Enhancement of photovoltaic system performance via passive cooling: Theory versus experiment

Accepted Manuscript Enhancement of Photovoltaic System Performance via Passive Cooling: Theory versus Experiment

Ayman Abdel-raheimAmr, A.A.M. Hassan, Mazen Abdel-Salam, AbouHashema M. El-Sayed PII:

S0960-1481(19)30353-2

DOI:

10.1016/j.renene.2019.03.048

Reference:

RENE 11320

To appear in:

Renewable Energy

Received Date:

04 January 2019

Accepted Date:

11 March 2019

Please cite this article as: Ayman Abdel-raheimAmr, A.A.M. Hassan, Mazen Abdel-Salam, AbouHashema M. El-Sayed, Enhancement of Photovoltaic System Performance via Passive Cooling: Theory versus Experiment, Renewable Energy (2019), doi: 10.1016/j.renene.2019.03.048

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ACCEPTED MANUSCRIPT

Enhancement of Photovoltaic System Performance via Passive Cooling: Theory versus Experiment

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Ayman Abdel-raheimAmra,*,A.A.M.Hassana, Mazen Abdel-Salamb,**, AbouHashema M. El-Sayeda

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aMinia

University, Minia, Egypt, bAssiut University, Assiut , Egypt *Corresponding author, E-mail address: [email protected] **IEEE Fellow, IET Fellow, IOP Fellow

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Abstract – Passive cooling of a photovoltaic module via fins attached to the rear surface of the module is investigated. A solar module with no air cooling was used as a base model for comparison against modules cooled by the attached fins, which serve as a heat sink. The modules with fins are cooled by still air and ventilation air. A theoretical study of heat transfer through PV modules with and without fins was conducted to investigate how the calculated cell temperature and module output power are influenced by the ambient temperature and solar irradiation. The results showed a drop of module temperature and increase of electrical efficiency due to fins cooling. The electrical efficiency of the module increases significantly with the increase of fins height and number. The calculated values of cell temperature, open-circuit voltage and short-circuit current of the module with and without fins agreed reasonably with those measured experimentally over the day hours. The output power over the day hours increases at first from sunrise until noon time followed by a decrease until sunset. On the contrary, the electrical efficiency decreases from sunrise until noon time followed by an increase until sunset in agreement with previous findings in the literature.

Keywords: Photovoltaic, passive cooling, temperature, module efficiency.

List of Symbols 𝐴=Area of flat plate, m2 𝐴𝑐𝑠𝑓 = Cross section of fin, m2 𝐴𝑚 = Module area, m2 𝐹𝐹 = Module fill factor 𝐺 = Solar Irradiance on module, W/m2 𝐺ℎ𝑟 = Value of G at the hour of the day, W/m2 𝐺𝑟 = Grashoff number 𝐹𝑅 = Heat removal factor for PV/T solar collectors. g = Gravity acceleration, m/s2 H = Height of fins, m ℎ𝑐𝑜𝑛𝑓 = Front convective heat transfer coefficient, W/m2.℃ ℎ𝑐𝑜𝑛𝑏 = Back convective heat transfer coefficient, W/m2.℃ ℎ𝑓 = Fins' heat transfer coefficient, W/m2.℃ ℎ𝑟𝑎𝑑𝑓 = Front radiative heat transfer coefficient, W/m2.℃ ℎ𝑟𝑎𝑑𝑏 = Back radiative heat transfer coefficient, W/m2.℃ ℎ𝑠 ― 𝑝 = Conductive heat transfer coefficient, W/m2.℃ 𝐼𝑚𝑎𝑥= Module output current at maximum power point, A 𝐼𝑠𝑐= Module short - circuit current, A 𝑘𝑎 = Thermal conductivity of air, W/m2 ᵒC 𝑘𝑓 = Thermal conductivity of fins, W/m2 ᵒC L = Length of fins, m 𝐿𝑐 = Characteristic length, m n = Number of fins 𝑁𝑢 = Nusselt number for flat plate 𝑁𝑢𝑠= Nusselt number for inclined plate p = Fin's perimeter, m 𝑃𝑚𝑎𝑥= Module output power at maximum power point, W 𝑃𝑜𝑢𝑡= Module output power, W Pr = Prandtl number

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𝑄 = Rate of heat radiation between a horizontal plate and the sky, W. 𝑄𝑓= Rate of heat transfer from fins to surrounding medium, W 𝑞𝑓 = Rate of heat transfer from one fin to surrounding medium, W 𝑅𝑎𝐿 = Rayleigh number S = Spacing between fins, m 𝑈𝐿= Overall heat loss coefficient for PV/T solar collectors, W/m2.℃ 𝑇 = Temperature of flat plate,℃ 𝑇𝐴 = Ambient temperature, ℃ 𝑇𝑐 = Cell Temperature, ℃ 𝑇𝑝 = Absorber plate temperature, ℃ 𝑇𝑖𝑛= Inlet air temperature,℃ 𝑇𝑟𝑒𝑓= Reference temperature, ℃ 𝑇𝑠𝑘𝑦 = 𝑇𝐴 ―6, ℃ t = Thickness of fins, m 𝑉𝑚𝑎𝑥= Module output voltage at maximum power point, V 𝑉𝑜𝑐= Module open-circuit voltage, V 𝑣𝑎 = Air velocity, m/s

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The operating temperature is one of the important factors that can affect the efficiency of the PV modules, which is usually low in the range 15-20% [1]. The effects of temperature on module efficiency can be attributed to the impact on the current and voltage of the modules. It results in a linear reduction of the efficiency of power generation with the increase of temperature [2].

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A number of researchers have worked on cooling the PV modules with different approaches. Air circulation is probably the most simple and natural way for this purpose. In order to enhance convection heat transfer, fins were used to extend the heat transfer area. Combination PV and solar thermal collectors (PV/T) is another way of cooling PV modules. The PV/T hybrid systems are classified according to kind of heat removal fluid into PV/T/water and PV/T/Air. The ventilation by natural or forced air presents a non-expensive and simple method of cooling and the solar preheated air could be utilized in built, industrial and agriculture sectors.

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Fig. 1a shows the current-voltage (I –V) curves of KC200 GT solar array plotted with the experimental data at three different values of ambient temperature and irradiation level of 1000 W/m2. The effect of temperature increase results in a decrease of

Greek Letters: α = Absorpitivity to express fraction of energy absorbed 𝛼𝑡ℎ= Thermal diffusivity, m2/s β = Inclination angle of the module 𝛽𝑟𝑒𝑓= Temperature coefficient, 1 ℃ 𝛾𝑐 = Fraction of the area of the absorber plate occupied by the solar cells. 𝛾𝑓= Fraction of the absorber-plate area by fins. ε = Emission coefficient 𝜂𝑎= Electrical efficiency evaluated at ambient temperature. 𝜂𝑒 = Energy efficiency 𝜂𝑒𝑥 = Exergy efficiency 𝜂𝑝𝑣 = Electrical efficiency for PV module 𝜂𝑃𝑉/𝑇 = Photovoltaic – thermal efficiency 𝜂𝑟𝑒𝑓= Reference efficiency 𝜂𝑡ℎ = Thermal efficiency σ = Stefan Boltzman constant, W/m2K4 ν = Kinematic viscosity, m2/s 𝜏 = Glass transmittance of module cover. ∆𝑇𝑐= Change in cell temperature, C° I- INTRODUCTION

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the module output voltage with a subsequent decrease of the output power [3]. Fig. 1b shows the I-V curves of the same array at four different values of irradiation level and ambient temperature of 25℃. The effect of irradiation increase results in a linear increase of the module output current with a subsequent increase of the output power.

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(a)

(b)

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Fig. 1a: I –V experimental curves of KC200GT PV array exposed to 1000W/m2 irradiance level at different temperatures

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Fig. 1b: I -V experimental curves of KC200GT PV array exposed to different irradiance levels at temperature of 25 ℃

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The efficiency of some types of PV cells is very much dependent on their operating temperature. For crystalline silicon solar cells, the reduction in conversion efficiency is ∼0.4–0.5% for every degree of temperature rise [4]. Therefore, reducing the operating temperature of the PV modules by using passive cooling system is sought to ensure their efficient operation and to protect them from irreversible damage.

