Evaluating the thermal performance of PV panels an ANSYS simulation of mixed convection and air spee

2.1. Analytical and mathematical methodology

Solar energy balance is the analytical model representing the core system approach of evaluating thermal performance that quantifies how energy enters and exits a photovoltaic (PV) system, from the moment the sun’s radiation enters the system at the front surface of the module, to the final switching off and dumping of electric energy. The amount of solar influx could be denoted by 𝑄solar, the amount of solar irradiance captured by the module. In this system there are specific components defined as: Optical Losses 𝑄op, loss, the radiation reflected in the module; Thermal Losses due to the Top Surface

𝑄th, loss, top or convective and radiative transported heat within the upper module surface; and Thermal Losses due to the Bottom Surface 𝑄th, loss, bottom that is convective and radiative heat transported through the bottom module surface. So, the full expression of incoming solar radiation into the energy in the PV panel, which is dissipated in the form of thermal and optical processes, and then transformed into electrical power, is described in detail in Equation 1 and Figure 1 below [20]: Q generated = Q solar - ^ Q th, loss, top + Q th, loss,bottom + Q op, loss h

Reflective losses are a notable source of future optical losses in photovoltaic (PV) setups. The amount of solar irradiance reflected from the solar-cell surface by the panel material itself is determined by the panel material’s reflectance. In most PV installations, the outermost layer almost always takes one of two forms, i.e., ETFE (Ethylene Tetrafluoroethylene) or glass. That solar modules are designed with optically thick substrates means they tend to reflect a measurable fraction of the incident solar irradiance, which has the practical consequence that the power density of the irradiance on the solar cells is noticeably reduced. There is a quantitative expression that can describe this optical phenomenon, and this is explained in equation (2) below [20]. Q op,loss = rETFE # Q solar (2)

Where: Q solar is the total incoming solar radiation, 𝑟 ETFE is the reflectivity of the ETFE layer. Relative reflectivity, symbolically r ETFE, is the ratio of solar radiation that does not go through a specific medium and the sun’s total radiation. Therefore, a reflectivity value of

0.1. means that only 10% of the incident’s irradiance is absorbed by

the material, resulting in an optical energy loss in the overall energy balance.

(ETFE), which receives the focused flux. The convection losses are a combination of free and forced convection. There is also thermal radiation loss between the glass layer and the environment; The top surface thermal losses 𝑄𝑡ℎ,𝑠𝑠,𝑡𝑜𝑝 can be expressed as [20]: Q th, loss,top = ^ Q Forced, conv, top + Q natural, conv, top + Q rad,top h (3)

The forced convection heat transfer coefficient, which is defined as a function of wind speed, air velocity, and module geometry, is proportional to the wind speed; therefore, a greater wind speed will result in a more significant coefficient of heat transfer and, as a result, increased heat dissipation. In contrast, natural convection occurs when the temperature of the PV panel’s surface is higher than that of the surrounding environment, warming the nearby air and making it less dense, causing it to rise and pushing cooler air away. Two non-conductive processes, in combination, lead to thermal losses on the upper side of the PV module. The forced convective coefficient can be estimated from the correlation of the Nusselt number value, which is the ratio of convective to conductive heat transfer, and a dimensionless ratio with the following expression [22]: Nu F,t = 0.13Re L0.703 (1 + sin (b) ) 0.38 (4)

where ReL is the Reynolds number, used to measure the comparative magnitude of inertial and viscous forces, and β is the tilt angle of the panel. In the case of natural convection, the Nusselt number equals [22]: Nu N,t = 0.7386RaL0.1826 (1 + cos (b) ) -0.4575 Nu N,t = 5.4412RaL0.1102 (1 + cos (b) ) -0.085

Therefore, the mixed convective coefficient is calculated using the formula: Nu 3M,t = Nu 3F,t + Nu 3N,t (7)

Figure 1. The distribution of the powers in the PV panel system [23] The losses through the top surface of an individual photovoltaic (PV) module arise from two related processes: convection and radiation. Forced convection occurs when air passes over the PV surface, making it easier to remove heat from the module. Convection and radiation are the two types of thermal losses on the top surface of the PV panel. These losses flow out from the surface of the glass

Where RaL is the intensity of buoyancy-driven flow with temperature differences, heat is lost through radiation at the top of the PV module and into the surrounding environment. Radiative heat transfer and the Stefan-Boltzmann law are temperature-dependent with respect to the temperature difference between the module surface and the outside air. Thermal losses from the bottom surface are like those on the top side, except that this surface is oriented differently relative to the ambient air and the flow. The tilt angle affects forced convection at the bottom, and the heat exchange is computed using a nearly identical formula to that used on the top surface, with some tilt-angle-dependent modifications. Conversely, the inflow angle and its interaction with the bottom surface, modeled after the natural convective coefficient, is described by a correlation similar to that used to define the top surface, but adjusted to the tilt angle. The thermal losses from the bottom surface can be expressed using the same relation given for the top surface [23].

