effectiveness of the HCMJPV cells for constant-width one-section and two-stepwise microchannels cooling systems are discussed in the following subsections. It has to be stated here that the study is conducted under the following boundary conditions: inlet water temperature of 21.7 °C, heat flux of 50 W/cm2, and inlet water velocity of 0.44 m/s. Those parameters are taken similar to test 1 of Reira et al. [9] to facilitate a comparison between present work and their existed design.

4.1.1. Effect of inlet jet width The effect of inlet slots is investigated for a width of 1.0, 1.5, 2.0, 2.5 or 3.0 mm while the outlet slot width remains unchanged at 0.75 mm. The effect of inlet slot width on the thermal characteristics of the cooling system and output power of the HCMJPV is presented in Fig. 5a and Table 1 (section a). Fig. 5a shows that jets of width lower than 2.5 mm have the lowest temperature at x = 12.5 mm as the inlet jet impinges the cell surface, whereas jets with a width of 2.5 and 3 mm have different temperature distribution along the length of the cell base. This is due to the reduction of the water velocity out of the jet with the increase in the jet width. It is clear that as the inlet slot width is increased the temperature distribution improves while its magnitude increases. Table 1a indicated that the lowest cell surface temperature and the largest net output power are produced with an inlet jet width of 1.0 mm. However, the temperature uniformity improves as the standard deviation of surface temperature decreases to reach its minimum value at a width of 3 mm. Thus, a compromise between the cell temperature and its associated standard deviation suggests that the inlet slot of 2 mm provides reasonable values for cell temperature (65.9 °C) and its standard deviation (0.334 °C), as listed in Table 1a. However, minute changes of overall heat transfer coefficients, total and microchannel thermal resistances occur within the investigated range of inlet slot width. It is noted that the difference between the average surface temperature and the average middle width temperature is small. Also, the difference between their corresponding standard deviation is small.

4.1. Constant-width one-section microchannels This section presents the simplest microchannel cooling system as it uses one microchannel section, with a constant width, for each water path instead of five stepwise microchannel sections [9]. Figs. 2b and 3b show the schematic of the proposed cooling system that is based on shortening the cooling fluid path. Thus, the length of this straight microchannel section is 9.95 mm, and the length of the cooling fluid path is about 11 mm. As such, the cooling system (5 cm × 1 cm) will be composed of only four sections of straight microchannels (Fig. 2b) with constant width compared to ten sections (Fig. 1) in the design reported by Riera et al. [9]. In order to obtain the best design of this constant-width one-section cooling system, five design parameters are investigated. These include inlet jet width (1, 1.5, 2, 2.5 and 3 mm), outlet slot width (0.5, 0.75 and 1 mm), microchannel width and depth (0.2, 0.3, 0.4 and 0.5 mm) and finally the thermal interface material, TIM (k = 0.82, 3 and 4 W/mK). Table 1 (sections a-e) lists the results of the stated effects of design parameters, respectively. Also, Fig. 5a–e show the temperature distributions along the cell surface of the cooling system shown in Fig. 3b, for the different stated design parameters.

4.1.2. Effect of outlet slot width Outlet water slots are investigated for a width of 0.5, 0.75 or 1 mm while the inlet width is kept unchanged at 2 mm. Fig. 5b and Table 1b demonstrated that the effect of outlet slot width is insignificant compared to that of inlet jet width. Table 1b indicated that a water outlet width of 0.75 mm provides slightly lower pressure drop and pumping power compared to the other considered water outlet width. Net output power is not sensitive to the investigated values of water outlets’ width. 4.1.3. Effect of microchannel width The microchannel width is changed from 0.2 to 0.5 mm with a step of 0.1 mm. Fig. 5c shows the temperature distribution along the cell surface of the cooling system for the different cases of microchannel width. The temperature and its variation along the surface decrease as

Table 1 Effect of design parameters on the thermal and electrical characteristics of constant-width one-section microchannels cooling system. Effect

Value

Ta °C

σa °C

Tmw °C

σmw °C

Rt × 10−5 m2K/W

Rm × 10−5 m2K/W

U kW/m2K

Δp kPa

Pp W

Pg W

Pnet W

a.

1.0 1.5 2.0 2.5 3.0 0.50 0.75 1.00 0.2 0.3 0.4 0.5 0.20 0.30 0.40 0.50 0.82 3.00 4.00

65.5 65.6 65.9 66.1 66.4 65.9 65.9 65.9 65.9 68.0 69.7 70.8 65.0 65.9 66.6 66.9 65.9 43.8 41.7

0.44 0.40 0.33 0.20 0.10 0.32 0.33 0.33 0.33 0.39 0.44 0.48 0.29 0.33 0.38 0.42 0.33 0.60 0.65

65.7 65.9 66.1 66.3 66.6 66.1 66.1 66.1 66.1 68.3 69.9 71.0 65.3 66.1 66.7 67.1 66.1 43.9 41.9

0.45 0.40 0.34 0.20 0.10 0.32 0.34 0.34 0.33 0.39 0.44 0.48 0.29 0.34 0.39 0.42 0.34 0.60 0.65

8.76 8.79 8.85 8.87 8.93 8.84 8.85 8.86 8.85 9.30 9.60 9.82 8.67 8.85 8.98 9.03 8.85 4.41 4.00

2.25 2.28 2.34 2.36 2.42 2.33 2.34 2.35 2.34 2.80 3.10 3.34 2.16 2.34 2.47 2.52 2.34 2.33 2.34

11.41 11.38 11.30 11.27 11.19 11.31 11.30 11.30 11.30 10.79 10.42 10.19 11.54 11.30 11.14 11.07 11.30 22.67 24.99

15.57 15.39 15.26 15.34 15.47 15.60 15.26 15.37 15.26 9.92 7.96 7.09 36.03 15.26 8.89 6.13 15.26 15.26 15.26

0.27 0.27 0.27 0.27 0.27 0.28 0.27 0.27 0.27 0.18 0.14 0.13 0.63 0.27 0.16 0.11 0.27 0.27 0.27

68.74 68.72 68.68 68.66 68.61 68.69 68.68 68.68 68.68 68.35 68.10 67.93 68.82 68.68 68.58 68.53 68.68 72.11 72.43

68.47 68.45 68.41 68.39 68.34 86.41 68.41 68.41 68.41 68.18 67.96 67.80 68.18 68.41 68.42 68.42 68.41 71.85 72.16

k = 0.82 k=4

66.1 41.8

0.49 0.91

66.2 42.0

0.49 0.91

8.88 4.02

2.37 2.36

11.26 24.85

9.174 9.151

0.16 0.16

68.65 72.42

68.49 72.25

b. c.

d.

e.

f.