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A passive system requires no added power for cooling system.The cooling takes place for a PV module, where air is allowed to flow naturally above and below the module. Natural cooling is not limited to still air (of low speed about 0.01 m/s) but also includes ventilation air with wind speed between 0.5 and 1 m/s based on the standards [5] at NOTC, normal operating cell temperature. A number of researchers have worked on cooling the PV modules with different approaches. Air circulation is probably the most simple and natural way for this purpose. In order to enhance convection heat transfer, fins were used to extend the heat transfer area. Two low-cost heat-extraction modifications were implemented experimentally [6, 7] in the channel of a photovoltaic/thermal (PV/T) air system to increase the thermal output and to cool the PV module seeking acceptable electrical efficiency of the system. The channel has a PV module at the top face and is wall-backed in the bottom face. The first modification is based on suspending a thin aluminum sheet in the middle of the channel. In the second modification, rectangular fins were attached at the back wall of the air channel. A theoretical model was developed to study the effect of the channel depth and length as well as the mass flow rate on the thermal and electrical efficiency values of the model. The model predicts that small channel depth and high flow rate yield higher thermal output and higher electrical efficiency. The use of fins showed superior results as regards the increase of thermal and electrical energy values due to enhanced cooling of the module when compared with the air channel and the thin aluminum sheet systems. A good agreement between the predicted theoretical results and those measured experimentally. The proposed two modifications improve both the thermal and electrical efficiency values of the PV/T/Air system. For finned back wall, steady-state thermal efficiency (as demonstrated in Appendix A) could reach 52% on assuming 9–10% as an average value for the electrical efficiency. This results in a total efficiency of 61–62% for the PV/T/air system. The electric-thermal performance of solar concentrating PV/T system was numerically simulated [8]. The system consisted of glass cover, reflectors, solar cells, absorber panel, back plate, fins and insulating material. The solar irradiation passing through the glass cover was focused onto solar cells by concentrators. Steady state heat transfer models were developed without experimental validation. The use of concentrating PV scheme results in increase of both the thermal and electrical efficiency values of the system. The study did not report on the impact of fins on the cell temperature and system efficiency. No experimental validation was provided to support the theoretical findings. 3

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An experimental study was made [9] to investigate the performance of two polycrystalline PV cells in controlled conditions. One cell is provided with and the other without aluminum - fins attached at the back of the PV cell. The cells were exposed to illumination with intensity in the range from 200 to 800 W/m2. The energy, exergy and power conversion efficiencies of PV cells with and without fins increase exponentially with the increase of illumination intensity. On exposing the PV cells to illumination intensity of 800 W/m2, the energy, power conversion and exergy efficiency reached~ 9, 13 and 20%, respectively. The study is supported by heat transfer analysis which showed that the rate of heat dissipation from the PV cell with fins was 5.49, 9.06 and 12.03 W when exposed to illumination intensity of 400, 600 and 800 W/m2, respectively. On the other hand, the PV cell without fins only dissipates 4.54, 6.91 and 9.61 W. An experimental model of a single concentrator solar cell was built [10] with fins fixed to a base plate of the cell. The thermal performance of the system was investigated by varying the number, height, and thickness of fins as well as the base thickness. A lens was used to concentrate the sunlight on to the solar cell to increase the light intensity. The results showed that the cell temperature showed a decrease at first followed by an increase due to increase of the number of fins or the thickness of the base plate. The temperature of the heat sink decreased with the increase of fins' height. No theoretical model was developed to confirm the obtained experimental results. An experimental study was reported [11] to investigate the electrical performance of a PV panel cooled with U- and L-shaped fins pasted on the panel back under natural ventilation. The average electrical efficiency of PV panel with fins was 0.3~1.8% higher than that without fins. The average output power of PV panel with fins was 1.8~11.8% higher than that without fins under varying panel inclination, solar radiation, ambient temperature and wind velocity. No theoretical model was developed to confirm the obtained experimental results. A comparative experimental study of PV panels with and without fins-cooling was carried out [12] to investigate the effect of panel operating temperature on the output voltage, current and power of the panel. The fins were made up of perpendicular aluminum sheet glued to the backside of the panel. Total of 9 fins with different cross sections were attached at spacing of 50 mm to restrict the flow of air in order to improve the heat transfer rate from the PV panel. Due to fins cooling, the operating temperature of the panel dropped significantly to about 4.2% with a subsequent increase of 5.5% in the output power. No theoretical model was developed to confirm the obtained experimental results. A numerical approach was proposed [13] to evaluate the reduction of PV-panel temperature by using air-cooled heat sink with ribs connected to base plate behind the panel. The cooling efficiency was studied for different configurations of the heat sink by modifying the angle between the ribs and the base plate. The maximum output power of the panel was found to increase from 6.97% to 7.55% on decreasing the angle of the ribs from 90° to 45°. No theoretical model was developed to confirm the obtained experimental results. A hybrid system consisting of PV cells attached to an absorber plate with fins fixed at the other side of the plate surface was implemented experimentally [14]. The electrical efficiency was 14.6% at mass flow rate of 0.35 kg/s against15.2% at 0.75 kg/s. Also, the efficiency was 15.2% at cell temperature of 46℃ against 14.6% at 56℃. No theoretical model was developed to confirm the obtained experimental results. An experimental multi cooling system was proposed [15] for PV module .The system includes three types of passive cooling, namely conductive cooling, air passive cooling and water passive cooling. The system provided with the application of watercooling at the surface of the PV module and fins from aluminum at the back of module as a heat sink. It was found that the output power increased with a subsequent increase of 3% for the efficiency. No theoretical model was developed to confirm the obtained experimental results. A theoretical model of hybrid PV/T system with parallel plate air collector was investigated [16] for cold climatic conditions. The PV module was mounted on a wooden structure and cooled using an air duct below the module with no use of fins. The results showed an increase of thermal exergy by about 2–3% in addition to 12% increase of electrical output from the PV system. This results in with an overall system efficiency of about 14–15% of the PV/T system. No experimental validation was provided to support the theoretical findings. A passive cooling of a standalone flat PV module was attempted [17] experimentally using moist cotton wick structure. The latter was positioned at the-rear surface of the module facing the ground. The results showed that the module temperature was reduced from 65oC to about 45oC due to its cooling with cotton wick combined with water. Subsequently, the module efficiency was increased from 9% to 10.4%. No theoretical validation was provided to support the experimental findings.

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Therefore, the present paper presents a study of how the temperature of a PV module is influenced by passive cooling using back fins. This reflects itself on reducing cell temperature, increasing output power, enhancing electric efficiency and improving the electrical performance of the module. The findings reported before [6-17] are summarized in Table I with classification of solar systems, cooling methods and adopted methods of analysis; theoretical or/ and experimental. This is in addition to a brief description of the performance of solar systems as a function of operative temperature. Table I: Literature Survey on Improvement of PV/T Solar Systems by Cooling Solar System Ref No.

PV

Cooling Method

Method of Analysis

Passive Air Cooling

Forced Air Cooling

With fin

With fin

Others

PV/T

Theoretical With ribs

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

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7

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8

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Experimental

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9

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10

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11

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12

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13

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14

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15

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

16

Theoretical & Experimental

Without fin

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  + water

 

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 Cotton wick. + water or nanofieds



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Table I: Continued No.

Performance of Solar System as a Function of Operative Temperature

- Measured electrical efficiency (𝜂𝑝𝑣) of themodule without fins decreased from 12.5% to 9.5% on increasing operating temperature 𝑇𝑐 from 27° to 77 C°. 6 - Measured thermal efficiency (𝜂𝑃𝑉/𝑇) increased over the range 22°-33% with fins against 16-28% without fins on increasing flow rate from 30 to 90 m3/ℎ𝑟 - Measured (𝜂𝑃𝑉/𝑇) with natural air flow at rate of 12.5m3/ ℎ𝑟 at noon time is 20% with fins agonist 16% without fins. - Developed a theoretical model based on thermal and electrical energy flows in a PV module without and with fins. - Curve fitting of measured𝜂𝑡ℎ results in equations (𝜂𝑃𝑉/𝑇) = 0.247-7.3 ∆t/G without fins against 𝜂𝑡ℎ = 0.297-6.1 ∆t/G with fins 7 ∆t = 𝑇𝑐 ― 𝑇𝑎 (no flow) = 𝑇𝑖𝑛- 𝑇𝑎 (with flow), 𝑇𝑖𝑛 = inlet air in C°. - Curve fitting of calculated results in equations close to those 𝜂𝑃𝑉/𝑇obtained from measurements. - Developed a numerical simulation of electric – thermal performance of a solar concentrating PV/T system to calculate values of 𝜂𝑝𝑣, 𝜂𝑡ℎ and 𝜂𝑃𝑉/𝑇. 8 - Calculated valves of 𝜂𝑡ℎ and 𝜂𝑃𝑉/𝑇 increased with system length However, 𝜂𝑝𝑣 decreased with the increase of length. - The use of parabolic concentrator and fins increased 𝜂𝑝𝑣/𝑡. 𝐼𝑠𝑐 ∗ 𝑉𝑜𝑐

