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Coupled natural convection and radiation heat transfer of hybrid solar energy conversion system
International Journal of Heat and Mass Transfer 107 (2017) 468–483
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Coupled natural convection and radiation heat transfer of hybrid solar energy conversion system Haolun Xu a, Hsiu-Hung Chen a, Sheng Wang a, Zheng Li a, Kuojiang Li a, Greg Stecker b, Wei Pan b, Jong-Jan Lee b, Chung-Lung Chen a,⇑ a b
Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA Sharp Laboratories of America, Camas, WA 98607, USA
a r t i c l e
i n f o
Article history: Received 28 July 2016 Received in revised form 17 November 2016 Accepted 18 November 2016
Keywords: Natural convection Radiation interaction Inclined heatsink Funnel effect
a b s t r a c t A hybrid solar energy conversion system described in this study is designed to exceed the efficiency of each type of technology alone by combining advantages of concentrated solar power (CSP) technology and high performance concentrated photovoltaic (CPV) cells. This hybrid system can be tilted at different inclination angles to track the solar power at different latitudes and different time zones. Thermal management is important to CPV cells, as 1000 concentrated solar radiation onto CPV not only leads to higher performance but also generates more waste heat flux. In this work, the effects of natural convection with and without the interaction of surface radiation in the system consisting of PV cells, optical funnels and a heatsink were numerically investigated with an experimentally validated model. The influence of inclination on the overall flow structure and heat transfer was examined. Under the effect of these funnels, the heat transfer was enhanced when the heat was transferred through PV cells to funnels. At the same time, the separation flow between the spaces of funnels would take the heat to the ambient. The minimum average temperature of surrogate PV cells occurred at the inclination angle of 60°. When the inclination angle varied from 0° to 90°, the stagnation point moved from the downward surface of the heat sink towards the edge of heat sink. From 0° to 60°, the stagnation point was at the downward surface of heat sink and there was a dramatic decrease in the average temperature of the surrogate PV cells. When inclination angles were less than 60°, except that there was a separation region above substrate, the side flow could flow in and out freely between adjacent funnels and then formed a pair of separation bubble, or spiral node, on top of the funnels. At these inclination angles, flow velocity was found to be the dominant factor influencing heat transfer because the flow pattern (separation bubble) was the same on top of the funnels. However, at inclination angles of 60° to 90° the stagnation point occurred at the edge of the heat sink, and the surrogate PV temperature increased. When the inclination angle reached 90°, the flow was trapped and recirculated among funnels, and the vortical wake on top of the funnel disappeared. It can be concluded that from 60° to 90°, the dominant factor influencing heat transfer is funnel effect because the flow velocity stayed almost constant. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Solar energy can be captured either as electricity by photovoltaic (PV) devices or as heat by concentrated solar power (CSP) systems. The former means are considered cost-effective, but cannot utilize the thermal spectrum. In addition, the storage of electricity is challenging. The latter has advantages of generating electricity from the stored heat (usually in the form of molten salt) even when the sun is not shining, but is pricy in construction and
⇑ Corresponding author. E-mail address: [email protected] (C.-L. Chen). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.11.061 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
operation. Both CSP and PV utility-scale power stations have been in operation at various locations around the world since the 1980s. Currently, the largest CSP installation is the Solana Generating Station located near Gila Bend, AZ; a parabolic trough field with capacity of 280 MW and associated thermal storage. On the other hand, the largest PV installation is at the California Valley Solar Ranch: a 250 MW ‘‘solar farm” in San Luis Obispo County, CA. Different from CSP plants that collect heat energy, systems with PV cells generate low-grade waste heat while solar energy is converted into electricity. Extreme temperature increase in PV cells (when waste heat cannot be dissipated efficiently) will not only lower the light-electricity conversion efficiency, but also damage
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Nomenclature qc k W
convective heat transfer rate (W/m2) thermal conductivity (W/(mK)) heatsink width (m)
the cell and other module materials. Several papers [1–5] have addressed various ways for the cooling of PV cells. Recently, Tari [6,7] showed the possibilities of dissipating unwanted heat by the interaction of natural convection with thermal radiation for the vertical orientation of plate-finned heat sinks in two separate applications. Leung and Probert [8,9] experimentally studied the effect of orientation on heat exchangers. They found that the vertical and upward facing horizontal orientations of a heat sink were preferred for maximizing the natural convection heat transfer rate. As a result, these two orientations were investigated extensively under convective and radiative heat transfer effect. However, there are only a few works investigating inclined orientations under the interaction of natural convection and surface thermal radiation [10,11]. In 2014, Sharp Labs of America collaborated with University of Arizona and University of Missouri-Columbia aiming to combine advantages of CSP and PV technologies to achieve greater exergy, better dispatchability, and higher capacity factor at more reasonable costs than can be achieved by either technology alone. High heat flux waste heat need to be dissipated with the solar energy system running. Therefore, high efficiency cooling is required to keep the solar energy system working safely. To gain high PV cell efficiency, plated-finned heat sinks under forced convection are employed to keep our system working at a targeting low temperature of 75 °C. However, for the purposes of avoiding the maximum temperature of surrogate PV exceed the melting temperature of solder (167 °C) when any fan fails, heat rejection by natural convection and radiation need to be considered in order to ensure the all-time reliability of operation. Natural convection plays a key role in the fan failure condition. Various numerical methods have been employed to solve the different natural convections [12–17]. In order to estimate the heat transfer performance on such a cooling assembly, researchers have derived the empirical heat transfer rate and Nusselt number with the relationship of some non-dimensional numbers. Bejan and Lee [18] derived an analytical solution of the convection heat transfer rate for packages of electronic components, and found that if the heat transfer mechanism was natural convection, the maximum density of heat generating electronics (or Q/HLW) was proportional to (Tmax T1)3/2 and H1/2. H, L and W are the fin height, the heatsink length and heatsink width, respectively. Mehrtash and Tari [10] scaled the equation with a factor obtained from the analysis of the simulation data which is (H/L)0.32. Leung and Probert [8] obtained a similar relation in which they had an exponential fin effectiveness term that can be neglected in the cases where fins have high thermal conductivity. They used equations to calculate the average Nusselt number based on the product of modified average Grashof number with Prandtl number. However, these reports do not include the inclination angle effect. Inclined orientations are important for hybrid solar energy conversion system for at least two reasons: (i) at different latitudes and different time zones, the hybrid solar system needs to be tilted at different inclination angles in order to track solar power, thus the maximum temperature at the assembly needs to be estimated; (ii) because funnels are used on top of PV cells for optical purposes, which can affect the overall flow structure, natural convection and heat
Tw Ta
average temperature of surrogate PV cells (°C) ambient temperature (°C)
transfer need to be further investigated. In order to obtain the heat transfer performance of heat sink cooling assembly with different inclination angles, Fujii and Imura [19] studied the relation of Nu vs GrPr for the horizontal plate facing downwards and when the flat plate was inclined from the vertical. When the heat sink was inclined from the vertical, Tari and Mehrtash [20] assumed that the flow structure stayed the same. The only change was in the body force, where the effective body force became qgcosh. With the same rationale, they suggested the vertical case correlation for plate fin heat sinks with the same modification was expected to be valid at small inclination angles, as long as the flow structure stayed the same. However, their equation can only be applied when there is convective heat transfer effect. If the surface thermal radiation is included, their equations are not applicable to calculate the corresponding Nusselt number. In this study, we validated our simulation results with the case when there was adiabatic boundary condition on top of cooling assembly without funnels. Then we applied our validated model to investigate the heat transfer performance of cases with funnels under various inclination angles. The average temperature of surrogate PV and average Nusselt number of cooling assembly were compared and discussed. We also studied the relationship between heat transfer and flow pattern at the heatsink side and funnel side.
2. Numerical method The assembly of PV cells cooling in hybrid solar energy conversion system is schematically depicted in Fig. 1. Fig. 1a is the isometric view of the assembly and Fig. 1b is the side view from the cutting plane with dimensions. The heat sink was provided by Aavid Thermalloy, LLC. The funnels were provided by Sharp Laboratory of America. The numerical model dimensions of our cooling assembly were listed in Table 1. In this system, thermal management is important to PV cells, as 1000x concentrated solar radiation onto PV cells not only leads to higher performance but also larger heat loads (heat flux on PV cells is over 105 W/m2). The module includes an optimized plate-fin heat sink, an aluminum substrate, fourteen equally spaced PV cells located on the substrate, and fourteen funnels attached to the surface of PV cells. The assembly shown in Fig. 1 is placed in a cubical room filled with air, with walls that are maintained at a constant temperature. The width, length and height of this cubical room are applied as 148.8 mm, 400 mm and 400 mm. Because the Rayleigh number of our cooling assembly is estimated to be 3.2 109 under a total power input of 84 W at the PV cells, the use of proper turbulence model to simulate this process is needed. In the analysis (with ANSYS CFX), steady state solutions were obtained by using the Shear Stress Transport Model (SST) with natural convection and surface to surface radiation. From the ANSYS user manual for natural convection [21], they applied four turbulent models (Standard and RNG k-epsilon, Standard and SST k-omega) to study the natural convection in a tall cavity and compared with the experimental data [22]. SST model shows better agreement with their experiment. Thus, we used SST model for our study. Boussinesq approximation was applied to assume the
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Fig. 1. Assembly view of photovoltaic cells cooling in hybrid solar energy conversion system.