Inlet jet width (mm)

Outlet slot width (mm) Width of microchannels (mm)

Channel depth (mm)

TIM k (W/mK) Maximum Pnet

7

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67

67 66

65

Inlet jet width: 1.0mm 1.5mm 2.0mm 2.5mm 3.0mm

64 63

a

62 80

TX (°C)

TX (°C)

66

Outlet slot width: 0.50mm 0.75mm 1.00mm

65 64

Inlet jet width of 2mm

b

Outlet slot width of 0.75mm

63 68

76 66

68 64

Width of microchannels: 0.2mm 0.3mm 0.4mm 0.5mm 1.0mm 1.5mm

60 56 52

c

48 70

TX (°C)

TX (°C)

72

55 50

44

45 40 0

42 40 The best designs (k=4W/m.K): Max. net ouput power Comparable design

38 36

e

35

d

60 46

TX (°C)

TX (°C)

60

Depth of microchannels: 0.2mm 0.3mm 0.4mm 0.5mm

62

65 Thermal conductivity of TIM: k=0.82W/m.K k=3.00W/m.K k=4.00W/m.K

64

f

34 5

10

15

X (mm)

20

25

0

5

10

15

X (mm)

20

25

Fig. 5. Effect of design parameters on the temperature distribution of the constant-width one-section microchannels cooling system, a. inlet jet width; b. outlet slot width; c. width of microchannels; d. depth of microchannels; e. thermal conductivity of TIM and f. best designs.

the microchannel width is decreased. Also, the lowest HCMJPV surface temperature occurs in the middle, where the inlet jet impinges the surface (x = 12.5). Then, the temperature of the cell base is increased gradually towards the water outlets. Table 1c indicates that reductions of about 5 °C in the area-weighted surface temperature (Ta) and 0.15 °C in its associated standard deviation (σa) are achieved as the microchannel width is decreased from 0.5 to 0.2 mm. Accordingly, enhancements of about 0.75 W for the generated power (Pg) and 0.61 W for net output power (Pnet) are attained. The difference between the augmentations in both powers is due to the increase in the pumping power (Pp) as the microchannel width decreases. As the microchannel width is decreased the microchannel thermal resistance (Rm) and total thermal resistance (Rt) decrease whereas the overall heat transfer coefficient (U) and the pressure drop (Δp) increase.

power as the microchannel depth is decreased. This is due to the increase in water velocity, which causes the pressure drop and consequently, the pumping power to increase. Therefore, the HCMJPV module that uses a cooling system with the smallest microchannel depth of 0.2 mm produces the largest generated power and the lowest net output power among the considered microchannel depth. Based on the data in Table 1d, a microchannel depth of 0.3 and 0.4 mm produce compromise results of net output power and temperature uniformity. 4.1.5. Effect of TIM properties Careful examination of the tabulated results revealed that the total thermal resistance is about three times the thermal resistance of microchannels. The main cause of that is the low thermal conductivity of the TIM material that seems to partially insulate the cell base from the microchannels in the cooling system. The available TIMs have various thermophysical properties than the one tested before by Riera et al. [9] and others. Table 2 lists the thermophysical properties of three considered materials with significant variations in their properties. Therefore, the effect of TIMs is studied for the two available commercial materials, namely GAP FILLER 4000, THERAM-A-GAP GELL (GELL 8010) in addition to the classical metal oxide filled silicone oil paste that was tested before. Each of the three materials was examined under the same design and boundary conditions. Although the TIM response is due to its thermal conductivity, specific heat, and mass density, the TIMs will be ranked according to their thermal conductivity as it is the

4.1.4. Effect of microchannel depth The depth of microchannels is studied for 0.2, 0.3, 0.4, and 0.5 mm. Fig. 5d shows that the average HCMJPV surface temperature increases from about 65 to 67 °C, and the fluctuations in the temperature distributions increase as the microchannel depth is increased from 0.2 to 0.5 mm. However, the effects of microchannel depth on the HCMJPV output power and the thermal characteristics of the HCMJPV cooling system are presented in Table 1d. The large increase in the pressure drop and pumping power overwhelms the enhancement of generated 8

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Changes in the microchannel thermal resistance and the pumping power for various TIMs are negligible. The increase in standard deviation as the thermal conductivity increases is in agreement with the finding reported by Riera et al. [40]. Thus, the use of the advanced TIM with k = 4 W/mK enhances the performance and characteristics of the cooling system over those with TIM of k = 0.82 W/mK substantially.

Table 2 Thermophysical properties of TIMs. Property

METAL OXIDE FILLED SILICONE OIL PASTE

THERAM-A-GAP GELL (GELL 8010)

2000 density, kg/m3 specific heat, J/kgK 712 thermal conductivity, W/mK 0.82

2700

GAP FILLER 4000 3100

1000 3

800 4

4.1.6. Closure Effects of the investigated design parameters on the thermal characteristics of the cooling system and the net output power of HCMJPV cells indicated the substantial effect of the thermal conductivity of TIM, followed by the width and depth of the microchannels. On the other hand, the temperature uniformity of the HCMJPV surface is most affected by the inlet jet width followed by the TIM and microchannel width and depth. The effect of outlet slot width is not important on either the output power or temperature uniformity. Based on the above discussion, a number of other combinations of design parameters have been exercised to achieve a maximum net output power. The combination with 1.0 and 0.75 mm for the inlet and outlet water slots and microchannel width and depth of 0.2 and 0.4 mm, respectively, achieves the highest net output power for TIM

most influential property. The simulation results are presented in Fig. 5e and Table 1e, where outstanding improvements in the system characteristics are noted. Table 1e indicates that the cell surface temperature decreases by over 24 °C, the overall heat transfer coefficient is doubled, and the total thermal resistance decreases to less than half its previous value with k = 0.82 W/mK. As the surface temperature decreases by about 24 °C, the generated and net output power increase by about 5.5% (3.74 W). On the other hand, the standard deviation is increased by about 0.26 and 0.31 °C for TIM with thermal conductivities of 3 and 4 W/mK. 72 71 70