Q th, loss,bottom = ^ Q Forced, conv, bottom + Q natural, conv, bottom + Q rad,botoom h

For the top and bottom surfaces, mixed convection is employed, involving both forced and natural convection. This is because, in most real-life situations, both processes occur simultaneously. Regarding the Nusselt numbers, the net convective heat transfer coefficient is the sum of the forced- and natural-convection Nusselt numbers. The PV panels have a tilt angle β that influences convective losses and radiative heat transfer. Convective heat transfer is greatly enhanced when the panel is tilted, as this affects the airflow around it. The forced convective coefficient can be estimated from the correlation [23]: 90 % - b h F,b = h F,t b 90 % l (9)

Where hF,t is the convective coefficient at the top surface, and hF,b is the convective coefficient at the bottom surface. The natural convective coefficient can be obtained from the correlation [23] Nu N,b =

Nu N,b = 0.7386 ^ Ra L h0.1826 ^ 1 + cos b h-0.4575 Nu N,b = 5.4412 ^ Ra L h0.1102 ^ 1 + cos b h-0.085

Therefore, the mixed convective coefficient is calculated using the formula: Nu 3M,b = Nu 3F,b + Nu 3N,b (13)

2.2. The thermal analysis assumptions

It is assumed that all material properties are isotropic and independent of temperature. The reflectivity of the various materials is considered of utmost importance to the analysis. Solar irradiation is not reflected on any surface and is completely passed to the surface beneath. The transmissivity of the EVA is assumed to be one. Internal reflection between the upper EVA and the solar cells is accounted for, but other internal reflections between layers are deemed unimportant. The portion of solar irradiation not reflected by the cell or turned into electricity is transformed into thermal energy. The ambient temperature is uniform across all areas exposed to the environment.

2.3. Simulation assumption

In this study, all material properties used in the photovoltaic (PV) panel model are assumed to be isotropic and temperature-independent, thereby simplifying computation. Broadband optical assumptions from the literature are used instead of idealized values for the EVA encapsulant layer. Notably, EVA transmissivity is assumed to range from 0.85 to 0.90; reflectivity around 0.05 to 0.10, and the remaining fraction consists of absorptivity, as is expected in light of the optical behavior of a solar panel in the solar range (300–1100

nm). These values provide more realistic light transmission and losses through the EVA layer, increasing model fidelity compared to the unrealistic 1.0 and 0.0 reflectivity transmissive values. The solar irradiance reflected from the external layers of the panel, such as ETFE or glass, is assumed to have a standard reflectivity of about 0.07-0.10, which affects the actual energy generation across the Si cells. High silicon cell-layer absorptivity (0.90 to 0.97) and low reflectivity (~0.03) are assumed, consistent with its status as an active photovoltaic material. Internal reflections are simplified between the layers; only the reflection between EVA and solar cells is considered significant. The incident solar radiation is 1000 W/m², and the PV cell can be assumed to act as a heat sink in thermal equilibrium, capable of converting absorbed solar energy into electrical energy. It has been carefully chosen in both the mesh properties and the spatial resolution to achieve a converged model and numerical accuracy. The mean skewness values were below 0.025, and the orthogonal quality was close to unity. A combination of these assumptions will enable simulation of the thermal characteristics and airflow effects on the temperature and power output efficiency of the PV panel at various wind speeds. The values in Table 2 below indicate the values of material (Emissivity(ε)values) applied in the simulation. Table 2. Emissivity values of photovoltaic panel materials Material Glass (cover layer) EVA (encapsulant) Silicon (solar cells) Back sheet material

0.85. – 0.95

These values are an average value of all infrared spectrums of interest at characteristic operating temperatures (~300-400 K). Emissivity depends on surface finish, roughness, and temperature; as mentioned, emissivity is typically measured for PV manufacturing materials. The emissivity is generally high because glass is smooth and polished, and it can effectively radiate heat through its surface (~0.90). EVA encapsulant can exhibit relatively varied values depending on formulation and surface treatment, but typical broadband values are around 0.85–0.90. Silicon solar cells have lower emissivity (~0.75–0.85) according to surface texture and antireflective coating conditions. Back sheets have high emissivity (>0.90) to facilitate thermal radiation. In performing the numerical simulations in ANSYS Fluent, airflow was modeled as approaching the PV panel, consistent with common engineering work on inclined panels, where ambient airflow is expected to be parallel to the ground and therefore hits the panel at its tilt angle, i.e., oblique to the panel surface.