Table 1 Detailed dimensions of funnel and heat sink. Parameter of heat sink and fin
Dimension (mm)
Parameter of substrate and PV cells
Dimension (mm)
Parameter of funnel
Dimension (mm)
Width of heat sink Height of heat sink Length of heat sink Width of fin Gap between fin Height of fin
50 35 200 1 2 32
Width of substrate Height of substrate Length of substrate Width of PV cell Length of PV cell Height of PV cell
50 6 200 5.5 5 0.5
Height of funnel Width of funnel base Length of funnel base
29.25 14.5 13.5
fluid density is constant in terms of the momentum equation except the body force term. The material properties applied for the heatsink and PV cells are aluminum; funnels are assumed to be glass flint. It is known that surface emissivity limits the amount of radiation heat transfer. For our heatsink, we used the emissivity of 0.85, which is suggested by Aavid Thermalloy, LLC. The emissivity of the funnel is given from the property of glass window (0.9). An unstructured mesh with a very fine grid combined with inflation layers around the heat removal assembly and a coarse grid for the rest of the room is employed. Grid independence study was achieved by examining three different grid densities with
Fig. 2. Mesh independence study.
3737,432, 8353,449 and 18601,158 cells. The local temperature along the center of the substrate for three different meshes is shown in Fig. 2. The local temperature calculated in the cases of 8,353,449 and 18,601,158 cells overlap with each other. We, therefore, selected the medium density mesh, i.e., the one with 8,353,449 cells, as it yielded results matching to those of the fine mesh. The boundary-layer meshes (inflation) were applied at the interface between the heatsink and air, as well as funnels and air. There are fourteen layers around each fin and Y+ around each fin is 0.420. The wall function in ANSYS CFX for SST k x turbulence model was set to be automatic. This enabled the near wall treatment to automatically switch from wall function to a low-Re near wall formulation while the mesh was refined. ANSYS CFX was used in solving the continuity, momentum and thermal energy equations for air and the heat conduction equation within the solids. To handle the radiative heat transfer, the discrete transfer model with surface to surface setup was applied. In our case, radiation was only passed from wall to wall and the fluid did not participate. This saves computational time and is appropriate since air does not absorb or emit significant thermal radiation on these length scales. The present study investigates the steady-state heat transfer performance covering the inclination angle 0°, 10°, 20°, 30°, 45°, 60°, 70°, 80°, and 90°. The inclination angle of 0° represents horizontal and 90° represents vertical for the cooling assembly. The case in Section 2.1 has been applied to adiabatic boundary condition on top of our cooling assembly without funnels in order to validate with our experiment. In the case at Section 3.1, the cooling assembly with funnels is placed at the center of a cubical room of filled with air.
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2.1. Adiabatic on top of cooling assembly and experimental validation An experimental setup without funnels shown in Fig. 3 was constructed to mimic heat rejected from each PV cell. A heating block, carrying cartridge heaters and heating fingers, was fastened to the cell card substrate and heat sink with a clamp, shown in Fig. 3(a). In Fig. 1, the funnels are used for optical purpose, they not only concentrate the solar power on the PV cells, but capture solar energy from the sun as electricity by PV devices. During the optical-electric transformation, a total waste heat of 84 W is generated from PV cells. In Fig. 3, we used 14 heating fingers to simulate the waste heat from PV cells. The heat, generated from the cartridge heaters, flowed down the heating fingers. The heat flux can be determined through monitoring the temperature difference collected by thermocouples embedded in each of the heating fingers. Each heating finger has two thermocouple ports (Type T, class 1 with accuracy of ±0.5 °C) to help collect the temperature difference, DT. The bottoms of the heating fingers touched the PV substrate. The cross section of each heating finger was machined to be 5.0 mm by 5.5 mm, which has the same size of the PV cell. The temperatures of the PV cells were estimated from the measured heat flux and the thermocouple closest to the cold block using a one-dimension thermal conduction model. Thermal insulation (R13) material was used to simulate the adiabatic boundary condition shown in Fig. 3(b). Power input was controlled by a variable power supply. Four cartridge heaters were used to provide the heat load; each cartridge heater can generate a maximum of 32 W at 120 V. A data acquisition (DAQ) system was used to continuously monitor the temperatures. The thermal test took about three hours to reach steady-state, or about one hour to reach 90% of the steady-state condition. Each test, therefore, took at least three and half hours to complete. We then averaged the steady-state temperature data from the last thirty minutes of each test for post processing. The overall uncertainty for the predicted average temperature of surrogate PV was calculated based on the method described by Moffat [23,24], determined from the measured temperatures and provided heat flux. The Type-T, class-1 thermocouples used for all temperature measurement have the accuracy uncertainty of ±0.5 °C (40 to 125 °C). The uncertainty caused by mechanical machining is ±0.0125 mm. In addition, the thermocouple positioning error was estimated to be ±0.25 mm (1/2 of the thermocouple AWG Gage of 24). The relative uncertainty in the estimated tip-end temperature of each heating finger was determined to be no larger than ±0.7%.
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Fig. 4 shows the experimental results of the steady state average tip end temperature under different heat loads for natural convection and radiation condition. The absolute uncertainties for 24.4 W, 45.4 W, 64.8 W and 84.3 W are 0.62 °C, 0.63 °C, 0.65 °C and 0.68 °C and the relative uncertainties are 0.7%, 0.51%, 0.42%, and 0.37%, respectively. Results show a nearly linear increasing tendency of average tip end temperature when heat loads were increased within our testing range. For a maximum heat load of 84.2 W, the average tip end temperature reached 185.7 °C. Although the thermal insulation was applied around the heating fingers in order to prevent heat loss, as well as to allow all heat flux to flow into the tip end, the ideal ‘‘adiabatic” condition still cannot be achieved during the experiments. Therefore, there was still heat flux inevitably flowing through the insulation material downwards to the cell card substrate. This extra heating power has a minor effect in force convection cases when heat can be effectively brought away, but cannot be neglected when natural convection occurs. During the tests for natural convection study, the overall heat provided by the power supply is much larger than the calculated heat flowing through the heating fingers, especially for high heat flux cases. After calculating the thermal resistance of the insulation material and aluminum tip, the deviation between actual
Fig. 4. Average temperature of surrogate PV for fan failure mode at 25 °C ambient.
Fig. 3. Experimental set up (a) without thermal insulation material (b) with thermal insulation material.
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Fig. 5. Geometry of adiabatic on top of cooling assembly and boundary conditions.
Fig. 6. Illustration of different inclination angles.
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Fig. 7. Geometry of air covered with cooling assembly and boundary conditions.
Fig. 8. Temperature contour of funnels (left) and heat sink (right).
Table 2 Average temperature of surrogate PV under different inclination angles. Inclination angle
Average temperature of surrogate PV under convective effect (°C)
Average temperature of surrogate PV under conjugate natural convection with radiation (°C)
0° 10° 20° 30° 45° 60° 70° 80° 90°
217.825 213.46 208.45 205.156 200.34 196.51 196.477 198.401 199.749
145.749 144.397 143.361 143.198 142.201 141.226 141.459 141.627 141.887
heating power transferred to the cell card substrate and calculated heat transfer through fourteen heating fingers was about 20% for a calculated heating power of 84 W. In order to validate our numerical model with the experimental results, we simulated the cooling assembly under different heat flux. Our simulation geometry and boundary conditions are shown in Fig. 5. Only half of the cooling assembly was simulated so as to save computational time. In order to be consistent with our experiment, we applied adiabatic boundary conditions on top of the cooling assembly around the PV cells, as shown in Fig. 5(a). Meanwhile, considering the deviation between actual
Fig. 9. Average temperature of surrogate PV with different inclination angles.
heat transferred to the cell card substrate and calculated heat transfer through heating fingers, an actual power of 100 W is applied in the simulation setting. In Fig. 5(b), a constant heat flux of 259,740.3 W/m2 is applied at the surface of PV cells. In Fig. 5(c), opening boundary condition is applied at the other surfaces at an
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orientations in the range of 0–90°. The positive inclination angle indicates the plates of the heat sink are facing downward and the funnels are facing upward, as shown in Fig. 6. The geometry of air covered with cooling assembly and boundary conditions are shown in Fig. 7. A constant heat of 84 W in total (218,181.8 W/m2) was applied at the interface between funnels and PV cells (Fig. 7(a)). Opening boundary conditions are applied at the outer surfaces of air cubic which maintained at a constant temperature of 35 °C (Fig. 7(b)). Only half of the geometry was simulated and the middle planes of fluid and solid were applied symmetry boundary condition (Fig. 7(c)). The temperature contour of funnels and heat sink is shown in Fig. 8 at an inclination angle of 0°. It is shown that the temperature difference on the funnel surface ranges from 82.1 °C to 146.3 °C because of the low thermal conductivity of funnels (Glass Flint: 0.8 W/(mK)). The maximum temperature occurred at the interface between funnels and PV cells. The temperature contour of heat sink shows that the minimum temperature happens at the two sides of heat sink because the flow accelerates at the sides of heat sink. Fig. 10. Local temperature distribution along the line at the center of substrate.