TX (°C)

TX (°C)

71

a

Inlet jet width: 1.0mm 1.5mm 2.0mm 2.5mm

69 68 67

Outlet slot width of 0.5mm

66 72

TX (°C)

TX (°C)

First section width: 0.4mm 0.6mm 0.8mm

TX (°C)

68

Second section width: 0.2mm 0.3mm 0.4mm

66

First section width of 0.6mm

f

TX (°C)

69 Depth of microchannels: 0.2mm 0.3mm 0.4mm 0.5mm

66 63

57 48

g

72

70

60

h

45

66

Thermal conductivity of TIM: k=0.82W/m.K k=3.00W/m.K k=4.00W/m.K

60 54

TX (°C)

TX (°C)

Length of first section: 5.6mm (+1.0mm) 5.1mm (+0.5mm) 4.6mm (Base model) 4.1mm (-0.5mm) 3.6mm (+1.0mm)

67 78

d

72

70

68

Inlet jet width of 2mm

62 75

e

69

69

64

Second section width of 0.3mm

64 71

Outlet slot width: 0.50mm 0.75mm 1.00mm

72

70

66

70

68 74

c

68

b

48

42 The best designs (k=4W/m.K): Min. standard deviation Max. generated power Max. net ouput power Comparable design

39 36

42

33 0

5

10

15

X (mm)

20

25

0

5

10

15

X (mm)

20

25

Fig. 6. Effect of design parameters on the temperature distribution of the two stepwise microchannels cooling system, a. inlet jet width; b. outlet slot width; c. width of first microchannel section; d. width of second microchannel section; e. length of microchannel sections; f. depth of microchannels; g. thermal conductivity of TIM and h. best designs. 9

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with thermal conductivity of either 0.82 or 4 W/mK as listed in Table 1 (section f). Fig. 5f shows a reasonable temperature distribution of the HCMJPV surface using TIM of 4 W/mK. Table 1f indicates an enhancement of about 0.08–0.09 W in the net output power and larger standard deviations of the temperature of about 0.15–0.26 °C, compared to the corresponding values in Table 1e. The main cause of the increase in the net output power is the reduction in the pumping power by about 0.1 W.

around the middle of the section length (x = 12.5 mm), where the inlet water jet impinges the cell surface. The distribution of surface temperature with cooling system length varies according to the values of design parameters. The fluctuations of the surface temperature may be represented by the standard deviation (σmw) listed in Table 3. As can be seen in Fig. 6, some design parameters have a significant effect on surface temperature and its fluctuations than others. Also, the thermal characteristics of the cooling system (T, σ, Rt, Rm, and U) and the associated electrical power of HCMJPV (Pp, Pg, and Pnet) for the various effects of design parameters are listed in Table 3 (sections a-g). The symbols have the same meanings indicated in section 4. Again the small difference is noted between the average area-weighted surface temperature (Ta) and the average temperature in the middle width of the cooling system (Tmw) and between their associated standard deviations (σa and σmw). Since the main aim of using two-stepwise instead of the one-section constant-width microchannels is to reduce the temperature fluctuations along the cell surface, the investigation of the design parameters will focus on those parameters that produce the lowest standard deviation of surface temperature. Those parameters will be compromised with the parameters produced maximum generated and net output power of the HCMJPV cells.

4.2. Two-stepwise microchannels sections As stated in the previous section, the constant-width one-section microchannel cooling system that is based on the short fluid path enhances the thermal and electrical characteristics, considerably. Nevertheless, temperature uniformity over the cell surface can be further improved using two microchannel sections per the same short fluid path. Therefore, the proposed cooling system that is described in Section 2.1 and shown in Fig. 2c is examined. As stated before due to the similarity, a quarter of the cooling system may represent the full cooling system where a cooling inlet exists in the middle (x = 12.5), and two-fluid outlets occur at the edges (x = 0 and x = 25) of the quarter of the cooling system as shown in Fig. 3c. The characteristics of the cooling system with two-stepwise microchannel sections are investigated thoroughly in this section under the same boundary conditions reported for the constant-width one-section cooling system. The cooling system has many design parameters that affect the performance of the cooling system and consequently, the output of the HCMJPV cells. Fig. 6 shows the effects of various design parameters on the HCMJPV surface temperature and its distribution along the middle width of the cooling system. These include the width of inlet jets (Fig. 6a), width of water outlet slots (Fig. 6b), width of microchannels of the first (Fig. 6c) and second sections (Fig. 6d), length of the two microchannel sections (Fig. 6e), depth of microchannels (Fig. 6f) and TIM (Fig. 6g). In all curves, the temperature distribution is similar

4.2.1. Effect of inlet slot jet width As stated earlier, the cooling system has two inlet slots, and their width is investigated for 1.0, 1.5, 2.0 and 2.5 mm while the outlet slot width remains unchanged at 0.5 mm. The effect of inlet slot width on the thermal and electrical characteristics of the HCMJPV and the cooling system is presented in Fig. 6a, and Table 3a. Fig. 6a shows that all jets yield the lowest temperature at x = 12.5 mm except for jet width of 2.5 mm that provides the highest temperature at this position because of the reduction in the jet water velocity as the jet width is increased. The temperature distribution of the inlet slot width of 2 mm has the best temperature uniformity, which

Table 3 Effect of design parameters on the thermal and electrical characteristics of two stepwise microchannels cooling system. Effect

Value

Ta °C

σa °C

Tmw °C

σmw °C

Rt × 10−5 m2K/W

Rm × 10−5 m2K/W

U kW/m2K

Δp kPa

Pp W

Pg W

Pnet W

a.