- Measured 𝜂𝑝𝑣 and energy efficiency𝜂𝑒= ( 𝐺𝐴 ) values where 𝐼𝑠𝑐 and 𝑉𝑜𝑐 are the short – circuit current and open – circuit voltage of the PVcell, respectively A is the surface area of cell. 9 - Measured 𝜂𝑝𝑣 and 𝜂𝑒 values increased with the solar irradiance level without and with fins. - Maximum output power with fins was 20% higher than that without fins. - 𝑉𝑜𝑐With fins was about 10% higher than that without fins. - Modeled a single concentrator solar-cell system with fins as a heat sink and investigated the model using a software package. 10 - Estimated cell temperature decreased from 46C° to 39C° on increasing fins height from 0.5 to 3cm. - Estimated cell temperature remained almost constant at about 42C°with the increase of thickness from 0.5 to 4mm. - Measured 𝜂𝑝𝑣versus inclination angle β and output power Pout of a PV panel without and with fins. - Maximum measured 𝜂𝑝𝑣value was 16% for panel without fins against 13.8% without fins and both occurred atβ= 45° - Maximum measured Pout value was 62W for panel without fins against 60.2W without fins and both occurred at β = 45° 11 - Measured 𝜂𝑝𝑣 decreased from 16% to 14.5% with fins and from 15.6% to 14.2% without fins on increasing ambient temperature from 43-53C°. - Measured 𝜂𝑝𝑣 increased from 17.7% to about 19% with fins and from 15.2% to 17.8% without fins on increasing cooling wind velocity from 1 to 3 m/s. - Measured temperature 𝑇𝑐 and Pout from a PV panel with fins’ cooling under natural convection over the hours of a day. 12 - Maximum value of 𝑇𝑐 was 62C° without fins against 59.5C° with fins’ cooling. - Maximum value of Pout was 53.24W without fins against 58.5W with fins i.e with an average increase of 5.5 % in Pout with fins cooling. - Modeled a PV panel with ribbed wall as a heat sink; the height, length and thickness of ribs as well as the as the spacing between ribs were variables. - Investigated the model using a software package. 13 - Estimated panel temperature 𝑇𝑐 reached 56C° for panel without ribs against 46C° with ribs. - Estimated Pout reached 86 % of the panel nominal value without ribs against 90 % with ribs. - Maximum Estimated Pout increased from 6.97 % to 7.55 % of the nominal value on changing angle of ribs from 90° to 45°. - Modeled a PV panel with fins as a heat sink and investigated the model using a software package. - Estimated 𝜂𝑝𝑣 of the panel decreased from 15.3% to 14.5% on increasing cell temperature from 45C° to 57C°. 14 - Estimated 𝜂𝑝𝑣 increased from 14.5% to 15.24% on increasing mass flow rate cooling fluid from 0.035 to 0.075 kg/s - Estimated cell temperature 𝑇𝑐 decreased from 57C° to 45C° on increasing mass flow rate of cooling fluid from 0.035 to 0.075kg/s. - Measured over the hours of a day, temperature 𝑇𝑐 and Pout of a 250W PV module with fins as a heat sink exposed to three types of passive cooling. 15 - With derating factor of 80%, 𝑃𝑜𝑢𝑡 of cooled module to 20C° exceeded 200W by 20.96W and 15.85Wat 12.45 pm and 14.45 pm. - 𝜂𝑝𝑣 at STC is 15.4% while the cooled module reached efficiency of 18.8% at 20C° and irradiation level of 108 W/m2. 16

- Developed a theoretical model to assess 𝜂𝑝𝑣 and exergy efficiency 𝜂𝑒𝑥 of a hybrid PV/ air collector based on measured data during four days of different conditions in India. - Calculated instantaneous values of 𝜂𝑝𝑣 and 𝜂𝑒𝑥of the collector varied between 55-65 and 12.15%, respectively.

- Measured over the hours of a day 𝑇𝑐, Pout and 𝜂𝑝𝑣 for a standalone flat PV module cooled by cotton wick in combination with water, Al2O3/water and CuO/water nanofluids. - 𝑇𝑐 throughout the day has maximum value of 65 C°, reduced to 45C° , 59 C° and 54 C° on cooling using wick in combination with water, CuO/water and Al2O3/water, respectively . 17 - Maximum values of Pout were 47.5W and 44.5W with cooling provided by wick in combination with water and nanofluids, respectively against 41W without cooling. - Maximum values of 𝜂𝑝𝑣 were 10.4 %, 9.7 % and 9.9 % with cooling provided by wick in combination with water, Al2O3/water and CuO/water nanofluids respectively against 9 % without cooling.

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The present paper is organized in five sections. Section I is assigned for the introduction. Section II is aimed to present proposed model for heat transfer through the PV module as influenced by passive air cooling using fins attached at the back surface of the module. III describes the experimental setup along with the used PV modules. Section IV is to report the obtained results including calculated cell temperature as influenced by ambient temperature with and without fins, calculated output power versus ambient temperature or air velocity or solar irradiation for module with fins cooled by still and ventilation air. This is in addition to the dependency of calculated efficiency on the fins particulars including thermal conductivity of fins material, height, thickness and number of fins cooled by still and ventilation air. Also, the cell temperature, the open-circuit voltage and short-circuit current over the day hours were calculated and measured for modules with and without fins. The agreement between calculated and measured values is satisfactory. The obtained results are discussed and correlated with those reported in the literature. Section V is to summarize the main findings of the present work. II.

PROPOSED MODELFOR HEAT TRANSFER THROUGH PV MODULE

The PV module is conceived as consisting of a layer of cells and absorber plate attached to the rear surface of the module using a tedlar film. The module has transparent cover and the fins are considered an extension of the absorber plate to increase its surface for a better cooling of the PV module. As is well known the PV module and plate absorber are inclined according to the latitude angle of the location where the module exists.

Fig. 2: Cross-sectional view of the PV module showing energy flow under exposure to solar radiation. The energy flow in Fig. 2 includes energy losses by convection, energy loss by radiation, energy loss by conduction, energy absorbed by PV cells and energy incident on the module from solar irradiation. In developing the heat transfer models for the PV module, the following assumptions have been made: (1) Steady-state energy transfer has been considered. (2) Side losses from the PV module are disregarded.

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II.1 Module's Heat Transfer Analysis

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The heat balance equation of the cell is expressed [18, 19] as:

Two cases have been considered. The first case assumes perfect thermal contact between the solar cell and the absorber plate, so the solar cell temperature is equal to the absorber plate temperature. Of course this is true at the contact points between the solar cell and the absorber plate. The second case considers the plate and cell temperatures are not equal. II.1.1 Energy balance equations for the PV module without fins. Let the temperatures of the cell, the absorber plate and the ambient are 𝑇𝑐,𝑇𝑝 𝑎𝑛𝑑 𝑇𝐴. (i) Heat balance equation of the cell

𝐺𝛼=ℎ𝑠 ― 𝑝(𝑇𝑐 ― 𝑇𝑃)+ℎ𝑟𝑎𝑑𝑓(𝑇𝑐 ― 𝑇𝑠𝑘𝑦)+𝐺𝛼𝜂𝑝𝑣

(1)

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where ℎ𝑠 ― 𝑝 = Conductive heat transfer coefficient, W/m2.℃ ℎ𝑟𝑎𝑑𝑓 = Front radiative heat transfer coefficient W/m2.ᵒC 𝑇𝑠𝑘𝑦 = 𝑇𝐴 ―6 (as defined in Appendix B) G = Solar irradiation incident on module in W/m2 α = Absorptivity to express fraction of energy absorbed by the PV module.

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The heat balance equation of the plate is expressed [18, 19] as:

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Equation (1) is still applicable to express the heat balance equation of the cell.