3.2. Convective heat transfer rates with different inclination angles
Fig. 11. Average Nusselt number of cooling assembly with different inclination angles.
ambient temperature of 25 °C. The average temperatures of the surrogate PV cells under convection and radiation effect at different heat flux are shown in Fig. 4. The difference between numerical and experimental results for 24.4 W, 45.4 W, 64.8 W and 84.3 W are 4.8%, 0.2%, 4.1% and 7.6% respectively. Thus the numerical results agree well with the experimental ones, and the numerical model is proved to be reasonable for further studies. 3. Results and discussion 3.1. Air covered of cooling assembly with funnels at different inclination angles The validated numerical model for investigating natural convection from a plate-fin heat sink in horizontal orientation was directly used for inclined case investigations. The angle of PV cell cooling system was varied in order to simulate forward inclined
The average temperatures of the surrogate PV cells under natural convection and conjugate natural convection with radiation are presented in Table 2. As illustrated in Fig. 9, when there was only natural convective heat transfer effect, the average temperature of surrogate PV decreased rapidly from the case for inclination angle of 0° to that of 60°. The minimum temperature appeared at an inclination angle of 60°. From 60° to 90°, the average temperature of surrogate PV only increases 3 °C. After the radiative heat transfer effect was included, the average temperature of surrogate PV dropped about 30% compared with the convective-only heat transfer case. Heat transfer due to radiation was proportional to the heatsink surface area exposed to its surroundings and to the temperature rise above ambient raised to the 4th-order power. From the simulation result, the heat dissipated via radiation was 40 W, which was over 47% of the total power. Fig. 10 shows the local temperature distribution along the center of substrate at cases with inclination angles of 0°, 30°, 60° and 90°. At 60°, the local temperature distribution reached the minimum values along the substrate. The local temperature distribution at the center of substrate decreases monotonically from 0° to 60°. At 90°, the local temperature at the left edge was larger than that of the 60° and the local temperature at the right edge was smaller than that of the 60°. But the average temperature of surrogate PV at the inclination angle of 90° was larger than that of 60°. The average Nusselt number of the cooling assembly was calculated from the following equation,
Nu ¼
qc W Tw Ta k
ð1Þ
where qc is the convective heat flux, Tw is the average temperature of surrogate PV, Ta is the ambient temperature, W is the width of heat sink, k is the thermal conductivity of air. When there is only convective heat transfer effect, the convective heat flux handles all of 84 W. When the interaction of natural convection and surface thermal radiation are both engaged, we can calculate the radiative heat power from simulation results, which is 40 W. Thus the convective heat transfer handles only 44 W. In Fig. 11, the variations of the average Nusselt number of the heatsink cooling assembly as a function of inclination angles are plotted for the interaction effects between surface thermal radiation and natural convection. The highest Nu value was achieved at an inclination angle of 60°. Between 0° and 60°, Nu changed monotonically until the inclination gets very close to 60°. This was reported by Mittelman [25] that
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Fig. 12. Streamlines at the symmetry plane of the cases with funnels for various downward inclination angle: (a) h = 0°; (b) h = 10°; (c) h = 20°; (d) h = 30°; (e) h = 45°; (f) h = 60°; (g) h = 70°; (h) h = 80°; (i) h = 90°.
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Fig. 12 (continued)
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Fig. 12 (continued)
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Fig. 13. Streamlines around the funnels at an inclination angle of 0° (a) Front view (b) Side view.
Fig. 14. Cutting-plane pseudo-streamlines between funnels at an inclination angle of 0° from side view (a) 3rd and 4th (b) 4th and 5th (c) 5th and 6th (d) 6th and 7th.
there is a substantial enhancement in the rate of heat transfer trend beyond a certain angle of inclination starting from the downward horizontal. In their work, they investigated the problem of laminar free convection underneath a hot isothermal and inclined fin array, which is different from our high heat flux (218,181.8 W/m2) transferred through fourteen equally spaced PV cells. In the 60–90° range, Nu decreases very slowly, staying nearly constant. The orientation of the cooling assembly also plays an important role on the heat transfer characteristic when turbulent natural convection interacts with surface radiation. Surface radiation reduces the convective Nusselt number and this reduction in convective Nusselt number is also reported by Balaji and Venkateshan [26] while investigating interaction of surface radiation with free convection in a differentially square cavity. Nusselt number distribution, reported in [26], shows that surface radiation leads to a drop in the convective component. The reduction is compensated by the radiation heat transfer between the hot and cold walls. The reason for this was attributed to surface radiation reducing
fluid temperatures approaching the cold wall and the increase of fluid temperature approaching the hot wall. In either case, the contribution to the convection heat transfer mode is reduced due to lower temperature difference between fluid and the cooling assembly. 3.3. Discussion of flow patterns and heat transfer 3.3.1. Heat sink side flow pattern and heat transfer The overall flow field and corresponding temperature contours of hot PV cells combined with heatsink and funnels at various inclination angles are shown in Fig. 12. In Fig. 12, the figures on the left column show the streamlines at the symmetrical plane and the figures on the right column show the temperature contour whose temperature range is scaled from 50 °C to 215 °C. The red color on the contour represents hot temperature region and the blue color represents cold temperature region. As shown in Fig. 12a (1), the streamlines underneath a horizontal array are symmetrical.
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Fig. 15. Streamlines around the funnels at an inclination angle of 30° from (a) Front view (b) Side view.
Fig. 16. Streamlines around the funnels at an inclination angle of 30° from (a) front view (b) side view.
The stagnation point (red arrow) is located at the array center when the inclination angle is 0°. On the top surface of the funnels, there exists a recirculation region enclosed with a saddle point. In Fig. 12a (2), the temperature contour at the solid and fluid part is also symmetrical. The highest temperature of PV cells is 218.6 °C, which is located at the center. The buoyancy force entrains the flow to impinge on the surface of the heat sink, and splits up symmetrically to bring the heat downstream to the edges of the heat sink. The thickness of the high temperature region becomes thinner on the left and right edges of the heat sink because of the rapid flow acceleration. It is clear that streamlines are clustered at the edges of the heatsink. Therefore, the thickness of thermal boundary rapidly vanishes at the edge of heatsink. Increasing the inclination angles moves the stagnation point towards the right side of the fin, as shown by the red arrow in Fig. 12a(1)–i(1). This phenomenon was also experimentally observed by Fujii [19] in the case of flat plate, whereupon the flow separates at the plate edge. From
Fig. 12b(1)–f(1), the recirculation region at the top of funnels gradually becomes spiral node. From Fig. 12g(1)–i(1), the spiral node on the top surface of the funnels vanishes. The peak temperature of PV cells moves toward the left side of the cooling assembly. As the inclination angle increases the buoyant force component parallel to the surface of the heat sink allows the flow to rise up to the left more easily. As shown in Fig. 12b(2)–f(2), the region of red color beneath the PV cells tends to decrease dramatically from 0° to 60°. As the stagnation point moves toward the right edge of the fin, an increasing amount of flow rises up along the heat sink with much higher velocity. Although the thermal boundary layer is increasing when the air flows up, a much higher velocity will result in better heat transfer performance. It can be found in Fig. 12a(1)–f (1) that, the maximum flow velocity increases dramatically, from 0.67 m/s to 0.95 m/s when the inclination angle changes from 0° to 60°. However, the maximum flow velocity only changes from 0.95 m/s to 1 m/s when inclination angle changes from 60° to 90°
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Fig. 17. Streamlines around the funnels at an inclination angle of 60° from (a) front view (b) side view.