1.0 1.5 2.0 2.5 0.5 0.75 1.0 0.4 0.6 0.8 0.2 0.3 0.4 −1.0 −0.5 Equal +0.5 +1.0 0.2 0.3 0.4 0.5 0.82 3.0 4.0

69.5 69.5 69.8 70.4 69.8 69.9 69.9 68.8 69.9 70.4 68.6 69.9 70.8 69.3 69.6 69.9 69.9 70.2 67.9 69.9 71.1 72.0 69.9 47.6 45.5

0.12 0.07 0.05 0.16 0.05 0.04 0.09 0.17 0.04 0.06 0.18 0.04 0.17 0.11 0.07 0.04 0.04 0.06 0.10 0.04 0.07 0.13 0.04 0.10 0.11

69.6 69.7 70.1 70.4 70.1 70.0 70.0 69.0 70.0 70.6 68.8 70.0 70.9 69.5 69.7 70.0 70.1 70.3 67.9 70.0 71.3 72.3 70.0 47.7 45.6

0.12 0.07 0.05 0.16 0.05 0.04 0.10 0.17 0.04 0.07 0.18 0.04 0.17 0.11 0.07 0.04 0.04 0.06 0.10 0.04 0.07 0.12 0.04 0.11 0.12

9.55 9.55 9.62 9.73 9.62 9.65 9.63 9.43 9.65 9.74 9.38 9.65 9.82 9.51 9.57 9.65 9.65 9.69 9.23 9.65 9.89 10.10 9.65 5.19 4.75

3.04 3.04 3.11 3.22 3.11 3.14 3.12 2.92 3.14 3.23 2.87 3.14 3.31 3.00 3.06 3.14 3.14 3.18 2.72 3.14 3.38 3.54 3.14 3.11 3.09

10.47 10.47 10.39 10.28 10.39 10.37 10.38 10.61 10.37 10.20 10.66 10.37 10.19 10.51 10.45 10.37 10.37 10.32 10.83 10.37 10.11 9.947 10.37 19.28 21.03

10.05 9.92 9.83 9.69 9.83 9.37 9.22 10.40 9.37 8.95 12.30 9.37 8.21 9.78 9.60 9.37 9.24 9.02 23.90 9.37 5.13 3.34 9.37 9.40 9.40

0.18 0.18 0.17 0.17 0.17 0.17 0.16 0.18 0.17 0.16 0.22 0.17 0.14 0.17 0.17 0.17 0.16 0.16 0.42 0.17 0.09 0.06 0.17 0.17 0.17

68.14 68.13 68.08 67.99 68.08 68.06 68.07 68.23 68.06 67.99 68.27 68.06 67.93 68.16 68.11 68.06 68.06 68.02 68.38 68.06 67.87 67.74 68.06 71.51 71.85

67.96 67.96 67.90 67.82 67.90 67.89 67.90 68.05 67.89 67.83 68.05 67.89 67.78 67.99 67.95 67.89 67.89 67.86 67.96 67.89 67.78 67.68 67.89 71.35 71.68

max. Pnet max. Pg min. σs comparable

42.2 41.2 45.5 42.6

0.14 0.21 0.11 0.12

42.4 41.4 45.6 42.8

0.14 0.20 0.12 0.13

4.10 3.91 4.75 4.19

2.43 2.25 3.09 2.53

24.42 25.59 21.03 23.88

13.38 31.81 9.40 12.25

0.24 0.56 0.17 0.22

72.36 72.50 71.85 72.29

72.13 71.95 71.68 72.07

b. c. d. e.

Inlet jet width (mm)

Outlet slot width (mm) First section width (mm) Second section width (mm) Length of first section (mm)

f. Channel depth (mm)

g.

h.

TIM k (W/mK) Best cooling systems

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is also confirmed by the lowest value of standard deviation (0.052) as listed in Table 3a. Table 3a indicated that the lowest HCMJPV surface temperature and the largest net output power are produced with an inlet jet width of 1.0 or 1.5 mm. However, the standard deviation of surface temperature decreases from jet width of 1 mm to reach its minimum value at jet width of 2 mm, then increases in inlet slot width of 2.5 mm. Small changes (less than 2%) of overall heat transfer coefficients, total and microchannel thermal resistances occur with the variation of the inlet jet width. Furthermore, the pumping power slightly decreases as the width of the inlet jet is increased. This is caused by the reduction in pressure drop through the inlet slot as the width is increased. To conclude this effect, the inlet jet width of 2 mm provides the best uniform temperature distribution over the cell base whereas the inlet jet width of 1.5 mm affords the best net output power of the HCMJPV cell.

0.4 and 0.8 mm cause a standard deviation larger than that caused by the width of 0.6 mm. As the width of the microchannels of the first section is increased, the surface temperature of the HCMJPV base increases. This is due to the decrease in the fluid velocity and the effective area of heat transfer which causes the heat exchange to decrease. Since the surface temperature increases as the microchannel width increases, the net output power is also decreased for this reason. This is because the effect of temperature increase overwhelms the effect of pumping power reduction. In conclusion, the microchannel width, which provides the best temperature uniformity, is 0.6 mm, whereas the best net output power is attained at the microchannel width of 0.4 mm. 4.2.4. Effect of the width of the second microchannel section The width of the second microchannel section is studied at 0.2, 0.3 and 0.4 mm (equivalent to microchannel pitch of 0.3, 0.4 and 0.5 mm) while the width of the first section is kept constant at 0.6 mm. The thermal and electrical characteristics of the HCMJPV using the cooling system of different width of the second microchannel section are presented in Fig. 6d, and Table 3d. Fig. 6d shows that increasing or decreasing the width of the second microchannel section from 0.3 mm causes higher fluctuations in the surface temperature. This is because microchannels with a width of 0.2 mm cause a high rate of cooling in the second section than in the first section and vice versa for microchannels with a width of 0.4 mm. It seems that the best temperature uniformity is achieved when the microchannel width of the second section is half that of the first section. The effect of the microchannel width of the second section on the characteristics of the HCMJPV cooling system is listed in Table 3d. Microchannels of the second section with a width of 0.2 and 0.4 mm cause a standard deviation of temperature higher than that provided by the width of 0.3 mm. As the width of the second microchannels section is increased, the temperature of the studied surface increases. This is due to the reduction in the fluid velocity caused by the increase in the cross-sectional area of flow, which reduces the convection heat transfer coefficient in the second section. This, in turn, causes poor temperature distribution. The net output power decreases slightly as the width of the microchannels of the second section increases. Again this is because the effect of temperature increase overcomes the effect of pumping power reduction. In summary, the second section microchannel width of 0.3 mm provides the best temperature uniformity, and the width of 0.2 mm provides the best net output power.