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The heat balance equation of the plate is expressed [18 19] as:

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𝐺𝛼(1 ― 𝛾𝑐)+ℎ𝑠 ― 𝑝𝛾𝑐(𝑇𝑐 ― 𝑇𝑝)= ℎ𝑟𝑎𝑑𝑓(1 ― 𝛾𝑐)(𝑇𝑝 ― 𝑇𝑠𝑘𝑦)+ℎ𝑐𝑜𝑛𝑓(1 ― 𝛾𝑐)(𝑇𝑝 ― 𝑇𝐴)+ℎ𝑐𝑜𝑛𝑏(1 ― 𝛾𝑓)(𝑇𝑝 ― 𝑇𝐴)+𝐴𝑚 where: 𝐴𝑚=Module area 𝛾𝑓=Area occupied by fins expressed as a fraction of the area of the absorber plate [21] 𝑄𝑓=Rate of heat transferred from fins to the surrounding medium and determined as follows: 𝑄𝑓 = 𝑛 𝑞𝑓 𝑞𝑓=Rate of heat transfer from one fin to surrounding medium as obtained in Appendix C.

The electrical efficiency of the PV module 𝜂𝑝𝑣 is related to the 𝜂𝑟𝑒𝑓, the efficiency at the reference temperature 𝑇𝑟𝑒𝑓 = 25℃ using a temperature coefficient 𝛽𝑟𝑒𝑓(K-1) as proposed by the manufacture through a linear relation expressed in the form. 𝜂𝑝𝑣 = 𝜂𝑟𝑒𝑓 [1 ― 𝛽𝑟𝑒𝑓(𝑇𝑐 ― 𝑇𝑟𝑒𝑓)] (2) The temperature coefficient is mainly a material property which is about 0.0045 K-1 for crystalline silicon modules. Normally; the values of 𝑇𝑟𝑒𝑓and 𝛽𝑟𝑒𝑓are given by the PV manufacturer [20]. (ii)

Heat balance equation of the absorber plate

𝐺𝛼(1 ― 𝛾𝑐)+ℎ𝑠 ― 𝑝𝛾𝑐(𝑇𝑐 ― 𝑇𝑝)=ℎ𝑟𝑎𝑑𝑓(1 ― 𝛾𝑐)(𝑇𝑝 ― 𝑇𝑠𝑘𝑦)+ℎ𝑐𝑜𝑛𝑓(1 ― 𝛾𝑐)(𝑇𝑝 ― 𝑇𝐴)+ℎ𝑐𝑜𝑛𝑏(𝑇𝑝 ― 𝑇𝐴)+ ℎ𝑟𝑎𝑑𝑏(𝑇𝑝 ― 𝑇𝐴) (3) where: 𝛾𝑐= Fraction of the area of the absorber plate occupied by the solar cells. ℎ𝑟𝑎𝑑𝑏 = Back radiative heat transfer coefficient, W/m2.℃ ℎ𝑐𝑜𝑛𝑓 = Front convective heat transfer coefficient, W/m2.℃ ℎ𝑐𝑜𝑛𝑏 = Back convective heat transfer coefficient, W/m2.℃ Equations (1) and (3) are solved simultaneously to determine the cell temperature 𝑇𝑐 and the plate temperature 𝑇𝑝 at given irradiation level G and ambient temperature𝑇𝐴 when 𝑇𝑐 ≠ 𝑇𝑝 (case 2). With perfect thermal contact between the cells and the absorber plate, 𝑇𝑐 = 𝑇𝑝 and the heat balance equation for determining 𝑇𝑐 at any value of G and 𝑇𝐴 is expressed as: 𝐺𝛼=𝐺𝛼𝜂𝑝𝑣 + ℎ𝑟𝑎𝑑𝑓(𝑇𝑐 ― 𝑇𝑠𝑘𝑦)+ ℎ𝑟𝑎𝑑𝑏(𝑇𝑐 ― 𝑇𝐴)+ℎ𝑐𝑜𝑛𝑓(𝑇𝑐 ― 𝑇𝐴)+ℎ𝑐𝑜𝑛𝑏(𝑇𝑐 ― 𝑇𝐴) (4) Equation (4) determines the cell temperature 𝑇𝑐 at given G and 𝑇𝐴 when 𝑇𝑐= 𝑇𝑝 (case 1). II.I.2 The energy balance equations for the PV module with fins. (i)

(ii)

Heat balance equation of the cell

Heat balance equation of the absorber plate 𝑄𝑓

sinh (𝑚𝐻) +

314

𝑞𝑓 = ℎ𝑓𝑝𝑘𝑓𝐴𝑐𝑠𝑓(𝑇𝑝 ― 𝑇𝐴) cosh (𝑚𝐻) +

( (

ℎ𝑓 ℎ𝑓

) )

𝑚𝑘𝑓 cosh (𝑚𝐻)

(5)

(6)

𝑚𝑘𝑓 sinh (𝑚𝐻)

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ℎ𝑓𝑝

315

𝑚2 =

316 317 318 319 320 321 322 323 324 325 326 327 328 329 330

where: n = Number of fins H = Height of fins ℎ𝑓= ℎ𝑐𝑜𝑛𝑏 = Fins' heat transfer coefficient W/m2 ℃ 𝑘𝑓= Thermal conductivity W/m2 ℃ p = Perimeter of fin ( = (𝐿 + 𝑡) ∗ 2 ) with L and t are length and thickness of the fin.

331 332 333 334 335 336

337 338 339 340 341 342

(7)

𝑘𝑓𝛾𝑓

In equation (6), 𝑞𝑓 is assumed the same for all fins. Equations (1) and (5) are solved simultaneously to determine the cell temperature 𝑇𝑐 and the plate temperature 𝑇𝑝 for a given irradiation level G and ambient temperature𝑇𝐴 when 𝑇𝑐 ≠ 𝑇𝑝 (case 2). Figure 3 shows a cross-sectional view of the PV module indicating where the different heat transfer coefficients apply without and with fins.

(a)

(b)

Fig. 3:Cross-sectional view of the PV module showing where the different heat transfer coefficients apply (a) without fins (b) with fins

Fig. 4: Fins length, height and thickness in X-Y-Z coordinate system II.2 Calculation of Heat Transfer Coefficients II-2-1: Natural Convection over Flat Plate 9

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This section is aimed at calculating the convective heat transfer coefficients from the front and back faces of the module in still air and ventilation air. The first step is to find the Rayleigh number 𝑅𝑎𝐿 using equation (8), which is the product of Grashoff number 𝐺𝑟 and Prandtl number Pr [19]. 𝑅𝑎𝐿 (8) The Grashoff number 𝐺𝑟 is expressed as:

=

𝐺𝑟*𝑃𝑟

𝐺𝑟 = 2 g Lc3/ ν2

(9)

Where g is the acceleration due to gravity, m/s2, 𝐿𝑐 is the characteristic length of the absorption plate, m and ν is the kinematic viscosity, m2/s. The characteristic length 𝐿𝑐is equal to the plate area 𝐴𝑚 divided by the plate perimeter, m. The Prandtl number 𝑃𝑟 is expressed as: Pr = ν / 𝛼𝑡ℎ Where 𝛼𝑡ℎ is the thermal diffusivity, m2/s.

(10)

From the Rayleigh number, the Nusselt number is determined using equation (11) over the range 104< 𝑅𝑎𝐿< 107. 𝑁𝑢 = 0.54 ∗ 𝑅𝑎1/4 𝐿

(11)

Finally, the front convective heat transfer coefficient is obtained [19] using equation (12). ℎ𝑐𝑜𝑛𝑓 =

367

𝑘𝑎 𝐿𝑐 ∗ 𝑁𝑢

(12)

368 369 370 371 372 373 374 375 376 377 378

The back convective heat-transfer coefficientℎ𝑐𝑜𝑛𝑏 is assumed [22-24] equal to that of the front coefficientℎ𝑐𝑜𝑛𝑓over the flat plate as determined by equation (12).

379

𝑁𝑢𝑠 = 0.645 𝑅𝑎𝐿

380 381 382 383

where L is the length of fins and S is the spacing between fins.