2.4. Pv model mesh

The quality of the mesh in ANSYS models of solar PV panels is crucial for determining how easily the model can be transported. The measures of mesh integrity typically employed include three met-

rics: skewness, orthogonal quality, and average element quality. The solution’s skewness is very high (near 1), which can lead to convergence issues and a numerically unstable heat-transfer simulation. However, the skew toward low value (< 0.5) improves simulation and reliability, as shown in Table 3 below. The closer to 1 quality is an orthogonal quality, which indicates that the elements correspond with the expectation of the solver to which these elements were to be applied, especially in the lay (boundary) resolution in CFD. Any figure less than 0.1 will be considered bad and can bring thermal forecasting to its knees. An average mesh quality, a composite measure of element shape, skewness, and alignment, is recommended, with the average mesh quality held above 0.8 in solar PV panel thermal calculations, where reliable calculation of temperature gradients and uniform heat transfer across panel surfaces is required [23]. Poor accuracy in these quantities may lead to false hot-spot forecasts, resulting in an inadequate assessment of the thermal performance of PV systems. Therefore, ANSYS requires refined meshing and quality checks to model the cooling and heating effects of solar energy modules.

form surface mesh is used for the Si cell layer. The mesh was also chosen as a Hexa type with free mesh and linear elements to ensure the best element order and distribution for each Si cell, as shown in Figure 2 below. The choice of element size starts from 10 mm. The mesh quality is checked for skewness and orthogonal conditions. The best element size should have an average skewness value between 0 and 0.25, with an orthogonal quality value between 0 and 1, where 0 is the worst, and 1 is the best. According to these conditions and the results in Table 4 below, the 7 mm element size was the suitable choice for this simulation model’s meshing, yielding the best orthogonal average value just below the single value.

0.25. — 0.5

The following paragraph explains the PV panel model’s mesh parameters and conditions. The mesh will start with a 10 mm element along all model edges, using a high smoothing option and hard behavior. The multi-Zone mesh method with a Hexa-mapped, uni-

Figure 2. (A) PV panel Si cells mesh, and (B)the model multizone mesh method arrangement

Table 4. Mesh parameters according to the element size Element size 10 mm 9 mm 8 mm 7 mm 6 mm

2.5. Integration of mesh quality and thermal model

Mesh generation is not a separate step in computational thermal modeling of PV panels; rather, it is a fundamental part of accurate heat transfer modeling. The accuracy of the temperature profiles obtained on a spatial scale and the heat flux calculated using ANSYS-based simulations is sensitive to mesh quality metrics such as skewness, orthogonal quality, and average element quality. Numerical instabilities arise from poor mesh quality, especially in thin

Skewness average 1.63e -002 1.80e -002 1.74e -002 1.24e -002 1.15e -002

boundary layers, where steep temperature gradients set the threshold for the efficiency of both forced and mixed convection. For instance, simulations with high skewness or low orthogonality can distort the thermal boundary layer thickness and the heat-dissipation rate of Si cells. Here, mesh parameters were selected to match physical behavior in the mixed- and forced-convection ranges. A multi-Zone mesh with Hexahedral elements, with a mean skewness below 0.15 and orthogonality near 1, allowed the mesh to accommodate the relevant boundary layer near the PV panel, where the

maximum temperature decreases occurred. Thus, the mesh convergence study concluded that decreasing the element size from 10 mm to 7 mm improved the accuracy of local heat flux forecasting and strengthened the correlation between wind speed and cell temperature, confirming that the mesh quality could effectively capture all differences. For instance, the thermal gradients captured in the 7 mm mesh align directly with the numerical performance of the reference experimental results, demonstrating the mesh’s ability to capture the airflow’s true dependence on thermal dissipation.

2.6. Boundary conditions and mesh-thermal

Boundary conditions such as stipulated heat fluxes, convective coefficients, and set or ambient-temperature surfaces are physically meaningful only if the mesh supports a stable, accurate solution of the governing equations. Heat conduction in the panel layers and convection at the panel-solid interface were also modeled in the simulation using properly chosen mesh element sizes and high-quality cell metrics. The fact that the simulated cell of the Si minimized uncertainty in temperature and that the numerical artifact (e.g., globally infamous hot spots) is also evidence of the positive relation between mesh quality and thermal results. The mesh quality and refinement will provide reasonable estimates of cooling efficiency, thermal stress, and the risk of long-term degradation of PV modules under different wind conditions. Thus, the meshing and choice of boundary conditions can now be better justified and aligned with the predictive ability of the thermal model, thereby enhancing the trustworthiness of both the scientific results and those made by the engineer.