Fig. 18. 3D flow pattern between the gap of funnels at an inclination angle of (a) 60° and (b) 90°.
Table 3 Flow pattern comparison with various inclination angles. Funnel side
Heatsink side
Inclination angle
Gap between funnels
Top of funnels
Above substrate
Stagnation point
0° 30° 60° 90°
Separation flow Separation flow Separation flow Z-direction vorticity
Separation bubble Strong spiral node Weak spiral node None
Recirculation region Recirculation region Recirculation region None
Downward of heat sink Downward of heat sink Edge of heat sink Edge of heat sink
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Fig. 19. Comparison of streamlines for the cases with and without funnels at the inclination angle of 30°: (a) Front view (b) Side view.
as shown in Fig. 12f(1)–i(1). From 0° to 30°, the location of stagnation point changes from the center of heatsink to the edge, thus the stagnation line position has a higher sensitivity to the inclination angle. This higher sensitivity is associated with larger fin spacing, higher temperature difference and smaller fin height, which has been discussed in Ref. [23]. Their configuration did not contain funnels and the fin was maintained as isothermal with laminar free convection. Larger fin spacing (less friction) and higher temperature difference (driving force) enhances the inertia of the fluid that flows to the left side of the heat sink. 3.3.2. Funnel side flow pattern and heat transfer Optical Funnels are used to concentrate solar power on to the PV cells. However, funnels also affect the overall flow structure, natural convection and the corresponding heat transfer. Fig. 13
(a) and (b) are the front view and side view of streamlines around funnels at the symmetrical plane when incidence angle is 0°. The cutting plane of the side view is between the 2nd and 3rd funnels. As shown in Fig. 13(a), there is a line of recirculation wake at the top of funnels. This line of recirculation corresponds to the saddle point on the top surface of funnels shown in Fig. 13(b). Flow comes from the sides and fills up the gap between funnels and then goes up. When this up-flow reaches the top of the funnels, the flow separates and forms a pair of separation bubbles enclosed with a saddle point downstream of the funnels. However, this pair of separation bubbles is in a near closed form and does not significantly benefit heat transfer from the funnels to ambient air remotely. Fig. 14 displays the cutting-plane pseudo-streamlines between the 3rd and 4th, the 4th and 5th, the 5th and 6th, and the 6th and 7th funnels separately. In addition to the pair of near
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closed separation bubbles appears on the top surface of the funnels, a recirculation region at the top of substrate can be observed. Fig. 15(a) shows the streamline around the funnels at 30° from the front view. Fig. 15(b) shows the cutting-plane pseudostreamlines between the 3rd and 4th, and the 6th and 7th funnels separately. There was still a line of recirculation wake because the saddle point occurs on top of the funnels. However, the centeredlike nodes (Fig. 15(b)) gradually become spiral foci (Fig. 16(b)). This implies this vortex flow swirls upward from the right end to the left end. Fig. 16(a) shows the streamline around the funnels at 60° from the front view. Fig. 16(b) shows the cutting-plane pseudo-streamlines at 60° between the 3rd and 4th, and the 6th and 7th funnels separately. As shown in Fig. 16(a) (front view), when the module was placed at 60°, the flow rose easier and the swirl pattern was weakened. Between the gap at the 3rd and 4th funnels, flow from the sides and top encountered the funnels to form a pair of spiral nodes on top of the funnels and then take the heat flowing up to the trailing edge of the module. The foci represent the flow swirl along the top surface of funnels to the trailing edge of the module. At the cutting plane between the 6th and 7th funnels, this pair of spiral nodes encloses a saddle point because part of the flow swirl remains along the top surface of funnels and the rest flows up. From Fig. 15(b) and Fig. 16(b), when the inclination angle is at 30° and 60° a spiral flow pattern forms above the substrate. After the module rotates to 90° (Fig. 17(b)), flow from the sides enters the funnels and then swirls in. The 3-D spiral recirculation region does not occur above the funnels and substrate and the air directly flows up from the leading edge to the trailing edge of the module. The flow topology above the funnels no longer has spiral up phenomena. This is observed from the side view, the air from the top separates as it passes the funnels and then flows into the room between each funnels. Fig. 18(a) shows the 3D flow patterns between the gaps of funnels at the inclination angle of 60°. Flow from the bottom goes into the gap between funnels and then takes the heat out when it separates. Also, a pair of spiral nodes is formed at the top surface of funnels (Fig. 18(a)). This spiral node will take the heat along the top of the funnels to the trailing edge of the module. However, when the inclination angle was increased to 90° (Fig. 18(b)), this pair of spiral vortices disappeared above the funnels and the air entered the space between funnels to form z-direction vorticity.
This z-direction vorticity swirls between the gap of funnels and it does not have a significant effect on heat transfer from the funnels to the ambient because heat is trapped and recirculated in the area between funnels. The flow patterns at heatsink side and funnel side have been concluded in Table 3. From 0° to 60°, air flows into the gap between funnels and separates when it encounters the top surface of funnels. However, when the inclination angle of the heatsink is at 90°, air flows into the gap between funnels to form Z-direction vorticity. The separation bubble appears above funnels at 0°. From 30° to 60°, the strength of spiral node weakens on top of the funnels because the flow is able to rise easier. When the stagnation point occurs at the downward side of the heat sink from 0° to 60°, flow velocity is the dominant factor in influencing heat transfer because the maximum flow velocity changes dramatically (0.67 m/s to 0.95 m/s). From 60° to 90°, the stagnation point happens at the edge of heatsink on the bottom of the module and the maximum flow velocity stays nearly constant (0.95 m/s to 1.0 m/s). Thus, the funnel effect will be the dominant factor to influence heat transfer when the stagnation point happens at the edge of the heat sink. 3.4. Funnel effect Fig. 19 displays the comparison of streamlines for the cases with and without funnels at the inclination angle of 30°. In Fig. 19a(1) and a(2), the location of stagnation point almost occurs at the same positon for both cases. However in Fig. 19b(1) and b(2), the flow patterns are dramatically different on funnels’ side in spite that the recirculation region still occurs at the top of substrate for both cases. Fig. 20 shows the average temperature of surrogate PV cells at an inclination angle of 0°, 30°, 60°, 90°. From Fig. 20(a), when there is only natural convection heat transfer, the average temperature of surrogate PV attached with funnels can be 8 °C lower than without funnels. The heat transfer enhancement with funnels is more obvious under only natural convection heat transfer effect. This temperature reduction is because the increase of surface area and the complex flow pattern around the funnels, as shown in Fig. 19b(1) and b(2). But when radiation heat transfer is included, the average temperature of surrogate PV attached with funnels is only 2 °C lower than without funnels as shown in Fig. 20(b).
Fig. 20. Comparison of average temperature at surrogate PV for the cases with and without funnels: (a) Under Convective heat transfer effect (b) Under conjugate natural convection with radiation.
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4. Conclusions A numerical investigation on the natural convection combined with radiative heat transfer underneath inclined heat sink cooling assembly was conducted. Numerical and experimental results agreed well with each other. The validated numerical model was employed for inclined case investigations. The effects of inclination angle, the location of the flow stagnation point and the flow structure around the funnels were demonstrated. After analyzing our simulation data, the following observations are concluded: The highest heat transfer rate and the lowest average temperature at surrogate PV cells occurred at an inclination angle of 60°. From an inclination of 0–60°, the heat transfer rate monotonically increased when the stagnation point occurred at the downward surface of heatsink. After the inclination angle exceeds 60°, the surrogate PV temperature increases 3 °C under natural convective heat transfer effect when the stagnation point occurs at the edge of heat sink. There is substantial enhancement in heat transfer when the inclination angle changes from 0° to 60° compared with the inclination angle changes from 60° to 90°. When the inclination angle changes from 0° to 60°, the maximum flow velocity increases dramatically, from 0.67 m/s to 0.95 m/s. The buoyancy force entrains the flow to impinge on the surface of the heat sink, and splits up to take the heat downstream to the edges of heat sink. Although the growth rate of thermal boundary layer increases as the stagnation point moves towards the edge of heat sink, high flow velocity overwhelms the growth rate of thermal boundary layer at the downstream, the high temperature region will gradually vanish at the end of heatsink. When the inclination angle changes from 60° to 90°, the flow velocity only changes from 0.95 m/s to 1 m/s and the growth rate of thermal boundary layer is nearly constant. The heat transfer has been enhanced with funnel effects. The flow patterns at funnels’ side become more complex and mixing is improved when funnels exist. However, at the heatsink side, the flow patterns are similar and location of stagnation point is near the same for both cases.