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ℎ𝑐𝑜𝑛𝑓 =

II-2-2: Natural Convection on Fins Natural convection across fins is calculated in a similar manner as that for natural convection over a flat plate. The Rayleigh number is obtained using Equation (8). The Nusselt number Nu is then found for flat plate (PV module) as follows: 𝑁𝑢 = 0.27 ∗ 𝑅𝑎1/4 (13) 𝐿 The Nusselt number 𝑁𝑢𝑠 for an inclined plate (PV module) with an inclination angle in the range 0 ≤ β ≤ 45◦ is expressed as: 1/4

( ( )) 𝑆 𝐿

(14)

The front convective heat transfer coefficient is determined from Equation (15) 𝑁𝑢𝑠 ∗ 𝑘𝑎

(15)

𝑆

The back convective heat-transfer coefficient ℎ𝑐𝑜𝑛𝑏 is assumed [22-24] equal to that of the front coefficient ℎ𝑐𝑜𝑛𝑓over the fins surface as determined by equation (15). II-2-3: Radiative heat transfer coefficients The front radiative heat transfer coefficientℎ𝑟𝑎𝑑𝑓 is calculated using equation (16) as reported before [18]. ℎ𝑟𝑎𝑑𝑓(𝑇𝑐 ― 𝑇𝑠𝑘𝑦) = 𝜎𝜀(𝑇4𝑐 ― 𝑇4𝑠𝑘𝑦)

(16)

Where ε is the emission coefficient, σ the Stefan Boltzman constant in W/m2 K4 10

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In analogy with equation (16), the back radiative heat transfer coefficient ℎ𝑟𝑎𝑑𝑏 is calculated using equation (17).

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𝜂𝑝𝑣 = 𝐺 ∗ 𝐴𝑚 (18) Where 𝑃𝑜𝑢𝑡 is the output power of the module. Equation (18) represents another approach for expression the electrical efficiency of the module which is different from equation (2). 𝑃𝑜𝑢𝑡 = 𝐼𝑠𝑐 ∗ 𝑉𝑜𝑐 ∗ 𝐹𝐹 (19)

429 430

Table III gives the range and accuracy of the used instruments measured values.

ℎ𝑟𝑎𝑑𝑏(𝑇𝑝 ― 𝑇𝑠𝑘𝑦) = 𝜎𝜀(𝑇4𝑝 ― 𝑇4𝑠𝑘𝑦)

(17)

II-2-4: Conductive heat transfer coefficient The value of the conductive heat transfer coefficient ℎ𝑠 ― 𝑝 is taken equal to 150 W/m2 ℃ [18]. II-3 PV Module Efficiency The electrical efficiency 𝜂𝑝𝑣 is calculated using the following formula for a given incident solar radiation G. 𝑃𝑜𝑢𝑡

where 𝐼𝑠𝑐 and 𝑉𝑜𝑐 are the measured short-circuit current and open-circuit voltage of the module over the day hour , FF is the fill factor as obtained from the data sheet of the module. III. PHOTOVOLTAIC MODULES AND EXPERIMENTAL SET-UP The experimental set-up consists of six PV modules, each of 250W installed on the roof of one of the buildings of the Faculty of Engineering, which is located on El-Minia City (lat 28.11oand long 30.74o), Egypt. Two of these identical modules were used in this study; one with fins and the other without fins. The layout of the experimental system is shown in Fig. 5. Table II gives the thickness, height, number and material- thermal-conductivity of the fins attached to the PV module. The instruments used for measurements are shown in Fig.5 as follows:  Thermometer Model (HANNA-HI 935009) and Potable K-Thermocouple to read out the temperature of the module surface.  Solar power meter model (TENMARS-TM-206) to read out the solar irradiance incident to the PV modules.  Thermal anemometer model (Testo 425) to read out the ambient temperature and air velocity.  Digital clamp meter model (SEW 3900 cl) and digital multi meter model (UT58DEC) to read out the open- circuit voltage and short-circuit current of the PV modules.

Thermocouple

431 432 433 434 435

Fig.5: Two identical module; one with fins and the other without fins with test bench contains: 1- Digital Clamp 2- Digital Multi meter 3- Thermometer 4- Anemometer 5-Solar power meter 6- Type –K Thermocouple 11

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TABLE II: Basic Fins Data Number N 10

Height H

Thickness t

0.10 m

0.002 m

Thermal Conductivity 𝑘𝑓

205 W/m℃

Fins

Module Back 443 444 445 446 447 448 449

Fig. 6: Scheme of fins under the module Table III Range and Accuracy of Used instruments: No.

Instruments

Range

Accuracy

1-

Thermometer Model (HANNA-HI 935009) and Potable KThermocouple to read out the temperature of the module surface.

-50.0 to199.9℃ / 200 to 1350 ℃

± 0.2% full scale

2-

Solar power meter model (TENMARS-TM-206) to read out the solar irradiance incident to the PV modules.

2 0 to 1999 𝑊 𝑚

2 Within ± 10 𝑊 𝑚

3-

Thermal anemometer model (Testo 425) to read out the ambient temperature and air velocity.

0 to + 20 𝑚 𝑠 -20 to +70℃

± 0.03m/s + 5% of reading ± 0.5℃

DC V 400 mV-1000V DC A 0 - 1500 A

± (0.75% rdg + 2 dgt) ± (1.5% rdg + 4 dgt)

DC V 200 mV-1000 V DC A 2 mA -20 A

0.5% 0.8%

4-

5-

450 451 452 453 454 455 456 457 458 459 460

Digital clamp meter model (SEW 3900 cl) to measure DC current and voltage

Digital multi meter model (UT58DEC) to read out the opencircuit voltage and short-circuit current of the PV modules.

The setup was designed to measure: (i)

(ii) (iii)

Solar irradiance G, air velocity 𝑣𝑎, ambient temperature 𝑇𝐴 and module temperature𝑇𝑐. To check how reproducible is the effectiveness of passive cooling on enhancing the performance of the PV system, measurements of G, 𝑣𝑎, 𝑇𝐴, and 𝑇𝑐were recorded over the day hours on April 15 and May 12, 2018. Open-circuit voltage 𝑉𝑜.𝑐 and short-circuit 𝐼𝑠.𝑐 over the day hours for modules with and without fins. Cell temperature over the day hours for modules with and without fins.

The electrical characteristics of the investigated PV SUNTECH module are listed in table IV.

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TABLE IV: Electrical Characteristic of PV Module Electrical Characteristics (DC) STC: Irradiance 1000 /m2, Module Temperature 25℃ ,AM 1.5

SUNTECH Module STP 250-20/wd

Maximum power at STC (Pmax)

250 W

Optimum operation voltage (Vmp) Optimum operation current (Imp)

30.7 V 8.15 A

Open circuit voltage (Voc)

37.4V

Short circuit current (Isc)

8.63 A 15.4 %

Module Efficiency Temperature Characteristic Nominal operating temperature (NOCT)

45 ± 2℃

Temperature coefficient of Pmax

-0.43%℃

Temperature coefficient of Voc

-0.33%℃

Temperature coefficient of Isc

0.067%℃

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477 478 479 480

IV. RESULTS AND DISCUSSION IV-1 Theoretical Results As predicted from equations (1), (3) and (4), Fig.7 shows how the calculated cell and plate temperatures, 𝑇𝑐and𝑇𝑝 increase linearly with the ambient temperature 𝑇𝐴when 𝑇𝑐≠𝑇𝑝(case 2) and 𝑇𝑐=𝑇𝑝(case 1) for the module without fins in still and ventilation air. The velocity of still air is considered 0.2 m/s against 0.8 for ventilation air. This linear increase confirms the standard relationship between 𝑇𝑐and 𝑇𝐴in terms of NOCT of the module. The average temperature difference between the plate and the cell is 1.0℃ and 1.1℃ when the module is exposed to solar irradiance level of 800 W/m2in still air and ventilation air, respectively.

Fig. 7: Calculated cell and plate Temperatures in still and ventilation air versus ambient Temperature without fins. G = 800 W/m2, H=0.13 m, t=0.002m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 13

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As predicted from equations (1) and (5), Fig. 8 shows the linear increase of the calculated values of𝑇𝑐 and 𝑇𝑝 with 𝑇𝐴 when 𝑇𝑐 ≠𝑇𝑝(case 2) and 𝑇𝑐=𝑇𝑝 (case 1) for the module with fins in still and ventilation air, the same as the module without fins, Fig. 7. Comparison of Fig. 8 against Fig. 7 shows how the fins reduce the cell and plate temperatures by about 4-5 ℃ on the average for the investigated two cases with cooling by still or ventilation air. In percentage, this reduction in cell temperature is about 3-4%, which conforms to that reported before [12]. This reduction in cell temperature is attributed to the increase of heat transfer surface area for the module with fins when compared with that without fins. The cooling effect by ventilation air is more significant when compared with still air because of the higher velocity of ventilation air which results in quick clearing of hot air molecules away from the module surface area.