4.2.2. Effect of outlet slot width The cooling system has one common outlet in the middle of the system and two other rear outlets. Outlet water width is changed from 0.5 to 1 mm with a constant step of 0.25 mm while the inlet width remains constant at 2 mm. The results of numerical simulation of those outlet water slots are presented in Fig. 6b, and Table 3b. In general, the effect of the outlet slot width is lower than the effect of inlet jet width. Fig. 6b shows that the temperature decreases slightly around the middle length of the section as the outlet water width is increased. This is because the distance between the two microchannel sections is decreased, which causes more turbulence to take place and the surface temperature decrease. The surface temperature near the water outlets increases as the outlet width is increased. This is because of the reduction in the outlet water velocity as the width is increased. The temperature close to the rear outlets decreases, particularly for small width, due to the increase in turbulence, which enhances the convection heat transfer coefficient. Table 3b indicated that the outlet slot width of 0.75 mm provides the lowest standard deviation of surface temperature compared to the water outlet width of 0.5 or 1 mm. As the water outlet width is increased the pressure drop and pumping power slightly decrease. Net output power is not sensitive to the investigated values of outlet slot width. In conclusion, the outlet width that causes the best temperature uniformity is 0.75 mm as it provides the lowest standard deviation of temperature with reasonable surface temperature and pressure drop. However, additional combinations of inlet and outlet slot width have been exercised where no combination achieved better temperature uniformity than the combination of 2.0 and 0.75 mm for the inlet and outlet water slots, respectively.

4.2.5. Effect of microchannels length Fig. 3c shows that the model quarter has two stages, where each one has two-stepwise microchannel sections; each section is 4.6 mm long. The effect of the length of the two-sections of microchannels is studied. Each section length is increased by 0.5 mm (10.87%) and 1 mm (21.74%) while the length of the other sections is decreased by the same value. The results of the effect of section length are presented in Fig. 6e, and Table 3e. Fig. 6e shows insignificant changes in the temperature distribution when the length of the first section is increased, and the second section is decreased by 0.5 mm. On the contrary, the decrease of the first section and increase of the second section length by 0.5 mm reduces the surface temperature by about 0.4 °C. Table 3e indicates that as the length of the first section is increased and the length of the second section is decreased the pressure drop and the pumping power decrease. However, net output power slightly decreases because the effect of temperature increase is more than the effect of pumping power decrease. The standard deviation increases slightly for any change of the first and second section length. As the length of the first section is increased the surface temperature increases. This indicates that the cooling effect of the second section is greater than that of the first section. In conclusion, the lengths of the sections which provide the best temperature uniformity are the base model which has equal lengths of each section (4.6 mm) as it has the lowest

4.2.3. Effect of the width of the first microchannel section The stepwise microchannels cooling system has two steps of microchannels with equal length but with different width. The width of the first section of the microchannel is studied for values of 0.4, 0.6 and 0.8 mm (equivalent to microchannel pitches of 0.5, 0.7 and 0.9 mm) while the width of the second microchannel section is kept unchanged at 0.3 mm (pitch of 0.4 mm). The variations in the thermal and electrical characteristics of the cooling system with the first section width are presented in Fig. 6c, and Table 3c. Fig. 6c shows that the smallest microchannel width of 0.4 mm attains the lowest temperature as it causes the highest rate of cooling in the first microchannel section. This is due to fluid velocity increase which causes the convection heat transfer coefficient to increase. Also, this case of 0.4 mm width has the largest number of fins among the studied cases, and the rate of cooling increases as the fin number is increased. However, this microchannel width causes the worst temperature uniformity among the tested width while the microchannel width of 0.6 mm attains the best temperature uniformity. Table 3c lists the characteristics of HCMJPV cells using the cooling system of different tested microchannel width. Microchannels width of 11

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standard deviation of temperature (0.038 °C). The sections lengths which have the best net output power is 3.6 mm (-21.74%) for the first section and 5.6 mm (+21.74%) for the second section.

4.2.8. Closure The effects of seven design parameters on the thermal characteristics of the cooling system and the net output power of HCMJPV cells are discussed in this section. Evaluations of the design parameters according to the magnitude of their effects define the most important ones. The net output power and the surface temperature of the cells are significantly affected by the thermal conductivity of TIM, followed by the depth and width of the microchannels. The effects of inlet jet width and microchannel length are moderate while the effect of outlet slot width is insignificant. On the other hand, the temperature uniformity of the cell surface is most affected by the microchannel width followed by the inlet jet width and the microchannel depth and length. Fortunately, the effect of thermal conductivity of TIM on the temperature uniformity of the cooling system with two-stepwise microchannels is moderate. Again, the effect of outlet slot width on the temperature uniformity is insignificant.

4.2.6. Effect of microchannels depth The depth of microchannels is studied from 0.2 to 0.5 mm with a constant step of 0.1 mm. The thermal and electrical characteristics of the cooling system are presented in Fig. 6f, and Table 3f. Fig. 6f shows that the HCMJPV surface temperature increases from about 68 to 72 °C as the microchannel depth is increased from 0.2 to 0.5 mm. This means the decrease of microchannel depth enhances the rate of cooling that reduces the surface temperature by about 4 °C. Table 3f indicates that the depth of microchannel has a substantial effect on pressure drop, pumping power, and surface temperature of HCMJPV cells. As the depth of microchannel is decreased the water velocity increases and causes the pressure drop to increase. The lowest value of standard deviation is achieved at a depth of microchannels of 0.3 mm. The generated power shows about 1.0% reduction while the net output power experiences a slight decrease (about 0.4%) as the microchannel depth is increased from 0.2 to 0.5 mm. This is due to the combined effect of generated power and pumping power increase. Based on the above discussion and within the investigated range of microchannel depth, the depth which provides the best temperature uniformity is 0.3 mm and the depth which provides the best net output power is 0.2 mm.