2.7. Heat flux calculations and the boundary conditions

The boundary conditions of this simulation are based on real PV panel specifications to achieve more realistic results and maximize their relevance to real-life applications. The PV panel’s Si cells produced 70 W at a working temperature of 25 °C and an incident solar 2 radiation (q solar) of 1000 W/m . The optical properties of PV panel layers are defined by three parameters, i.e., absorptivity (α), transmissive (τ), and reflectivity (ρ), fulfilling the energy conservation equation as follows: a + x + t = 1 (14)

Each term represents the fraction of incident solar irradiance absorbed, transmitted, or reflected by the material, respectively. It should be noted that reflectivity (ρ) is the fraction of radiation reflected away from the surface and not absorbed or transmitted through the layer. A reflectivity value of 0.10 means that only 10% of the solar irradiance is reflected, not absorbed. Then the remaining percentage (derived from transmissivity and reflectivity, respectively) gives the absorbed energy fraction. Accurate interpretation of optical parameters is needed to determine the optimal energy balance across the panel layers, temperature distributions, and actual performance. Table 5 summarizes the transmissivity and reflectivity

values for each layer, using established optical properties literature to reflect the transmissivity and reflectivity available in the public domain, thereby enabling physically consistent simulations. The sequence of PV panel layers is illustrated in Figure 3, and their absorptivity, transmissivity, and reflectivity are listed in Table 5. Table 5. The physical properties of the first three layers. Material ETFE EVA Si

Figure 3. PV Panel Layers Sequence Layout [26] According to Figure 3, the first three layers were the ETFE, then EVA, and the last layer was silicon cells. According to Table 4, the ETFE Absorptivity was 0.1 for 1000 W/m2 incident solar radiation (q solar), corresponding to 100 W/m2, and 0.07 was reflected, re2 sulting in 70 W/m2 in optical losses. The 100 W/m will be set as the ETFE layer heat flux value; the second EVA layer has zero absorptivity and reflectivity, and the heat flux for this layer will be produced from the silicon cell layer. The incident solar radiation from the first layer has a transmissivity of 0.83, corresponding to 830 W/m2, and will transfer to the third silicon cell layer. This layer has a reflectivity of 0.03, which means 0.03 of the 830 W/m2 will be reflected to the second layer above it, so the heat flux for the second layer will be 2

24.9. W/m .

The heat flux for the third layer will equal the transmitted incident 2 solar radiation from the first layer (830 W/m ) minus the reflect2 2 ed heat flux (approximately 25 W/m ), which equals 805 W/m . As mentioned above, the third silicon cell layer also generates a heat flux at its surface, arising from the PV panel’s power output (70 W). To transform this value to heat flux, the generated power must be divided by the total surface area of the 36 Si cells in this layer. In the ANSYS modeler, the single cell surface area is 0.01468 m2; for 2 36 cells, it is 0.52848 m . So, the surface heat flux will be 70 divided by 0.52848, which equals 132.455, and the total heat flux for the 2 third layer will be 805 minus 132.455, which equals 672.455 W/m . The first and last layers (ETFE and CFRP) will experience heat radiation, and they must be treated as boundary conditions using the emissivity value (0.89) from Table 4 above for both layers. The Si

layer in the PV panel absorbs some of the energy from incident solar radiation and transforms part of it into electrical energy. The rest is absorbed as heat. The electrical power generated corresponds to the energy removed and is therefore considered a heat sink (i.e., energy removed) for the Si layer in the thermal model. The optical losses in the outer layers (e.g., ETFE and EVA) reduce the amount of solar radiation reaching the Si layer. For example, with incident radiation of 1000 W/m², after losses in the previous layers, only around 830 W/m² reaches the Si layer. The heat flux absorbed by the Si layer is calculated by subtracting the reflected portion at the Si surface from the transmitted radiation. In this example, approximately 805 W/m² reaches the Si layer after reflection losses. The electrical power generated by the PV cells, for example, 70 W total across 36 cells, is energy diverted from heat storage and does not contribute to temperature rise. This power is treated as a heat sink by converting it into a heat flux value after dividing the total generated power by the total Si cell area (surface area). For 36 cells with a total area of 0.52848 m², 2 the power-generated heat flux is 70 / 0.52848 ≈ 132.455 W/m . The heat flux that decreases the electrical power absorbed (heat sink) is the net heat flux absorbed (changed to heat) by the Si layer: Q net = Q absorbed – Q generated power, using the example numbers: 2