Fig.8: Calculated cell and plate temperatures in still and ventilation air versus ambient temperature with fins. G = 800 W/m2, H=0.13 m, t=0.002 m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 At solar irradiation of 800 W/m2 for the module with fins, Fig. 9 shows almost a linear decrease of the calculated output power Pout with the increase of ambient temperature TA irrespective of cooling by ventilation or still air. As 𝑇𝐴 increases from 25 ᵒC to 50 ᵒC, 𝑃𝑜𝑢𝑡 decreases from 151.2 to 139.6 W in still air against 180.9 to 162.3 W in ventilation air with a subsequent decrease of the electrical efficiency as reported before [14]. The output power values on cooling by ventilation air are higher than those by still air. This is simply attributed to more effective cooling by ventilation air. At ambient temperature of 20℃, the calculated values of 𝑃𝑜𝑢𝑡 increases with the increase of solar irradiation G, Fig. 10, for the module with fins cooled by still or ventilation air. As G increases from 700 W/m2 to 800 W/m2 𝑃𝑜𝑢𝑡increases from 159.9 W to 180.9 W for cooled module by ventilation air against 142.3 W to 157.5 W for module cooled by still air. This is self-explained. Again, the calculated output power values for cooling by ventilation air are higher than those by still air due to more effective cooling by ventilation air. The rate of increase of 𝑃𝑜𝑢𝑡with the increase of G for air ventilation is higher than that for still air.

Fig. 9: Calculated output power in still and ventilation air versus ambient temperature for module with fins. G = 800 W/m2H=0.13 m, t=0.002 m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 14

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Fig. 10: Calculated output power in still and ventilation air versus solar irradiance for module with fins. TA = 25oC, H=0.13 m, t=0.002 m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 (0% represents reference irradiance = 500 W/m2and corresponding Pout = 116.3 W) At G = 800 W/m2 and 𝑇𝐴of 20℃, Fig. 11 shows how the calculated values of 𝑃𝑜𝑢𝑡 increases with the increase of ventilation air velocity 𝑉𝑎 due to the corresponding increase of the cooling effect. The output power𝑃𝑜𝑢𝑡records 182.7W and 175.7 W for the modules with and without fins, respectively at 𝑉𝑎 of 1.5 m/s against 185.03 W and 178.8W at 𝑉𝑎of 3 m/s. This is self explanatory as the cooling effect increases with the air velocity for modules with and without fins. In still air, the value of 𝑉𝑎is very small and the output power is almost constant as shown in Fig.11

Fig. 11: Calculated output power in still and ventilation air versus air velocity for module with and without fins. G = 800 W/m2, 𝑇𝐴 = 25℃, H=0.13 m, t=0.002 m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 (0% represents reference air velocity =1.5 m/s and corresponding Pout = 181.79 W)

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Fig.12: Calculated electrical Efficiency in still and ventilation air versus thermal conductivity 𝑘𝑓 for fins. G = 800 W/m2, 𝑇𝐴= 25℃ , H=0.13 m, t=0.002 m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 (0% represents reference 𝑘𝑓= 200 W/m2and corresponding electrical efficiency = 13.79%) Figures 12 – 15 show how the calculated electrical efficiency 𝜂𝑝𝑣 according equation (2) changes with the particulars of the fins including fin's thermal conductivity 𝑘𝑓, fin's thickness t, Fin's height H and fin's number n. The base values of these variables are 205𝑊 𝑚°𝑘 for the thermal conductivity, 0.002 m for the thickness, 0.13 m for the length and 20 for the number of fins as listed in Table II. The range of thermal conductivity in Fig.12 is selected to cover values for fins made from steel, aluminum and copper. Over this range of the conductivity, the calculated electrical efficiency of the module did not increase more than 0.5% with cooling made by still or ventilation air, Fig. 12. With the decrease of the conductivity below205𝑊 𝑚°𝑘, the electrical efficiency 𝜂𝑝𝑣decreases by 1-2 % for the module cooled by still or ventilation air. Again, 𝜂𝑝𝑣 values are higher on cooling by ventilation air when compared with those for still air. As stated above, this is because cooling the module by ventilation air is more effective than that by still air with a subsequent decrease of 𝑇𝐶and increase of both𝑃𝑜𝑢𝑡as shown in Fig. 9 and 𝜂𝑝𝑣. Figure 13 shows how the calculated electrical efficiency 𝜂𝑝𝑣 is influenced by the fin's thickness. It is quite clear that the fins' thickness has little effect on 𝜂𝑝𝑣 of the module whatever the cooling is made by still or ventilation air. This is attributed to that fact that the heat-transfer area of fins is slightly influenced by changing the fins' thickness. Again, the values of 𝜂𝑝𝑣 are higher on cooling by ventilation air when compared with those for still air with a subsequent decrease of 𝑇𝑐 and increase of both 𝑃𝑜𝑢𝑡as shown in Fig. 9and 𝜂𝑝𝑣.

Fig. 13: Calculated electrical efficiency in still and ventilation air versus thickness of fins. G = 800 W/m2, 𝑇𝐴= 25oC, H=0.13 m, t=0.002 m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 (0% represents reference thickness=2.5 mm and corresponding electrical efficiency = 13.86%) 16

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Fig. 14: Calculated electrical efficiency in still and ventilation air versus height of fins G = 800 W/m2, 𝑇𝐴= 25oC, H=0.13 m, t=0.002 m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 (0% represents reference Height = 0.1 m and corresponding electrical efficiency = 13.4%) Figure 14 shows how the calculated electrical efficiency𝜂𝑝𝑣 is influenced by fins' height H for the module cooled by still or ventilated air. The longer the height H of fins, the higher is the electrical efficiency 𝜂𝑝𝑣irrespective how the module is cooledby still or ventilated air. This is attributed to the increase of fins' heat-transfer area as H increases with a subsequent improvement of module cooling, decrease of 𝑇𝑐, increase of both𝑃𝑜𝑢𝑡and𝜂𝑝𝑣. Again, 𝜂𝑝𝑣values are higher on cooling by ventilation air when compared with those for still air because cooling the module by ventilation air is more effective than that by still air. This reflects itself on more decrease of cell temperature 𝑇𝑐with a subsequent more increase of both𝑃𝑜𝑢𝑡and 𝜂𝑝𝑣on cooling by ventilation air rather than still air.

Fig. 15: Calculated electrical efficiency in still and ventilation air versus number of fins, G = 800 W/m2, TA = 25oC, H=0.013 m, t=0.002 m, 𝑘𝑓= 205 W/m2 ᵒC, n=20 (0% represents reference fins number=20 and corresponding electrical efficiency = 13.85%) Figure 15 indicates that the number of fins appears to have the greatest effect on the calculated electrical efficiency. As the number of fins' increases, the cell temperature decreases because the increase of find heat-transfer area with a subsequent better cooling of the module, more decrease of 𝑇𝑐, and more increase of both𝑃𝑜𝑢𝑡and𝜂𝑝𝑣. The same as the effect of H, the 𝜂𝑝𝑣 values are higher on cooling by ventilation air when compared with those for still air because cooling the module by ventilation air is more effective than that by still air. As shown in Fig.15, the efficiency values with ventilation air and still air tend to assume constant values. With excessive increase of the number of fins, the efficiency values tend to decrease due to expected deterioration of fins’ cooling. This conforms to pervious findings [10], where cell temperature decreases at first with the increase of number of fins n followed by an increase of the temperature with further increase of n. Therefore, Fig.15 dictates that the optimum value of n is around 40 fins. 17

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IV-2 Experimental validation of the proposed theoretical model The experiments were conducted and the data was recorded daily every thirty minutes from 8:00 am to 5:00 pm during two selected days, April 15thand May 12th, 2018.The data includes G, 𝑇𝐴,𝑣𝑎,𝑉𝑜𝑐 and 𝐼𝑠𝑐 as given in Tables V and VI. Every recorded value is the average of 6 successive readings with 5-minute time-span between them. The basic fins data is given in Table II. TABLE V: Measurements Recorded on 15th April 2018 Time (Hrs)