Acknowledgements The authors gratefully acknowledge the support of ARPA-E under Grant No. SLA-UM DE-AR0000465. The authors would like to acknowledge undergraduate student, Brian J. Hernan, for his constructive comments. References [1] A. Royne, C.J. Dey, D.R. Mills, Cooling of photovoltaic cells under concentrated illumination: a critical review, Sol. Energy Mater. Sol. Cells 86 (4) (2005) 451– 483.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Coupled natural convection and radiation heat transfer of hybrid solar energy conversion system Haolun Xu a, Hsiu-Hung Chen a, Sheng Wang a, Zheng Li a, Kuojiang Li a, Greg Stecker b, Wei Pan b, Jong-Jan Lee b, Chung-Lung Chen a,⇑ a b
Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA Sharp Laboratories of America, Camas, WA 98607, USA
a r t i c l e
i n f o
Article history: Received 28 July 2016 Received in revised form 17 November 2016 Accepted 18 November 2016
Keywords: Natural convection Radiation interaction Inclined heatsink Funnel effect
a b s t r a c t A hybrid solar energy conversion system described in this study is designed to exceed the efficiency of each type of technology alone by combining advantages of concentrated solar power (CSP) technology and high performance concentrated photovoltaic (CPV) cells. This hybrid system can be tilted at different inclination angles to track the solar power at different latitudes and different time zones. Thermal management is important to CPV cells, as 1000 concentrated solar radiation onto CPV not only leads to higher performance but also generates more waste heat flux. In this work, the effects of natural convection with and without the interaction of surface radiation in the system consisting of PV cells, optical funnels and a heatsink were numerically investigated with an experimentally validated model. The influence of inclination on the overall flow structure and heat transfer was examined. Under the effect of these funnels, the heat transfer was enhanced when the heat was transferred through PV cells to funnels. At the same time, the separation flow between the spaces of funnels would take the heat to the ambient. The minimum average temperature of surrogate PV cells occurred at the inclination angle of 60°. When the inclination angle varied from 0° to 90°, the stagnation point moved from the downward surface of the heat sink towards the edge of heat sink. From 0° to 60°, the stagnation point was at the downward surface of heat sink and there was a dramatic decrease in the average temperature of the surrogate PV cells. When inclination angles were less than 60°, except that there was a separation region above substrate, the side flow could flow in and out freely between adjacent funnels and then formed a pair of separation bubble, or spiral node, on top of the funnels. At these inclination angles, flow velocity was found to be the dominant factor influencing heat transfer because the flow pattern (separation bubble) was the same on top of the funnels. However, at inclination angles of 60° to 90° the stagnation point occurred at the edge of the heat sink, and the surrogate PV temperature increased. When the inclination angle reached 90°, the flow was trapped and recirculated among funnels, and the vortical wake on top of the funnel disappeared. It can be concluded that from 60° to 90°, the dominant factor influencing heat transfer is funnel effect because the flow velocity stayed almost constant. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Solar energy can be captured either as electricity by photovoltaic (PV) devices or as heat by concentrated solar power (CSP) systems. The former means are considered cost-effective, but cannot utilize the thermal spectrum. In addition, the storage of electricity is challenging. The latter has advantages of generating electricity from the stored heat (usually in the form of molten salt) even when the sun is not shining, but is pricy in construction and
⇑ Corresponding author. E-mail address: [email protected] (C.-L. Chen). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.11.061 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
operation. Both CSP and PV utility-scale power stations have been in operation at various locations around the world since the 1980s. Currently, the largest CSP installation is the Solana Generating Station located near Gila Bend, AZ; a parabolic trough field with capacity of 280 MW and associated thermal storage. On the other hand, the largest PV installation is at the California Valley Solar Ranch: a 250 MW ‘‘solar farm” in San Luis Obispo County, CA. Different from CSP plants that collect heat energy, systems with PV cells generate low-grade waste heat while solar energy is converted into electricity. Extreme temperature increase in PV cells (when waste heat cannot be dissipated efficiently) will not only lower the light-electricity conversion efficiency, but also damage
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Nomenclature qc k W
convective heat transfer rate (W/m2) thermal conductivity (W/(mK)) heatsink width (m)
the cell and other module materials. Several papers [1–5] have addressed various ways for the cooling of PV cells. Recently, Tari [6,7] showed the possibilities of dissipating unwanted heat by the interaction of natural convection with thermal radiation for the vertical orientation of plate-finned heat sinks in two separate applications. Leung and Probert [8,9] experimentally studied the effect of orientation on heat exchangers. They found that the vertical and upward facing horizontal orientations of a heat sink were preferred for maximizing the natural convection heat transfer rate. As a result, these two orientations were investigated extensively under convective and radiative heat transfer effect. However, there are only a few works investigating inclined orientations under the interaction of natural convection and surface thermal radiation [10,11]. In 2014, Sharp Labs of America collaborated with University of Arizona and University of Missouri-Columbia aiming to combine advantages of CSP and PV technologies to achieve greater exergy, better dispatchability, and higher capacity factor at more reasonable costs than can be achieved by either technology alone. High heat flux waste heat need to be dissipated with the solar energy system running. Therefore, high efficiency cooling is required to keep the solar energy system working safely. To gain high PV cell efficiency, plated-finned heat sinks under forced convection are employed to keep our system working at a targeting low temperature of 75 °C. However, for the purposes of avoiding the maximum temperature of surrogate PV exceed the melting temperature of solder (167 °C) when any fan fails, heat rejection by natural convection and radiation need to be considered in order to ensure the all-time reliability of operation. Natural convection plays a key role in the fan failure condition. Various numerical methods have been employed to solve the different natural convections [12–17]. In order to estimate the heat transfer performance on such a cooling assembly, researchers have derived the empirical heat transfer rate and Nusselt number with the relationship of some non-dimensional numbers. Bejan and Lee [18] derived an analytical solution of the convection heat transfer rate for packages of electronic components, and found that if the heat transfer mechanism was natural convection, the maximum density of heat generating electronics (or Q/HLW) was proportional to (Tmax T1)3/2 and H1/2. H, L and W are the fin height, the heatsink length and heatsink width, respectively. Mehrtash and Tari [10] scaled the equation with a factor obtained from the analysis of the simulation data which is (H/L)0.32. Leung and Probert [8] obtained a similar relation in which they had an exponential fin effectiveness term that can be neglected in the cases where fins have high thermal conductivity. They used equations to calculate the average Nusselt number based on the product of modified average Grashof number with Prandtl number. However, these reports do not include the inclination angle effect. Inclined orientations are important for hybrid solar energy conversion system for at least two reasons: (i) at different latitudes and different time zones, the hybrid solar system needs to be tilted at different inclination angles in order to track solar power, thus the maximum temperature at the assembly needs to be estimated; (ii) because funnels are used on top of PV cells for optical purposes, which can affect the overall flow structure, natural convection and heat
Tw Ta
average temperature of surrogate PV cells (°C) ambient temperature (°C)
transfer need to be further investigated. In order to obtain the heat transfer performance of heat sink cooling assembly with different inclination angles, Fujii and Imura [19] studied the relation of Nu vs GrPr for the horizontal plate facing downwards and when the flat plate was inclined from the vertical. When the heat sink was inclined from the vertical, Tari and Mehrtash [20] assumed that the flow structure stayed the same. The only change was in the body force, where the effective body force became qgcosh. With the same rationale, they suggested the vertical case correlation for plate fin heat sinks with the same modification was expected to be valid at small inclination angles, as long as the flow structure stayed the same. However, their equation can only be applied when there is convective heat transfer effect. If the surface thermal radiation is included, their equations are not applicable to calculate the corresponding Nusselt number. In this study, we validated our simulation results with the case when there was adiabatic boundary condition on top of cooling assembly without funnels. Then we applied our validated model to investigate the heat transfer performance of cases with funnels under various inclination angles. The average temperature of surrogate PV and average Nusselt number of cooling assembly were compared and discussed. We also studied the relationship between heat transfer and flow pattern at the heatsink side and funnel side.