This net flux is the heat load that drives the rise in temperature of the Si layer. In electrical generation, a heat sink is designed to reflect the physical reality that it essentially absorbs energy in the thermal system, thereby reducing the heat load on the object’s total radiation. This matches optical and electrical energy flows, enabling the thermal simulation to predict the real cell temperature of Si under operating conditions. Adding this heat sink term to the energy balance and boundary conditions of the Si layer can enable the model to capture the interactions between electrical output and thermal behavior, as observed with increased airflow (greater convection), which reduces silicon cell temperatures and thereby increases power efficiency. T he computational domain may include the PV panel and a sufficient surrounding air region to prevent boundary effects (blockage ratio <5% relative to the inlet cross-sectional area, based on a preliminary domain sensitivity test). Dynamic equilibrium temperature modeling and controlled airflow modeling representing normal operating conditions were used to perform steady-state simulations. Effects of turbulence are modeled using the k−ω SST turbulence model, which provides superior treatment of wall structures, with y+ values between 1 and 3 to resolve the boundary layer. Radiative heat transfer was modeled using the Discrete Ordinates (DO)radiation model, if the media (air with negligible absorption/ scattering) was excluded. The thermal contact resistance between the PV layers were neglected due to their negligible thickness, which also meant good thermal contact within the normal construction of a PV panel. These boundary conditions include a velocity inlet and a pressure outlet for airflow, symmetry conditions at the lateral domain boundaries, and convective and radiative heat exchange across

exposed surfaces. Second-order terms in the momentum, energy, and turbulence equations were used for numerical accuracy in the spatial discretization. Residuals were set to 10−6 for all transport equations, and stability was ensured by monitoring key solution variables, such as the maximum silicon cell temperature and other parameters. The convective heat transfer between the upper and lower layers will be calculated using the following equation. [25]: h=

Where: Nu is Nusselt number, 𝑘 is the thermal conductivity of air (approximately 0.0257 W/m.K at room temperature), and 𝐿 is the characteristic length of the surface. The Nusselt number can be calculated from the following equation: Nu = C # Re m # Pr n (16)

Where: 𝐶𝑚, and 𝑛 are constants that depend on the geometry and flow conditions. For forced convection over a flat surface, typical values are: 𝐶 = 0.332, 𝑚 = 0.5, and 𝑛 = 0.33. (𝑃𝑟) is the Prandtl number, which equals 0.6904, and Re is the Reynolds number, which is calculated from the following equation [26]: Re =

Where: U is the wind velocity (4 m/s), 𝐿 is the characteristic length of the surface, and 𝜈 is the kinematic viscosity of air (m²/s), which is temperature dependent. From the above equations, the wind speed variation will change the value of the mixed convection coefficient (h) in equation (13) and, in turn, the Si cells’ temperature and the generated power. Figure 4 below illustrates the effects of mixed convection and its direction on the PV panel.

Figure 4. The PV panel mixed convection, solar irradiation, and reflected radiation direction The numerical simulation carried out in this study is a three-dimensional (3D) steady-state thermal analysis using the software ANSYS Fluent to represent the actual spatial temperature distribution and

airflow on the PV panel. The PV panel modeled for simulation is a traditional monocrystalline silicon module with 36 cells in a sixby-six configuration. The surface area of each Si cell is equal to ∼0.01468 m², and the Si cell layer area is equal to ∼0.52848 m². The 36-cell combined size (the total panel size) is proportional to the size of an average panel, the average surface area is 0.52848 m2, the active surface length (parallel with the wind flow) is approximately

0.3. m, and a width that differs with the number of cells (that of a

commercial panel is typically comparable). The mesh construction is performed using a multi-zone approach with hexahedral (Hexa) elements to achieve a structured, uniform cell field, particularly in the Si cell layer and the boundary layer. In a mesh convergence study, the element dimensions ranged from 6 mm to 10 mm. The choice of an optimal element size of 7 mm is the preferred minimum size to achieve the highest resolution and optimal solution accuracy at the lowest computational cost. Mesh spatial resolution is chosen to ensure that the thermal boundary layer, which has steep temperature gradients, is resolved; mesh resolution is directly controlled. This made it possible to perform effective computations of the convective heat transfer coefficient and the panel’s surface temperature distribution. All skewness values for the average mesh were less than -0.25, and the orthogonal quality approached the skewness level that meets ANSYS CFD criteria, indicating good mesh and numerical quality. This 3D mesh resolution and model dimensioning allow the forced versus mixed convection regime, temperature gradient of the Si cells, and overall thermal characteristic of the PV panel to be captured with high accuracy.

generation. In the Si layer, the net heat generation is then: Qnet = Qabsorbed − A Pelec, where Q absorbed is the absorbed solar radiation heat flux. The removal of electrical power is used as a heat-flux boundary condition (sink) on the Si cell surface, thereby reducing the source term of the heat-flux field. This converter converts solar energy into useful electrical energy, minimizing heat production and, therefore, panel temperature.