4.2.9. Identification of the best designs characteristics Based on the reported results in Section 4.2, four main cooling systems may be proposed for further considerations. The first two systems yield the maximum net output power and generated power (lowest surface temperature); the third system yields the best temperature uniformity (minimum standard deviation) of the HCMJPV and the fourth system yields comparable results to the three systems. Subsequently, those cooling systems are compared to select the best one that improves the thermal and electrical performance of HCMJPV and avoid any limitations of those designs. The characteristics of these cooling systems are evaluated using the TIM with thermal conductivity of 4 W/mK. Table 4 lists the specifications of the proposed cooling systems, and Table 3h gives the thermal and electrical characteristics of the systems. Table 4 indicates that the specifications of the two cooling systems, which produce high power are similar except for the microchannel depth. Maximum net output power is produced for the depth of 0.3 mm, whereas the maximum generated power is produced for the depth of 0.2 mm. On the other hand, the lowest standard deviation is produced for microchannels width of 0.6 and 0.3 for the first and second sections, respectively. This design is developed to improve its characteristics by changing the width of the first section to 0.4 mm and width of the second section to 0.2 mm. This cooling system yields compatible characteristics to the other three systems and designated as a comparable design in Tables 3h and 4. Comparing the characteristics of the considered three proposed cooling systems listed in Table 3h indicates that the system yields the largest generated power, achieves the lowest surface temperature among the systems. This system also requires the largest pumping power. Thus, its net output power is not the largest. On the other hand, the cooling system that yields the largest net output power achieves lower surface temperature by about 4.23 °C and higher net output power by about 0.365% than the system of the lowest standard deviation of temperature. The small difference in the net out power between the HCMJPV working with the four cooling systems is due to the larger pressure drop and pumping power required by the system of maximum generated power which increases by about 0.394 W (238.3%). The comparable design yields higher net output power by

4.2.7. Effect of thermal interface material (TIM) It has been shown in Section 4.1.5 that the use of TIMs with k = 3 and 4 W/mK enhances the performance and characteristics of the cooling system over those with TIM of k = 0.82 W/mK substantially. Therefore both TIMs were, also, exercised with the two-stepwise microchannel cooling system and the simulation results are presented in Fig. 6g, and Table 3g. It is clear that significant improvements in the thermal characteristics of the cooling system and the output power of the HCMJPV cells are observed. In particular, the HCMJPV surface temperature has a considerable reduction of about 24.5 °C (Fig. 6g) as the thermal conductivity of the TIM increases from 0.82 to 4 W/mK. The results reported in Table 3g indicate that TIM has an outstanding effect on the thermal and electrical characteristics of the HCMJPV cells and its cooling system. As the TIM thermal conductivity is increased from 0.82 to 4 W/mK, the total thermal resistance decreases to less than half its value, and the overall heat transfer coefficient is doubled. As the surface temperature decreases by about 24.5 °C, the generated and net output power increase by about 3.79 W (5.6%) for TIM with thermal conductivity of 4 W/mK compared to that with k = 0.82 W/mK. In conclusion, the TIM which provides the best cooling and electrical characteristics of HCMJPV cells, is GAP FILLER 4000 with thermal conductivity of 4 W/mK. As discussed in Section 4.1.5, the use of TIM with high thermal conductivity increases the fluctuations in the temperature distribution of the HCMJPV base, which is represented by the standard deviation of temperature. It was shown that as the thermal conductivity of TIM increases from 0.82 to 4 W/mK, the standard deviation of constantwidth one-section microchannels increases by an average value of 0.31 °C. But the same change of thermal conductivity of TIM increases the standard deviation in the case of two-stepwise microchannels by only 0.076 °C. In light of the results reported by Riera et al. [40], the standard deviation increase in both cases is considered very small. This indicates that the use of a short cooling fluid path enables the use of high conductivity TIM with a limited increase in the standard deviation of temperature, particularly in the case of the cooling system with twostepwise microchannels. In conclusion, the HCMJPV surface temperature decreases by about 24.5 °C with a small increase in the standard deviation (0.076 °C) when TIM with thermal conductivity of 4 W/mK is used in the cases of short fluid path cooling system.

Table 4 Design parameters of the best cooling system designs.

12

Design parameters (mm)

Max. Pnet

Max. Pg

Min. σ

Comparable

Inlet jet width Outlet slot width Width of first section Width of second section Depth of microchannels Length of first section Length of second section

1.5 0.5 0.4 0.2 0.3 3.6 5.6

1.5 0.5 0.4 0.2 0.2 3.6 5.6

2.0 0.75 0.6 0.3 0.3 4.6 4.6

2.0 0.75 0.4 0.2 0.3 4.6 4.6

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Table 5 Comparison between Riera’ design and cooling systems for maximum net output power with TIM thermal conductivity of 0.82 W/mK. No. of sections

Conditions

Width mm

Five Riera’ design 1.53–0.14 One same velocity 0.2 Two same velocity 0.4–0.2 Two half velocity 0.4–0.2 Comparison between Riera’ design and one constant section Comparison between Riera’ design and two stepwise microchannels (same velocity) Comparison between Riera’ design and two stepwise microchannels (half velocity) One section with Large width 1 1.0 Large width 2 1.5