2. Numerical method The assembly of PV cells cooling in hybrid solar energy conversion system is schematically depicted in Fig. 1. Fig. 1a is the isometric view of the assembly and Fig. 1b is the side view from the cutting plane with dimensions. The heat sink was provided by Aavid Thermalloy, LLC. The funnels were provided by Sharp Laboratory of America. The numerical model dimensions of our cooling assembly were listed in Table 1. In this system, thermal management is important to PV cells, as 1000x concentrated solar radiation onto PV cells not only leads to higher performance but also larger heat loads (heat flux on PV cells is over 105 W/m2). The module includes an optimized plate-fin heat sink, an aluminum substrate, fourteen equally spaced PV cells located on the substrate, and fourteen funnels attached to the surface of PV cells. The assembly shown in Fig. 1 is placed in a cubical room filled with air, with walls that are maintained at a constant temperature. The width, length and height of this cubical room are applied as 148.8 mm, 400 mm and 400 mm. Because the Rayleigh number of our cooling assembly is estimated to be 3.2 109 under a total power input of 84 W at the PV cells, the use of proper turbulence model to simulate this process is needed. In the analysis (with ANSYS CFX), steady state solutions were obtained by using the Shear Stress Transport Model (SST) with natural convection and surface to surface radiation. From the ANSYS user manual for natural convection [21], they applied four turbulent models (Standard and RNG k-epsilon, Standard and SST k-omega) to study the natural convection in a tall cavity and compared with the experimental data [22]. SST model shows better agreement with their experiment. Thus, we used SST model for our study. Boussinesq approximation was applied to assume the
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Fig. 1. Assembly view of photovoltaic cells cooling in hybrid solar energy conversion system.
Table 1 Detailed dimensions of funnel and heat sink. Parameter of heat sink and fin
Dimension (mm)
Parameter of substrate and PV cells
Dimension (mm)
Parameter of funnel
Dimension (mm)
Width of heat sink Height of heat sink Length of heat sink Width of fin Gap between fin Height of fin
50 35 200 1 2 32
Width of substrate Height of substrate Length of substrate Width of PV cell Length of PV cell Height of PV cell
50 6 200 5.5 5 0.5
Height of funnel Width of funnel base Length of funnel base
29.25 14.5 13.5
fluid density is constant in terms of the momentum equation except the body force term. The material properties applied for the heatsink and PV cells are aluminum; funnels are assumed to be glass flint. It is known that surface emissivity limits the amount of radiation heat transfer. For our heatsink, we used the emissivity of 0.85, which is suggested by Aavid Thermalloy, LLC. The emissivity of the funnel is given from the property of glass window (0.9). An unstructured mesh with a very fine grid combined with inflation layers around the heat removal assembly and a coarse grid for the rest of the room is employed. Grid independence study was achieved by examining three different grid densities with
Fig. 2. Mesh independence study.
3737,432, 8353,449 and 18601,158 cells. The local temperature along the center of the substrate for three different meshes is shown in Fig. 2. The local temperature calculated in the cases of 8,353,449 and 18,601,158 cells overlap with each other. We, therefore, selected the medium density mesh, i.e., the one with 8,353,449 cells, as it yielded results matching to those of the fine mesh. The boundary-layer meshes (inflation) were applied at the interface between the heatsink and air, as well as funnels and air. There are fourteen layers around each fin and Y+ around each fin is 0.420. The wall function in ANSYS CFX for SST k x turbulence model was set to be automatic. This enabled the near wall treatment to automatically switch from wall function to a low-Re near wall formulation while the mesh was refined. ANSYS CFX was used in solving the continuity, momentum and thermal energy equations for air and the heat conduction equation within the solids. To handle the radiative heat transfer, the discrete transfer model with surface to surface setup was applied. In our case, radiation was only passed from wall to wall and the fluid did not participate. This saves computational time and is appropriate since air does not absorb or emit significant thermal radiation on these length scales. The present study investigates the steady-state heat transfer performance covering the inclination angle 0°, 10°, 20°, 30°, 45°, 60°, 70°, 80°, and 90°. The inclination angle of 0° represents horizontal and 90° represents vertical for the cooling assembly. The case in Section 2.1 has been applied to adiabatic boundary condition on top of our cooling assembly without funnels in order to validate with our experiment. In the case at Section 3.1, the cooling assembly with funnels is placed at the center of a cubical room of filled with air.
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2.1. Adiabatic on top of cooling assembly and experimental validation An experimental setup without funnels shown in Fig. 3 was constructed to mimic heat rejected from each PV cell. A heating block, carrying cartridge heaters and heating fingers, was fastened to the cell card substrate and heat sink with a clamp, shown in Fig. 3(a). In Fig. 1, the funnels are used for optical purpose, they not only concentrate the solar power on the PV cells, but capture solar energy from the sun as electricity by PV devices. During the optical-electric transformation, a total waste heat of 84 W is generated from PV cells. In Fig. 3, we used 14 heating fingers to simulate the waste heat from PV cells. The heat, generated from the cartridge heaters, flowed down the heating fingers. The heat flux can be determined through monitoring the temperature difference collected by thermocouples embedded in each of the heating fingers. Each heating finger has two thermocouple ports (Type T, class 1 with accuracy of ±0.5 °C) to help collect the temperature difference, DT. The bottoms of the heating fingers touched the PV substrate. The cross section of each heating finger was machined to be 5.0 mm by 5.5 mm, which has the same size of the PV cell. The temperatures of the PV cells were estimated from the measured heat flux and the thermocouple closest to the cold block using a one-dimension thermal conduction model. Thermal insulation (R13) material was used to simulate the adiabatic boundary condition shown in Fig. 3(b). Power input was controlled by a variable power supply. Four cartridge heaters were used to provide the heat load; each cartridge heater can generate a maximum of 32 W at 120 V. A data acquisition (DAQ) system was used to continuously monitor the temperatures. The thermal test took about three hours to reach steady-state, or about one hour to reach 90% of the steady-state condition. Each test, therefore, took at least three and half hours to complete. We then averaged the steady-state temperature data from the last thirty minutes of each test for post processing. The overall uncertainty for the predicted average temperature of surrogate PV was calculated based on the method described by Moffat [23,24], determined from the measured temperatures and provided heat flux. The Type-T, class-1 thermocouples used for all temperature measurement have the accuracy uncertainty of ±0.5 °C (40 to 125 °C). The uncertainty caused by mechanical machining is ±0.0125 mm. In addition, the thermocouple positioning error was estimated to be ±0.25 mm (1/2 of the thermocouple AWG Gage of 24). The relative uncertainty in the estimated tip-end temperature of each heating finger was determined to be no larger than ±0.7%.
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Fig. 4 shows the experimental results of the steady state average tip end temperature under different heat loads for natural convection and radiation condition. The absolute uncertainties for 24.4 W, 45.4 W, 64.8 W and 84.3 W are 0.62 °C, 0.63 °C, 0.65 °C and 0.68 °C and the relative uncertainties are 0.7%, 0.51%, 0.42%, and 0.37%, respectively. Results show a nearly linear increasing tendency of average tip end temperature when heat loads were increased within our testing range. For a maximum heat load of 84.2 W, the average tip end temperature reached 185.7 °C. Although the thermal insulation was applied around the heating fingers in order to prevent heat loss, as well as to allow all heat flux to flow into the tip end, the ideal ‘‘adiabatic” condition still cannot be achieved during the experiments. Therefore, there was still heat flux inevitably flowing through the insulation material downwards to the cell card substrate. This extra heating power has a minor effect in force convection cases when heat can be effectively brought away, but cannot be neglected when natural convection occurs. During the tests for natural convection study, the overall heat provided by the power supply is much larger than the calculated heat flowing through the heating fingers, especially for high heat flux cases. After calculating the thermal resistance of the insulation material and aluminum tip, the deviation between actual
Fig. 4. Average temperature of surrogate PV for fan failure mode at 25 °C ambient.
Fig. 3. Experimental set up (a) without thermal insulation material (b) with thermal insulation material.
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Fig. 5. Geometry of adiabatic on top of cooling assembly and boundary conditions.
Fig. 6. Illustration of different inclination angles.
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Fig. 7. Geometry of air covered with cooling assembly and boundary conditions.
Fig. 8. Temperature contour of funnels (left) and heat sink (right).