2.8. Optical-thermal energy budget per layer

In these simulations, the authors assume the total solar irradiance incident on the PV panel surface is 1000 W/m². Layer-wise Optical Budget (Incident → Reflected → Transmitted → Absorbed). The energy flows are computed for each layer (ETFE, EVA, Si cell). For the ETFE Layer, the Reflectivity (ρ ETFE) ≈ is 0.07, so 7% of the incident radiation is reflected (optical loss). Transmissivity (τETFE) ≈ 0.83, allowing 83% of the signal to be transmitted to the next layer. Absorptivity (αETFE) = 1 − ρETFE − τETFE = 0.1, reflecting the absorbed energy transformed into thermal energy in ETFE. The transmissivity (τ ) for the EVA Layer is 0.85–0.90(realistic assumption). AbsorpEVA tivity (αEVA) and reflectivity (ρEVA) sum to the remaining fraction, with reflectivity typically low. The absorbed energy in EVA raises its temperature. The low reflectivity (ρSi) ≈ is 0.03 for the Silicon Cell Layer. Absorptivity (αSi) is high (~0.90), so most transmitted energy is absorbed. Silicon cells absorb energy as heat, which generates heat and electrical energy. Electrical power generated, P elec, is calculated as: Pelec = η × G × A

where η = efficiency (either experimental or literature), G = incident irradiance, and A = total Si cell surface area. As electrical generation removes energy from the system, this power acts as a heat sink (energy removed) in the Si cell energy balance, reducing thermal heat

Figure 5. Maximum and minimum temperature and thermal distributions for 1 m/s inlet velocity(A)Si cells layers, and( B)PV panel Figure 5 (A) and (B) show the temperature distributions at a silicon cell layer in a photovoltaic (PV) panel and the whole PV module, respectively. The temperature readings are also significant in both pictures: the highest is around 53.255 °C in Figure 5 (A) and 34.376 °C in Figure 6 (B), and the lowest is 46.743 °C in Figure 5 (A). These variations indicate how much thermal energy is radiated across the module’s entire surface. The differences in Figure 6 (A) are a product of thermal absorption in the silicon (Si) cells, the active material that makes up the device, subsequently heating the localized areas. The transmission of this temperature increase occurs through heat conduction and convection, producing temperature gradients of 46.75 °C to 53.3 °C, likely due to differences in thermal conductivity and the convective atmosphere around the panel. Figure 5 (B) shows the

complete temperature profile of the module; the module temperature is highest in the hot region (33.255 °C) and decreases to 34.376 °C at the cold junction. The least directionally exposed regions of solar irradiance, or those regions of an air mass with paved areas or external surfaces of surface-cooling material, are the low-temperature spheres (less than 34.376 °C), which are statistically the least accessible. [27]. The simulation results show that the heat loss rate of photovoltaic (PV) panels depends on the inlet air speed, which is the most important parameter. The present analysis shows a constant inlet velocity of 1 m/s. At such a velocity, mixed-mode convective heat transfer, also known as mixed convection, appears in the system. In mixed convection, natural convection driven by spontaneous density currents due to the temperature gradient occurs simultaneously with forced convection due to air movement. The greater the air velocity, the more pronounced the forced-convection effects, thereby increasing the heat-removal performance of the PV surfaces. However, at low velocities, such as 1 m/s, forced convection is only relatively inefficient compared to velocities above 3 m/s. In these circumstances, the passing air creates a boundary layer on the surface of a PV module, generating a high-temperature contrast. Low-velocity boundary layers are intense and resistive, thereby impeding heat dissipation. On the other hand, layer thickness in the boundary layer decreases at higher velocities, the gradients become smaller, and the convective heat transfer rate increases. As such, the thermal resistance of the air layer decreases, resulting in greater cooling. When the inlet flow is reduced to 1 m/s, the convective heat transfer rate decreases, and hence the module temperatures increase, as indicated in the simulation data plot, peaking at 53.255 °C. For photovoltaic (PV) modules, it is necessary to determine the spatial radiation distribution (in terms of the silicon (Si) layer) using the air velocity. Experimental studies show that the convective heat-transfer coefficient increases with air velocity, thereby decreasing the temperature of the surface layer. Although the available power of the machine to increase heat extraction has been moderately boosted at a velocity of 1 m/s, the best performance is observed at higher velocities, i.e., 3-5 m/s. What is important here is that, with the Si layers hot, the recombination rates must be high, which will consequently lower the open-circuit voltage and the overall efficiency of the module. The extended stay under high temperatures also results in thermal expansion and, correspondingly, mechanical stress, which can compromise material integrity. [28]. The overall temperature distribution within the panel is therefore representative of the Si-layer’s overall effects and the cooling mechanism, which is by air flowing at 1 m/s. Thermal non-homogeneity occurs naturally: areas where airflow is stronger cool faster, and regions in the center experience more intense heat buildup due to low convective capacity. Effective heat dissipation is critical to proper thermal balance in the module and, consequently, to its operational functionality. When air velocity equals the ventilator’s movement, the system is thermally disadvantaged at 1 m/s.