Tmw °C

σmw °C

Rt × 10−5 m2K/W

Rm × 10−5 m2K/W

U kW/m2K

Δp kPa

Pp W

Pg W

Pnet W

77.5 66.2 66.6 72.8 −11.3 °C −10.9 °C

0.90 0.49 0.06 0.20 −0.41 °C −0.84 °C

11.10 8.88 8.94 10.10 −20.0% −19.46%

4.68 2.37 2.43 3.64 −49.4% −48.08%

9.01 11.26 11.19 9.85 +25.0% +25.43%

28.97 9.17 13.40 4.85 −68.3% −53.7%

0.26 0.16 0.24 0.09 −36.6% −7.49%

66.89 68.65 68.61 67.67 +2.63% +2.57%

66.63 68.49 68.37 67.58 +2.79% +2.61%

−4.7 °C

−0.70 °C

−9.0%

−22.2%

+9.37%

−83.3%

−66.5%

+1.17%

+1.42%

74.2 75.2

0.58 0.62

10.43 11.00

3.92 4.20

9.591 9.367

5.269 4.935

0.093 0.087

67.45 67.26

67.36 67.17

the present cooling system. The comparable standard deviation of temperature is achieved with 35.5 °C lower surface temperature and 175.8% higher overall heat transfer coefficient. About 5.62 W (8.44%) larger net output power than Riera’s design is achieved for the present cooling system. This excess power yields about 820.5MWh per square meter of cells, based on ten working hours daily during 25 years lifetime of cells. In a trial to reach the same characteristics of Riera’s design with the concept of the short fluid path, the microchannels were changed from micro-scale to mini-scale, where the width increases to 1 and 1.5 mm. Table 5 indicates that the constant-width cooling system using the short fluid path concept still provides better characteristics than the five stepwise microchannels, even with such wide mini channels. In conclusion, the cooling of HCMJPV cells may be achieved using a more efficient and simpler system that is based on the concept of the short fluid path and constant-width microchannels.

0.54% and lower HCMJPV temperature by 2.83 °C than the system of the lowest standard deviation with a minute increase in the standard deviation of temperature. 4.3. Comparison with existing design The critical review in Section 1 revealed that the most advanced and efficient cooling system for HCMJPV is developed and reported by Riera et al. [9]. Therefore, a comprehensive comparison between the characteristics of the cooling systems developed during the present work and that in [9] is conducted in this section. In order to evaluate the geometrical design and the concept of short water path of the present work, the comparison is performed first, while the present cooling system uses TIM with k = 0.82 W/mK (Table 5). Then, a comparison with the new TIM with thermal conductivity of 4 W/mK (Table 6) is performed to assess the final achievements of the present work. Tables 5 and 6 list the numerical values of the comparison where “+” sign means higher than and “−” sign lower than Riera’s cooling system.

4.3.2. Comparison between Riera’s design and two-stepwise microchannels Table 5 presents the characteristics of Riera’s design along with those of the present two-stepwise microchannel cooling system that yields the maximum net output power. Both systems are compared at the same water velocity used in test 1 (Riera’s system) and at half that velocity. The other boundary conditions of both systems are remain the same with the inlet water temperature of 21.7 °C, heat flux of 50 W/ cm2, and flow rate of 8.8 mL/s. Concerning Table 5, the comparison between the two-stepwise cooling system and Riera’s design under the same inlet water velocity indicates better characteristics for the first. This is confirmed by lower surface temperature by 10.88 °C, lower standard deviation of temperature by 0.842 °C, lower pressure drop by about 53.7%, lower pumping power by 7.49%, higher net output power by 2.61%, lower thermal resistance by about 19.46% and higher overall heat transfer coefficient by about 25.43%. In addition, the comparison between Riera’s design and present system under half the velocity reveals marginally better characteristics of the present cooling system. In particular, lower pressure drop and pumping power and better temperature

4.3.1. Comparison between Riera’s design and constant-width microchannels Table 5 presents the characteristics of Riera’s design along with those of the present cooling system that yields the maximum net output power using TIM with thermal conductivity of 0.82 W/mK. Comparing the results of the one-section microchannel with those of the five stepwise microchannels [9] indicated that the surface temperature and its standard deviation of the first, are lower than the second by 11.3 and 0.41 °C, respectively. Also, the generated and the net output power and the overall heat transfer coefficient of the one-section cooling system are better than those in [9]. Specifically, the generated power is better by 2.63%, the net output power by 2.79%, the overall heat transfer coefficient is better by about 25.0% and the thermal resistance of microchannels is better by 49.4%. Table 6 provides the same comparison between Riera’s design and the present cooling systems, but with TIM of k = 4 W/mK. Comparing characteristics of Riera’s design with those of the constant-width onesection cooling system revealed the significant and outstanding effect of

Table 6 Comparison between Riera’ design and present cooling systems for maximum net output power with TIM thermal conductivity of 4 W/mK. No. of sections

Design Conditions

Width mm

Five Riera’ design 1.53–0.14 One Maximum Pnet 0.2 0.4–0.2 Two Maximum Pnet Comparison between Riera’ design and one constant section Comparison between Riera’ design and two stepwise microch. Comparison between one and two sections cooling systems

Tmw °C

σmw °C

Rt × 10−5 m2K/ Rm × 10−5 m2K/ U W W kW/m2K

Δp kPa

Pp W

Pg W

Pnet W

0.26 0.16 0.24 −36.80% −7.65%

66.89 72.42 72.36 +8.27% +8.18%

66.63 72.25 72.13 +8.44% +8.25%

77.5 0.90 11.10 42.0 0.91 4.02 42.4 0.14 4.10 −35.5 °C +0.01 °C −63.78% −35.1 °C −0.76 °C −63.11%

4.68 2.36 2.43 −49.57% −48.01%

9.01 24.85 24.42 +175.8% +171.1%

28.97 9.15 13.38 −68.41% −53.81%

+0.38 °C −0.77 °C +0.02%

+3.09%

−1.73%

−46.21% −46.21% −0.08% −0.17%

13

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uniformity (lower standard deviation of temperature) than Riera’s design (Table 5). Therefore, the comparison of the present two-stepwise microchannels cooling system under the same velocity and half the velocity revealed the better characteristics of the present cooling systems over Riera’s design. In addition, the comparison is conducted between the characteristics of Riera’s design and those of the present cooling system using TIM of k = 4 W/mK under the same inlet water velocity (Table 6). The present two-stepwise cooling system achieves much better characteristics than Riera’s design in terms of lower surface temperature by 35.12 °C, lower standard deviation of temperature by 0.76 °C, lower pressure drop by about 53.81%, lower pumping power by 7.65%, higher net output power by 8.25%, lower thermal resistance by about 63.11% and higher overall heat transfer coefficient by about 171.1%.