Table 2 Average temperature of surrogate PV under different inclination angles. Inclination angle
Average temperature of surrogate PV under convective effect (°C)
Average temperature of surrogate PV under conjugate natural convection with radiation (°C)
0° 10° 20° 30° 45° 60° 70° 80° 90°
217.825 213.46 208.45 205.156 200.34 196.51 196.477 198.401 199.749
145.749 144.397 143.361 143.198 142.201 141.226 141.459 141.627 141.887
heating power transferred to the cell card substrate and calculated heat transfer through fourteen heating fingers was about 20% for a calculated heating power of 84 W. In order to validate our numerical model with the experimental results, we simulated the cooling assembly under different heat flux. Our simulation geometry and boundary conditions are shown in Fig. 5. Only half of the cooling assembly was simulated so as to save computational time. In order to be consistent with our experiment, we applied adiabatic boundary conditions on top of the cooling assembly around the PV cells, as shown in Fig. 5(a). Meanwhile, considering the deviation between actual
Fig. 9. Average temperature of surrogate PV with different inclination angles.
heat transferred to the cell card substrate and calculated heat transfer through heating fingers, an actual power of 100 W is applied in the simulation setting. In Fig. 5(b), a constant heat flux of 259,740.3 W/m2 is applied at the surface of PV cells. In Fig. 5(c), opening boundary condition is applied at the other surfaces at an
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orientations in the range of 0–90°. The positive inclination angle indicates the plates of the heat sink are facing downward and the funnels are facing upward, as shown in Fig. 6. The geometry of air covered with cooling assembly and boundary conditions are shown in Fig. 7. A constant heat of 84 W in total (218,181.8 W/m2) was applied at the interface between funnels and PV cells (Fig. 7(a)). Opening boundary conditions are applied at the outer surfaces of air cubic which maintained at a constant temperature of 35 °C (Fig. 7(b)). Only half of the geometry was simulated and the middle planes of fluid and solid were applied symmetry boundary condition (Fig. 7(c)). The temperature contour of funnels and heat sink is shown in Fig. 8 at an inclination angle of 0°. It is shown that the temperature difference on the funnel surface ranges from 82.1 °C to 146.3 °C because of the low thermal conductivity of funnels (Glass Flint: 0.8 W/(mK)). The maximum temperature occurred at the interface between funnels and PV cells. The temperature contour of heat sink shows that the minimum temperature happens at the two sides of heat sink because the flow accelerates at the sides of heat sink. Fig. 10. Local temperature distribution along the line at the center of substrate.
3.2. Convective heat transfer rates with different inclination angles
Fig. 11. Average Nusselt number of cooling assembly with different inclination angles.
ambient temperature of 25 °C. The average temperatures of the surrogate PV cells under convection and radiation effect at different heat flux are shown in Fig. 4. The difference between numerical and experimental results for 24.4 W, 45.4 W, 64.8 W and 84.3 W are 4.8%, 0.2%, 4.1% and 7.6% respectively. Thus the numerical results agree well with the experimental ones, and the numerical model is proved to be reasonable for further studies. 3. Results and discussion 3.1. Air covered of cooling assembly with funnels at different inclination angles The validated numerical model for investigating natural convection from a plate-fin heat sink in horizontal orientation was directly used for inclined case investigations. The angle of PV cell cooling system was varied in order to simulate forward inclined
The average temperatures of the surrogate PV cells under natural convection and conjugate natural convection with radiation are presented in Table 2. As illustrated in Fig. 9, when there was only natural convective heat transfer effect, the average temperature of surrogate PV decreased rapidly from the case for inclination angle of 0° to that of 60°. The minimum temperature appeared at an inclination angle of 60°. From 60° to 90°, the average temperature of surrogate PV only increases 3 °C. After the radiative heat transfer effect was included, the average temperature of surrogate PV dropped about 30% compared with the convective-only heat transfer case. Heat transfer due to radiation was proportional to the heatsink surface area exposed to its surroundings and to the temperature rise above ambient raised to the 4th-order power. From the simulation result, the heat dissipated via radiation was 40 W, which was over 47% of the total power. Fig. 10 shows the local temperature distribution along the center of substrate at cases with inclination angles of 0°, 30°, 60° and 90°. At 60°, the local temperature distribution reached the minimum values along the substrate. The local temperature distribution at the center of substrate decreases monotonically from 0° to 60°. At 90°, the local temperature at the left edge was larger than that of the 60° and the local temperature at the right edge was smaller than that of the 60°. But the average temperature of surrogate PV at the inclination angle of 90° was larger than that of 60°. The average Nusselt number of the cooling assembly was calculated from the following equation,
Nu ¼
qc W Tw Ta k
ð1Þ
where qc is the convective heat flux, Tw is the average temperature of surrogate PV, Ta is the ambient temperature, W is the width of heat sink, k is the thermal conductivity of air. When there is only convective heat transfer effect, the convective heat flux handles all of 84 W. When the interaction of natural convection and surface thermal radiation are both engaged, we can calculate the radiative heat power from simulation results, which is 40 W. Thus the convective heat transfer handles only 44 W. In Fig. 11, the variations of the average Nusselt number of the heatsink cooling assembly as a function of inclination angles are plotted for the interaction effects between surface thermal radiation and natural convection. The highest Nu value was achieved at an inclination angle of 60°. Between 0° and 60°, Nu changed monotonically until the inclination gets very close to 60°. This was reported by Mittelman [25] that
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Fig. 12. Streamlines at the symmetry plane of the cases with funnels for various downward inclination angle: (a) h = 0°; (b) h = 10°; (c) h = 20°; (d) h = 30°; (e) h = 45°; (f) h = 60°; (g) h = 70°; (h) h = 80°; (i) h = 90°.
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Fig. 12 (continued)
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Fig. 12 (continued)
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Fig. 13. Streamlines around the funnels at an inclination angle of 0° (a) Front view (b) Side view.
Fig. 14. Cutting-plane pseudo-streamlines between funnels at an inclination angle of 0° from side view (a) 3rd and 4th (b) 4th and 5th (c) 5th and 6th (d) 6th and 7th.
there is a substantial enhancement in the rate of heat transfer trend beyond a certain angle of inclination starting from the downward horizontal. In their work, they investigated the problem of laminar free convection underneath a hot isothermal and inclined fin array, which is different from our high heat flux (218,181.8 W/m2) transferred through fourteen equally spaced PV cells. In the 60–90° range, Nu decreases very slowly, staying nearly constant. The orientation of the cooling assembly also plays an important role on the heat transfer characteristic when turbulent natural convection interacts with surface radiation. Surface radiation reduces the convective Nusselt number and this reduction in convective Nusselt number is also reported by Balaji and Venkateshan [26] while investigating interaction of surface radiation with free convection in a differentially square cavity. Nusselt number distribution, reported in [26], shows that surface radiation leads to a drop in the convective component. The reduction is compensated by the radiation heat transfer between the hot and cold walls. The reason for this was attributed to surface radiation reducing
fluid temperatures approaching the cold wall and the increase of fluid temperature approaching the hot wall. In either case, the contribution to the convection heat transfer mode is reduced due to lower temperature difference between fluid and the cooling assembly. 3.3. Discussion of flow patterns and heat transfer 3.3.1. Heat sink side flow pattern and heat transfer The overall flow field and corresponding temperature contours of hot PV cells combined with heatsink and funnels at various inclination angles are shown in Fig. 12. In Fig. 12, the figures on the left column show the streamlines at the symmetrical plane and the figures on the right column show the temperature contour whose temperature range is scaled from 50 °C to 215 °C. The red color on the contour represents hot temperature region and the blue color represents cold temperature region. As shown in Fig. 12a (1), the streamlines underneath a horizontal array are symmetrical.
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Fig. 15. Streamlines around the funnels at an inclination angle of 30° from (a) Front view (b) Side view.
Fig. 16. Streamlines around the funnels at an inclination angle of 30° from (a) front view (b) side view.
The stagnation point (red arrow) is located at the array center when the inclination angle is 0°. On the top surface of the funnels, there exists a recirculation region enclosed with a saddle point. In Fig. 12a (2), the temperature contour at the solid and fluid part is also symmetrical. The highest temperature of PV cells is 218.6 °C, which is located at the center. The buoyancy force entrains the flow to impinge on the surface of the heat sink, and splits up symmetrically to bring the heat downstream to the edges of the heat sink. The thickness of the high temperature region becomes thinner on the left and right edges of the heat sink because of the rapid flow acceleration. It is clear that streamlines are clustered at the edges of the heatsink. Therefore, the thickness of thermal boundary rapidly vanishes at the edge of heatsink. Increasing the inclination angles moves the stagnation point towards the right side of the fin, as shown by the red arrow in Fig. 12a(1)–i(1). This phenomenon was also experimentally observed by Fujii [19] in the case of flat plate, whereupon the flow separates at the plate edge. From
Fig. 12b(1)–f(1), the recirculation region at the top of funnels gradually becomes spiral node. From Fig. 12g(1)–i(1), the spiral node on the top surface of the funnels vanishes. The peak temperature of PV cells moves toward the left side of the cooling assembly. As the inclination angle increases the buoyant force component parallel to the surface of the heat sink allows the flow to rise up to the left more easily. As shown in Fig. 12b(2)–f(2), the region of red color beneath the PV cells tends to decrease dramatically from 0° to 60°. As the stagnation point moves toward the right edge of the fin, an increasing amount of flow rises up along the heat sink with much higher velocity. Although the thermal boundary layer is increasing when the air flows up, a much higher velocity will result in better heat transfer performance. It can be found in Fig. 12a(1)–f (1) that, the maximum flow velocity increases dramatically, from 0.67 m/s to 0.95 m/s when the inclination angle changes from 0° to 60°. However, the maximum flow velocity only changes from 0.95 m/s to 1 m/s when inclination angle changes from 60° to 90°
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Fig. 17. Streamlines around the funnels at an inclination angle of 60° from (a) front view (b) side view.