Figures 6 (A) and (B) illustrate the Si layer, PV panel temperature, and thermal distributions. Figure 6(A)shows that the maximum temperature inside the silicon cell layer increases to 47.011 °C and the minimum decreases to 41.376 °C, at a wind speed of 2 m/s. Figure 6(B) shows the matching panel temperature distributions, yielding a maximum value of 47.011 °C. Minimal value of 30.884 °C. Such values indicate that, compared to the 1 m/s conditions, under which the highest temperatures at the cell layers were found to be 53.255 °C, the increased air velocity has reduced both the extreme and mean cell-layer temperatures by ~6.2 °C. The matching minimum temperature also drops similarly by 46.743 °C to 41.376 °C upon the imposition of 2 m/s. Notably, the heat flux distribution over the silicon cell layer is relatively uniform at higher velocities, implying more even convection and heat transfer through the boundary layer, resulting in more uniform heat removal. The spatial profile indicates that the gradient is smoother, and the center point of the profile barely suggests it is hotter than the outer regions. A similar pattern is observed in the total number of PV panels in the 2 m/s case presented in Figure 6 (B): the maximum temperature is 47.011 °C, and the minimum is 30.884 °C. This significantly improved the 1 m/s case, where the minimum temperature was approximately 34.376 °C. The enhanced convective heat transfer rates at high velocity are evident in the temperature profiles shown in Figure 6 (B), where cold water has colonized a significant portion of the PV surface by many degrees. At 1 m/s, the dominant heatremoval process is mixed convection, which, in this instance, is primarily natural convection since the air flow is rather small [29].

Figure 6. Maximum and minimum temperature and thermal distributions for 2 m/s inlet velocity(A)Si cells layers, and( B)PV panel The comparatively slow flow leads to a thicker thermal boundary layer near the surface, reducing heat dissipation capability. At an air velocity of 2 m/s, forced convection is more dominant; the air’s ki-

netic energy helps reduce the thermal boundary layer and optimize heat removal from the Si cells and the entire PV module. The role of forced convection thus increases the overall heat-transfer rate. Since the flow velocity is low at 1 m/s, efficiency is low due to a thicker boundary layer, leading to high temperatures and a high thermal gradient throughout the Si-cell array. Only the boundary layer reduces at 2 m/s; therefore, with more vigorous mixing of ambient air with near-surface air, heat exchange increases, and temperature changes are smoothed. At 1 m/s, the maximum temperature in the Si-cell layer is 53.255 °C, indicating low heat-removal efficiency at this velocity, leading to non-uniform cooling. In comparison, at 2 m/s, a maximum layer temperature of 47.011 °C is attained, a decrease of about 6.2 °C, which translates into efficiency advantages elsewhere demonstrated by eliminating the detrimental thermal effects. PV-panel temperatures correspondingly show relevant differences. The maximum temperature of the panel reaches 53.255

6.2. °C at 2 m/s. Performance is reduced slightly, and thermal stress

is consequently alleviated. Under these circumstances, the PV module has a longer operating life than when working at 1 m/s. Further increase in the wind velocity to 3 m/s will reduce the maximum temperature by 4 °C compared to 2 m/s and improve system performance. The resulting heat-exchange process is forced convection at this air speed, which enhances both efficiency and durability. The peak cooling is attained at 4 m/s. A maximum cell temperature of 40.552 °C indicates a benign temperature for the Si cells and the entire PV array. System efficiency is optimized, thermal degradation is minimized, and the system sustains the longest operating life and optimal performance. [32]. When the wind is at 5 m/s, the highest temperature found in the Si cell layer in Figure 10 (A) is 38.809 °C, which decreases by 1.7 °C compared to the corresponding level at 4 m/s and 2.0 °C compared to 3 m/s. This observation indicates that the heat-rejection performance of the photovoltaic array improves with increasing wind speed. Comparatively, the lowest temperature in the cell layer is 34.791 °C, thereby defining the amplified cooling effect at 5 m/s. The maximum and minimum temperature differences have decreased, suggesting better spatial thermal homogeneity within the Si cell layer.

As the air velocity increases to 4 m/s, the total cooling efficiency rises considerably, and forced convection becomes the dominant cooling mechanism. Convective mixing remains predominant in this regime, but natural convection plays an essential role because the thick boundary layer slows heat dissipation. Comparatively, forced convection at 2 m/s is increasingly dominant, leading to an increase in the heat transfer coefficient and in bodies with narrow boundary layers. More efficient cooling capacity (as seen at 3 m/s) can also be observed, as the boundary layers formed are thicker; in this case, there should be more mixing of air with the surface, leading to cooler temperatures. At a velocity of 4 m/s, forced convection is complete, the boundary layer is almost negligible, and the surface minimum and maximum temperatures decrease substantially. The increase in cooling efficiency with increasing flow velocity is accompanied by a corresponding thinning of the bounding layer as flow velocity decreases from 1 m/s to 4 m/s, allowing a more rapid heat exchange with the moving air. The low surface temperatures measured under the minimum boundary layer precipitate have been maximized at the lowest surface temperatures and, correspondingly, have the greatest cooling performance at the highest velocities under examination. At high ambient temperatures and 1 m/s, the system experiences high thermal losses, reduces Si cell efficiency, and