cooling system is demonstrated in Fig. 7a as it varies from 42.0 to 42.6 °C, whereas that of one-section varies from 40.5 to 43.3 °C (Fig. 8a). In both cooling systems, the rear ends close to the outlet water slots are slightly higher than the rest of the HCMJPV surface. On the other hand, the velocity contours for both cooling systems are shown in Fig. 7b and 8b. The lowest velocity occurs at the inlet jet locations and the rear ends of the cooling systems. It is clear that the velocity in the second section of the two-stepwise cooling system (Fig. 7b) is larger than that in the one-section constant-width system (Fig. 8b). Although the width of the microchannels is the same for the second section and the constant width systems, the depth of the microchannels in the first is 0.3 mm and in the second is 0.4 mm. This causes the noticed difference in velocity between the systems. Finally, the pressure contours in Fig. 7c and 8c show a larger pressure difference in the case of twostepwise microchannels than that in the case of one-section constant width microchannels. This is mainly attributed to the small depth of microchannels in the case of stepwise microchannels.

4.3.3. Comparison between one and two microchannels sections Table 6 provides the comparison between the characteristics of the cooling systems with constant-width one-section and two-stepwise microchannels cooling systems using TIM with thermal conductivity of 4 W/mK. It is indicated that the constant-width one-section microchannel with a width of 0.2 mm achieves slightly better results than the two-stepwise microchannel sections with widths of 0.4 and 0.2 mm. The only exception is that the two-stepwise microchannels cooling system achieves its main purpose and attains a lower standard deviation of temperature than the constant-width microchannel by about 0.77 °C. In other words, the standard deviation of the two-stepwise microchannels is about 1/6th that of the constant-width cooling system. Also, the net output power of the two systems is almost equal, as the difference is about 0.12 W (0.17%). Figs. 7 and 8 compare the temperature, velocity, and pressure contours of both one-section and two-stepwise microchannels cooling systems. The excellent temperature uniformity of the two-stepwise

4.3.4. Cost considerations The cost of PV cooling consists of the initial, running, and maintenance costs of the cooling system of the solar module. Since the materials of both cooling systems are the same, the initial cost is mainly for the production of the cooling system of the solar module. The present cooling system consists of four sections of constant-width microchannels, whereas the state of the art cooling system contains ten sections of various microchannels width from 1.53 to 0.14 mm. Thus, the present cooling system is simpler than the state of the art cooling system, and the cost of production and maintenance of the present simpler cooling system is lower than the other cooling system. Since the running cost of the cooling system is considerably larger than the initial cost, the reported work in literature focuses only on the pumping power [12,42] on the module level. The literature compares the pumping power of different systems and relates the cost to the ratio of pumping

(a) HCMJPV temperature at Z=-1.6mm

(a) HCMJPV temperature at Z=-1.6mm

(b) Water velocity distribution at Z=0.4mm

(b) Water velocity distribution at Z=0.4mm

(c) Pressure distribution at Z=0.4mm

(c) Pressure distribution at Z=0.4mm

Fig. 7. Contours of two-stepwise microchannels cooling system.

Fig. 8. Contours of constant-width one-section microchannels cooling system. 14

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• The net output power and the surface temperature of the HCMJPV

power. The comparison between the present work and the state of the art cooling system revealed that the pumping power of the present system (one-section) is lower than the stated system by 36.8% (Table 6). Therefore, the cost of the pumping power will be less than 2/ 3 of the state of the art system in addition to the lower initial and maintenance costs, as discussed earlier. In conclusion, the proposed cooling system costs less, and when installed on the PV cell, it produces higher net output power by 5.62 W (8.44%) and requires less pumping power by 0.1 W (36.8%) than the state of the art cooling system [9]. In conclusion, the proposed constant-width one-section microchannel cooling system with a width of 0.2 mm that is based on the idea of shortening the length of the cooling water path is the simplest design compared to the two or five stepwise microchannels. Thus, the production, operation, and maintenance costs of this system will be considerably lower than any stepwise system. Moreover, this simpler system achieves the best thermal and electrical characteristics among the considered systems as revealed in Tables 5 and 6. It achieves the highest net output power and overall heat transfer coefficient with the lowest thermal resistance. On the other hand, the two-stepwise microchannels cooling system that is based on a short fluid path concept achieves the best temperature uniformity among the considered systems as its standard deviation is about 1/6th that of the constant-width one-section microchannels.

•

cells are significantly affected by the thermal conductivity of TIM, followed by the depth and width of the microchannels whereas the effects of inlet jet width and microchannel length are moderate and the effect of outlet slot width is not important. Temperature uniformity of the HCMJPV surface is most affected by the microchannel width followed by the inlet jet width and the microchannel depth and length for the two-stepwise microchannels cooling system.

CRediT authorship contribution statement Hosny Abou-Ziyan: Conceptualization, Methodology, Writing original draft, Writing - review & editing, Project administration, Supervision. Mohammed Ibrahim: Methodology, Investigation, Software, Validation, Data curation, Writing. Hala Abdel-Hameed: Supervision, Software, Writing, Visualization. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

5. Conclusion

References

Two simple, effective, and economic microchannel cooling systems for high-concentration multi-junction photovoltaic (HCMJPV) cells are developed during this work. While the state of the art cooling system used five stepwise microchannels per fluid path, the developed cooling systems are using either one or two microchannel sections with a short fluid path. The results confirm that the short fluid path enhances the thermal characteristics of the cooling systems that allow the HCMJPV cells to generate larger power and produce larger net output power. The design of the new systems was based on a comprehensive investigation of the effects of various design parameters on the characteristics of the cooling system. Based on the reported results, the following conclusions may be drawn:

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• Two-stepwise microchannels cooling system achieves the best tem-

• •

• •

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