Fig. 18. 3D flow pattern between the gap of funnels at an inclination angle of (a) 60° and (b) 90°.
Table 3 Flow pattern comparison with various inclination angles. Funnel side
Heatsink side
Inclination angle
Gap between funnels
Top of funnels
Above substrate
Stagnation point
0° 30° 60° 90°
Separation flow Separation flow Separation flow Z-direction vorticity
Separation bubble Strong spiral node Weak spiral node None
Recirculation region Recirculation region Recirculation region None
Downward of heat sink Downward of heat sink Edge of heat sink Edge of heat sink
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Fig. 19. Comparison of streamlines for the cases with and without funnels at the inclination angle of 30°: (a) Front view (b) Side view.
as shown in Fig. 12f(1)–i(1). From 0° to 30°, the location of stagnation point changes from the center of heatsink to the edge, thus the stagnation line position has a higher sensitivity to the inclination angle. This higher sensitivity is associated with larger fin spacing, higher temperature difference and smaller fin height, which has been discussed in Ref. [23]. Their configuration did not contain funnels and the fin was maintained as isothermal with laminar free convection. Larger fin spacing (less friction) and higher temperature difference (driving force) enhances the inertia of the fluid that flows to the left side of the heat sink. 3.3.2. Funnel side flow pattern and heat transfer Optical Funnels are used to concentrate solar power on to the PV cells. However, funnels also affect the overall flow structure, natural convection and the corresponding heat transfer. Fig. 13
(a) and (b) are the front view and side view of streamlines around funnels at the symmetrical plane when incidence angle is 0°. The cutting plane of the side view is between the 2nd and 3rd funnels. As shown in Fig. 13(a), there is a line of recirculation wake at the top of funnels. This line of recirculation corresponds to the saddle point on the top surface of funnels shown in Fig. 13(b). Flow comes from the sides and fills up the gap between funnels and then goes up. When this up-flow reaches the top of the funnels, the flow separates and forms a pair of separation bubbles enclosed with a saddle point downstream of the funnels. However, this pair of separation bubbles is in a near closed form and does not significantly benefit heat transfer from the funnels to ambient air remotely. Fig. 14 displays the cutting-plane pseudo-streamlines between the 3rd and 4th, the 4th and 5th, the 5th and 6th, and the 6th and 7th funnels separately. In addition to the pair of near
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closed separation bubbles appears on the top surface of the funnels, a recirculation region at the top of substrate can be observed. Fig. 15(a) shows the streamline around the funnels at 30° from the front view. Fig. 15(b) shows the cutting-plane pseudostreamlines between the 3rd and 4th, and the 6th and 7th funnels separately. There was still a line of recirculation wake because the saddle point occurs on top of the funnels. However, the centeredlike nodes (Fig. 15(b)) gradually become spiral foci (Fig. 16(b)). This implies this vortex flow swirls upward from the right end to the left end. Fig. 16(a) shows the streamline around the funnels at 60° from the front view. Fig. 16(b) shows the cutting-plane pseudo-streamlines at 60° between the 3rd and 4th, and the 6th and 7th funnels separately. As shown in Fig. 16(a) (front view), when the module was placed at 60°, the flow rose easier and the swirl pattern was weakened. Between the gap at the 3rd and 4th funnels, flow from the sides and top encountered the funnels to form a pair of spiral nodes on top of the funnels and then take the heat flowing up to the trailing edge of the module. The foci represent the flow swirl along the top surface of funnels to the trailing edge of the module. At the cutting plane between the 6th and 7th funnels, this pair of spiral nodes encloses a saddle point because part of the flow swirl remains along the top surface of funnels and the rest flows up. From Fig. 15(b) and Fig. 16(b), when the inclination angle is at 30° and 60° a spiral flow pattern forms above the substrate. After the module rotates to 90° (Fig. 17(b)), flow from the sides enters the funnels and then swirls in. The 3-D spiral recirculation region does not occur above the funnels and substrate and the air directly flows up from the leading edge to the trailing edge of the module. The flow topology above the funnels no longer has spiral up phenomena. This is observed from the side view, the air from the top separates as it passes the funnels and then flows into the room between each funnels. Fig. 18(a) shows the 3D flow patterns between the gaps of funnels at the inclination angle of 60°. Flow from the bottom goes into the gap between funnels and then takes the heat out when it separates. Also, a pair of spiral nodes is formed at the top surface of funnels (Fig. 18(a)). This spiral node will take the heat along the top of the funnels to the trailing edge of the module. However, when the inclination angle was increased to 90° (Fig. 18(b)), this pair of spiral vortices disappeared above the funnels and the air entered the space between funnels to form z-direction vorticity.
This z-direction vorticity swirls between the gap of funnels and it does not have a significant effect on heat transfer from the funnels to the ambient because heat is trapped and recirculated in the area between funnels. The flow patterns at heatsink side and funnel side have been concluded in Table 3. From 0° to 60°, air flows into the gap between funnels and separates when it encounters the top surface of funnels. However, when the inclination angle of the heatsink is at 90°, air flows into the gap between funnels to form Z-direction vorticity. The separation bubble appears above funnels at 0°. From 30° to 60°, the strength of spiral node weakens on top of the funnels because the flow is able to rise easier. When the stagnation point occurs at the downward side of the heat sink from 0° to 60°, flow velocity is the dominant factor in influencing heat transfer because the maximum flow velocity changes dramatically (0.67 m/s to 0.95 m/s). From 60° to 90°, the stagnation point happens at the edge of heatsink on the bottom of the module and the maximum flow velocity stays nearly constant (0.95 m/s to 1.0 m/s). Thus, the funnel effect will be the dominant factor to influence heat transfer when the stagnation point happens at the edge of the heat sink. 3.4. Funnel effect Fig. 19 displays the comparison of streamlines for the cases with and without funnels at the inclination angle of 30°. In Fig. 19a(1) and a(2), the location of stagnation point almost occurs at the same positon for both cases. However in Fig. 19b(1) and b(2), the flow patterns are dramatically different on funnels’ side in spite that the recirculation region still occurs at the top of substrate for both cases. Fig. 20 shows the average temperature of surrogate PV cells at an inclination angle of 0°, 30°, 60°, 90°. From Fig. 20(a), when there is only natural convection heat transfer, the average temperature of surrogate PV attached with funnels can be 8 °C lower than without funnels. The heat transfer enhancement with funnels is more obvious under only natural convection heat transfer effect. This temperature reduction is because the increase of surface area and the complex flow pattern around the funnels, as shown in Fig. 19b(1) and b(2). But when radiation heat transfer is included, the average temperature of surrogate PV attached with funnels is only 2 °C lower than without funnels as shown in Fig. 20(b).
Fig. 20. Comparison of average temperature at surrogate PV for the cases with and without funnels: (a) Under Convective heat transfer effect (b) Under conjugate natural convection with radiation.
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4. Conclusions A numerical investigation on the natural convection combined with radiative heat transfer underneath inclined heat sink cooling assembly was conducted. Numerical and experimental results agreed well with each other. The validated numerical model was employed for inclined case investigations. The effects of inclination angle, the location of the flow stagnation point and the flow structure around the funnels were demonstrated. After analyzing our simulation data, the following observations are concluded: The highest heat transfer rate and the lowest average temperature at surrogate PV cells occurred at an inclination angle of 60°. From an inclination of 0–60°, the heat transfer rate monotonically increased when the stagnation point occurred at the downward surface of heatsink. After the inclination angle exceeds 60°, the surrogate PV temperature increases 3 °C under natural convective heat transfer effect when the stagnation point occurs at the edge of heat sink. There is substantial enhancement in heat transfer when the inclination angle changes from 0° to 60° compared with the inclination angle changes from 60° to 90°. When the inclination angle changes from 0° to 60°, the maximum flow velocity increases dramatically, from 0.67 m/s to 0.95 m/s. The buoyancy force entrains the flow to impinge on the surface of the heat sink, and splits up to take the heat downstream to the edges of heat sink. Although the growth rate of thermal boundary layer increases as the stagnation point moves towards the edge of heat sink, high flow velocity overwhelms the growth rate of thermal boundary layer at the downstream, the high temperature region will gradually vanish at the end of heatsink. When the inclination angle changes from 60° to 90°, the flow velocity only changes from 0.95 m/s to 1 m/s and the growth rate of thermal boundary layer is nearly constant. The heat transfer has been enhanced with funnel effects. The flow patterns at funnels’ side become more complex and mixing is improved when funnels exist. However, at the heatsink side, the flow patterns are similar and location of stagnation point is near the same for both cases.
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