Average Solar Irradiance W/m^2

Average Ambient Temp. ℃

Average Air Velocity m/s

Average Average 𝐼𝑠.𝑐 𝑉𝑜.𝑐 Amp Volt Without Fins

Average Average 𝐼𝑠.𝑐 𝑉𝑜.𝑐 Amp Volt With Fins

8:00

370

27.0

0.14

35.0

3.85

35.0

4.40

9:00

630

28.2

0.12

34.8

7.50

34.7

7.00

9:30 10:00 10:30

815

28.5

0.19

34.2

7.34

34.3

7.42

11:00

930

30.3

0.10

33.8

8.25

33.4

8.33

12:00

1010

32.0

2.4

33.5

8.71

33.6

8.77

12:30 13:00 13:30

950

36.0

0.45

33.5

8.90

33.5

8.40

14:00

810

34.2

0.9

33.7

7.28

33.7

7.47

650

33.6

1.8

34.0

5.88

34.2

5.99

390

34.0

0.6

33.9

3.7

33.9

3.79

175

33.0

0.45

33.5

1.88

33.6

1.94

8:30

11:30

14:30 15:00 15:30 16:00 16:30 17:00

590 591

592 593 594 595 596 597 598 599 600 601 602

Fig.16 Measured and calculated cell temperatures with and without Fins Figures16 and 17show a comparison between the measured and calculated cell temperatures for modules with and without fins during the selected two days. The figures show also the variation of ambient temperature 𝑇𝐴 and solar irradiation G over the day hours. The figures have the same trend as the module cell temperature, which increases with time over the period from 8:00 am to 13:00 pm and decreases until the end of the day. It is satisfactory that the calculated temperature cell values over the day agree reasonably with those measured. It is quite clear that the fins decrease the cell temperature with consequent increase of the calculated output power 𝑃𝑜𝑢𝑡 and efficiency 𝜂𝑝𝑣 of the PV module. 18

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TABLE VI: Measurements Recorded on 12th May 2018 Average 𝑉𝑜.𝑐 Volt

Average 𝐼𝑠.𝑐 Amp

Average Ambient Temp. ℃

Average Air Velocity m/s

8:00

450

26.0

0.12

35.0

3.85

35.0

4.40

8:30

575

26.3

0.14

34.8

4.80

34.8

5.00

9:00 9:30 10:00 10:30

760 805 915 990

26.4 26.9 27.0 28.4

0.27 0.11 0.28 0.45

34.7 34.5 34.2 34.1

7.50 7.40 7.34 7.83

34.7 34.5 34.4 34.3

7.00 7.10 7.42 7.90

11:00

1028

28.5

0.13

34.0

8.25

34.3

8.33

Time (Hrs)

Without Fins

11:30

1035

29.0

0.91

34.0

8.50

34.0

8.50

12:00

1040

30.1

0.60

33.8

8.71

33.8

8.77

12:30

1010

30.5

1.60

33.9

8.80

34.0

8.80

13:00

985

31.3

1.6

33.9

8.90

34.1

8.40

13:30

932

31.8

1.9

33.8

7.85

34.1

8.00

14:00

827

31.8

2.3

34.2

7.28

34.4

7.47

14:30

770

31.7

0.16

34.1

6.64

34.4

6.77

15:00

695

31.4

0.4

34.2

5.88

34.3

5.99

15:30

540

31.3

0.19

34.4

4.64

34.5

4.74

16:00

425

30.7

0.1

34.1

3.7

34.3

3.79

16:30

375

30.5

0.5

34.0

2.82

34.1

2.90

17:00

240

30.2

0.3

33.7

1.88

33.8

1.94

604 605 606

607 608 609 610

Average Average 𝐼𝑠.𝑐 𝑉𝑜.𝑐 Amp Volt With Fins

Average Solar Irradiance W/m^2

Fig.17 Measured and calculated cell temperatures with and without Fins

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617 618 619 620 621 622 623 624 625 626 627 628 629

Fig.18 Measured solar irradiance level over the day hours of April 15 and May 12, 2018 Fig.18 shows how the measured solar irradiance changes over the day hours of April 15 and May 12, 2018. It is quite clear that the solar irradiation increases at first during early hours of the day up to noon time and later decreases toward the end of the day.

Fig.19 Measured and calculated open-circuit-voltage values over the day hours of May 12 Figure 19 shows how the measured open-circuit voltage of the PV module with and without fins changes over the day hours of May 12, 2018. The open circuit voltage 𝑉𝑜𝑐 decreases at first during early hours of the day and later on increases toward the end of the day. The open circuit voltage depends on the ambient temperature 𝑇𝐴and the solar irradiation G [25]. The decrease of 𝑉𝑜𝑐 with the increase of 𝑇𝐴 is more pronounced when compared with its increase with the increase of G as dictated by Fig.1. This is why the variation of 𝑉𝑜𝑐 in Fig. 19 is almost determined by the change of 𝑇𝐴 over the day as shown in Fig. 17. The measured values of 𝑉𝑜𝑐 for module with fins are slightly higher than those without fins. With the use of the calculated cell temperatures in Fig. 18 and the data sheet values of 𝑉𝑜𝑐at STC as well as the temperature coefficient of 𝑉𝑜𝑐, the values of 𝑉𝑜𝑐 are calculated over the day hours for modules with and without fins. It is satisfactory that the calculated 𝑉𝑜𝑐values are almost close to those measured experimentally with slightly higher values with fins when compared with the case without fins.

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645 646 647 648 649 650 651 652 653

Fig.20 Measured and calculated short-circuit-current values over the day hours of May 12 Figure 20 shows how the measured short-circuit current of the PV module with and without fins changes over the day hours of May 12, 2018. The short circuit current 𝐼𝑠𝑐 increases at first during early hours of the day and later on decreases toward the end of the day. The short-circuit current depends on the ambient temperature 𝑇𝐴 and the solar irradiation G [25]. The increase of 𝐼𝑠𝑐 with the increase of 𝑇𝐴 is so small to be disregarded as dictated by Fig.1. However, 𝐼𝑠𝑐 is linearly related to G. This is why the variation of𝐼𝑠𝑐 in Fig. 20 is almost determined by the change of G over the day hours. The measured values of 𝐼𝑠𝑐 for module with fins are slightly higher than those without fins. With the use of the calculated cell temperatures in Fig. 17 and the datasheet values of 𝐼𝑠𝑐 at STC after being multiplied by 𝐺ℎ𝑟/1000 as well as modified by the temperature coefficient of 𝐼𝑠𝑐, the values of 𝐼𝑠𝑐are calculated over the day hours for the modules with and without fins. The irradiation level at any hour of the day 𝐺ℎ𝑟 is the value of G at each hour of the day. The calculated 𝐼𝑠𝑐values with and without fins are almost the same at any hour of the day. It is satisfactory that the 𝐼𝑠𝑐 values are almost close to those measured experimentally with slightly higher values with fins when compared with the case without fins.

Fig.21 Measured output power values over the day hours of May 12 Figure 21shows how the measured output power 𝑃𝑜𝑢𝑡values of the module with fins are slightly higher than those without fins during the day hours of May 12. This agrees with measurements reported before [10] where the output power with fins was 1.8 -11.8% higher than that without fins. Reference is made to equation (18), 𝑃𝑜𝑢𝑡 is approximately proportional to the product of both 𝑉𝑜𝑐 and 𝐼𝑠𝑐. The change of 𝑉𝑜𝑐 is limited with the change of either G or 𝑇𝐴. However, the change of 𝐼𝑠𝑐 is directly proportional to the change of G as the change with 𝑇𝐴 is minor. Thus the change of 𝑃𝑜𝑢𝑡 over the day hours is mostly determined by the change of G. This is why the trend of variation of 𝑃𝑜𝑢𝑡in Fig. 23 follows that of the irradiation level G.

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654 655

656 657 658 659 660 661 662 663 664 665 666 667 668

Fig.22 Measured electrical efficiency values over the day hours of April 15

Fig. 23 Measured electrical efficiency values over the day hours of May 12 Figures 22 and 23 show over the day hours of the selected two days, the measured electrical efficiency 𝜂𝑝𝑣decreases at first starting from sunrise until noon time followed by an increase until sunset for the module with and without fins. As stated in the above paragraph, the change of G over the day hours determines the change of both 𝑃𝑜𝑢𝑡and𝜂𝑝𝑣. Therefore, thechange of 𝜂𝑝𝑣 over the day hours in Figs. 22 and 23 is determined by that of G with an increase at first from sunrise until noon time followed by a decrease until sunset as given in Tables V and VI. On May 12th, the electrical efficiency𝜂𝑝𝑣 values of module with fins are 14.8%, 14.0% and 14.7% at 8:00 am, 12:00 pm and 17:00 pm, respectively, Fig. 22. Without fins, 𝜂𝑝𝑣 has a value of 14.6%, 13.1% and14.4% at 8:00 am, 12:00 pm and 17:00 pm, respectively. As stated in section Ⅲ, the PV modules are installed on the roof of a building, which is covered with ceramic plates. In May,

669

the weather in Egypt is usually so hot and the temperature at noon time between 11:00 am – 1:00 pm is so high to the extent

670

that the heated ceramic floor emits radiation toward the module to heat up the fins underneath. The metallic fins absorb such

671

radiation and heat the module in addition to its heating by the incident radiation on the front face. This may decrease the

672

effectiveness of fins in cooling the PV module. This may result in a decrease of the output power when compared with the

673

module without fins over the same period of noon time as shown in Fig. 21. On the other hand, the electrical efficiency value

674

according to equation (2) is decided by the surface cell temperature which is smaller for the module with fins in comparison

675

with that without fins as shown Fig. 17. This is why the electrical efficiency of the module with fins in higher than that without

676

fins over the hours of May day as shown in Fig. 23. 22

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V.

CONCLUSIONS

1- A theoretical and experimental validation study on performance improvement of PV module with passive cooling using fins in still and ventilated air is presented. 2- The cell temperature increases linearly with the increase of ambient temperature for modules with and without fins irrespective of their cooling by still or ventilation air. The fins result in about 4-5oC reduction in cell temperature. 3- At solar irradiation level of 800 W/m2, the module output power 𝑃𝑜𝑢𝑡 decreases linearly with the increase of ambient temperature𝑇𝐴. As 𝑇𝐴increases from 25 to 50℃, 𝑃𝑜𝑢𝑡for a 250W module decreases from 151.2 to 139.6 W in still air against 180.9 to 162.3 W in ventilation air. 4- At ambient temperature of 20℃, 𝑃𝑜𝑢𝑡 increases with the increase of the irradiation level G with and without fins. As G increases from 700 to 800 W/m2, 𝑃𝑜𝑢𝑡 increases from 159.9 to 180.9W for a 250-W module cooled by ventilation air against 142.3 to 157.5W for cooling by still air. 5- Increase of air flow velocity 𝑉𝑎results in effective cooling by fins with a subsequent increase of output power. 𝑃𝑜𝑢𝑡 records 182.7 and 175W for a 250W module with and without fins at 𝑉𝑎 of 1.5 m/s against 185 and 178 W at 3 m/s. 6- The electrical efficiency of the module with fins is significantly increased by the increase of fins' height and number. However, the effect of fins' thickness and thermal conductivity is not noticeable. 7- Over the day hours, the calculated and measured values of cell temperature 𝑇𝑐increase at first from sunrise until noon time followed by a decrease until sunset. 8- Over the day hours, the calculated and measured values of short-circuit current𝐼𝑠𝑐 increase at first from sunrise until noon time followed by a decrease until sunset. 9- Over the day hours, the calculated and measured values of open-circuit voltage 𝑉𝑜𝑐decrease at first from sunrise until noon time followed by an increase until sunset. 10- Over the day hours, the output power 𝑃𝑜𝑢𝑡increases at first from sunrise until noon time followed by a decrease until sunset. 11- The calculated values of cell temperature, short- circuit current and open-circuit voltage of the investigated 250W module agree reasonably with those measured experimentally. APPENDIX: A Steady-state Thermal Efficiency The steady-state thermal efficiency of the PV/T air collector [7] is expressed as:

[

(

𝑇𝑖𝑛 ― 𝑇𝐴

)]

707

𝜂𝑡ℎ =𝐹𝑅 𝜏𝛼(1 ― 𝜂𝑎) ― 𝑈𝐿

708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723

where:

724

the sky. The sky can be considered an a blackbody at some equivalent sky temperature 𝑇𝑠𝑘𝑦 so that the actual net radiation

725

between a horizontal flat plate of area A with emittance εand temperature T to the sky at 𝑇𝑠𝑘𝑦is expressed as [26].

𝐺

(A-1)

𝑇𝑖𝑛= Inlet air temperature 𝑇𝐴= Ambient temperature 𝜂𝑎 =Module efficiency evaluated at ambient temperature. 𝛼 = Average absorpitivity 𝜏 = Glass transmittance of module cover 𝑈𝐿 and 𝐹𝑅 are the modified overall heat loss coefficient and heat removal factor for PV/T solar collectors [26].

APPENDIX: B 𝑇𝑠𝑘𝑦 in Relation to Ambient Temperature To predict the performance of a solar collector, it will be necessary to evaluate the radiation exchange between a surface and

23

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726

𝑄 = ε 𝐴 (𝑇4 ― 𝑇4𝑠𝑘𝑦)

727

Where ε is the emission coefficient and σ is Stefan Boltzmann.

728

The equivalent blackbody sky temperature accounts for the fact that the atmosphere is not at uniform temperature and the

729

atmosphere radiates only in certain wavelength bands. Several relations have been proposed to relate 𝑇𝑠𝑘𝑦 to measured

730

metrological ambient temperature 𝑇𝐴.

731

One of the simple expressions is to subtracted 6C° from the air temperature to obtain an estimate for 𝑇𝑠𝑘𝑦, so

732

𝑇𝑠𝑘𝑦= 𝑇𝐴 ―6

733 734 735 736 737 738 739

APPENDIX: C

740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762

(B-2)

Rate of Heat Transfer from One Fin to Surrounding Medium Consider a fin exposed to surrounding air at a temperature 𝑇𝐴 as shown in Fig. 3. The temperature of the base of the fin is𝑇𝑝. The fin has height H, length L and thickness t as shown in Fig.4. The fins are spaced by distance S. The equation describing the distribution of fin's temperature rise above ambient one along the y-axis is expressed as [26]: 𝑑2𝜃 𝑑𝑦2

― 𝑚2𝜃 = 0

Where 𝜃 = 𝑇𝑦 2) 𝑚2 =

764 765 766 767 768 769

(C-1)

(C-

― 𝑇𝐴

ℎ𝑓𝑝

𝑘𝑓𝐴𝑓 ℎ Where 𝑓 (= ℎ𝑐𝑜𝑛𝑏) is the fins' heat transfer coefficient W/m2℃, kf is the fins' thermal conductivity W/m2℃, p is the perimeter of fin and θ is the fins' temperature. The perimeter p is expressed as: 𝑝 = (𝐿 + 𝑡) ∗ 2 , The general solution for equation (1) is 𝜃𝑦 = 𝑐1𝑒𝑚𝑦 + 𝑐2𝑒 ―𝑚𝑦(C-3) One boundary condition is 𝜃 = (𝑇𝑝 ― 𝑇𝐴) 𝑎𝑡 𝑦 = 0 (C-4) The subscript b denotes where the fins contact with the absorber plate. The other boundary condition is based on the assumption that the heat losses take place by convection from its end [19] at y = H. 𝑑𝜃

― 𝑘𝑓𝑑𝑦|𝐻 = ℎ𝑓𝜃|𝐻 The solution is obtained algebraically to express the distribution of θ along the y-direction as: 𝑐𝑜𝑠ℎ [𝑚(𝐻 ― 𝑦)] +

763

(B-1)

𝜃 (𝑇𝑝 ― 𝑇𝐴)

= cosh (𝑚𝐻) +

( (

ℎ𝑓

ℎ𝑓

) )

𝑚𝑘𝑓 sinh [𝑚(𝐻 ― 𝑦)]

(C-5)

(C-6)

𝑚𝑘𝑓 sinh (𝑚𝐻)

All the heat lost from the absorber plate by the fin's base takes place at: y = 0, Using the equation for the temperature distribution, one can calculate the heat loss 𝑞𝑓 from one fin to the surrounding medium as: 𝑑𝑇

(C-7)

𝑞𝑓 = ― 𝑘𝑓𝐴𝑐𝑠𝑓𝑑𝑦|𝐻

24

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sinh (𝑚𝐻) +

770

𝑞𝑓 = ℎ𝑓𝑝𝑘𝑓𝐴𝑐𝑠𝑓(𝑇𝑝 ― 𝑇𝐴) cosh (𝑚𝐻) +

ℎ𝑓

( (

ℎ𝑓

) )

𝑚𝑘𝑓 cosh (𝑚𝐻)

(C-8)

𝑚𝑘𝑓 sinh (𝑚𝐻)

771 772

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Acknowledgement: The authors would like to thank the reviewers for their fruitful comments which enhanced the clarity of the paper. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

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Highlights 12345-

Performance of a PV-module with passive cooling is studied by theory and experiments. Cell temperature, I-sc and V-oc by theory agree with those measured experimentally. Passive cooling with fins results in about 4-5℃ reduction in cell temperature. Cooling by ventilation air is better than that by still air as output power increases. Electrical efficiency of the PV-module increases with fins’ height and number.