Figure 10. Maximum and minimum temperature and thermal distributions for 5 m/s inlet velocity (A) Si cells layers, and (B) PV panel Across the entire PV panel shown in Figure 10 (B), the highest temperature is again 38.809 °C, 1.7 °C lower than at 4 m/s and 4.2 °C lower than at 3 m/s. The lowest temperature value of 27.213 °C represents an unprecedented decrease in absolute temperature relative to the earlier velocities and, significantly, a drop of 5 °C relative to

the 1 m/s velocity (32.213 °C) and 1 °C relative to the 2 m/s velocity (28.290 °C). Maximum forced convection is achieved at a wind speed of 5 m/s, significantly enhancing heat dissipation from the silicon (Si) solar cells and the entire photovoltaic (PV) panel. When the heat transfer mechanism changes to mixed convection at 1 m/s, natural convection still plays a significant role in maintaining relatively high surface temperatures, thereby reducing the efficacy of thermal control. At velocities of 2 m/s -4 m/s, the natural convection is progressively replaced by the forced convection, as the physical process cools down and the thickness of the boundary layers reduces. Since the flow has a velocity of 5 m/s, forced convection plays a significant role, and the resulting thin thermal boundary layer most effectively extracts heat from the PV surface. The conditions affected lead to low temperature profiles in both the Si cells and the PV panel, as the fast-moving air aids cooling. [33]. As wind velocity increases, the thermal boundary layer thins, increasing heat transfer between the PV surface and the air near the surface. This is because the cold surface layer is replaced with fresh air as soon as possible to prevent heat from stagnating in the system, and hence the system temperature remains low. Based on empirical experiments, as wind speed increases (1 m/s), the temperature of the

Si cells rises, causing thermal stress and leading to lower efficiency and accelerated long-term degradation. Achieving that by a high speed of the wind to 2 m/s will decrease the maximum cell temperature and minimize the risks of thermal degradation and thus will raise operating efficiency. The greater the temperature rises to reach 3 m/s, the greater the airflow cools, which means the Si cells can be operated at lower temperatures, leading to increased electrical performance and elimination of thermal stress. It is kept at a low temperature (4 m/s), and the panel is subjected to the best thermal conditions it has experienced to date, thereby optimizing efficiency. The panel’s lifespan is extended even further. Finally, a wind speed of 5 m/s offers the greatest cooling ability and yields the lowest temperatures across the entire device, which can enable the Si cells and the PV module to operate at peak efficiency with minimal thermal degradation and optimal reliability. Table 6 below will compare five velocities of air (1, 2, 3, 4, and 5 m/s) and the temperature of the active layer of the PV panel (Max and Min) to illustrate how the active layer of the PV panel heats under different cooling conditions, 53.255 i C in the Si cells at 1 m/s but 38.809 °C in the Si. The overall thermal load of the glass and frame is reported by the PV Panel Temperatures (Max & Min).

Table 6. Comparison of the Si cells and PV panel temperature at different air velocities. Air Velocity (m/s)

This evidence shows that increased airflow has a cooling effect on the cells and the panel as a whole and appears to be the key to improved structural stability and reduced stress. In addition, the findings explain the effects on Mixed Convection and Power Generation and show that air velocity is the primary determining factor for the dominant heat-transfer mechanism. Mixed convection is dominated by Natural convection, thick boundary layers, and inefficient cooling at low speeds (1 m/s to 2 m/s). On the other hand, at large velocities (3 to 5 m/s), it becomes apparent that forced convection is predominant, the boundary layer is thin, and heat is more easily removed.

Impact on Power & Convection High temperatures, mixed-convectiondominated, thick boundary layer, low power output, high thermal stress. Temperature reduction ~6.2°C; forced convection is more effective; improved cooling; increased power; reduced thermal stress. Further temperature drops of 4°C; forced convection dominant; thinner boundary layer; better cooling; higher power output. Maximum temperature reduction 2.5°C; forced convection fully established; uniform cooling; optimal efficiency; minimal thermal stress. Lowest temperatures; forced convection maximized; thermal boundary layer nearly eliminated; optimal power output; minimal degradation.

High temperatures, as indicated in the sequences, will reduce electrical output due to lower open-circuit voltage. In contrast, effective cooling will improve production, reduce thermal degradation, and extend life. Such findings have an obvious physical interpretation: the higher the air velocity, the greater the component of forced convection in mixed convection [34]. Increasing the air velocity over the PV panel from 1 m/s to 5 m/s systematically reduced the maximum and minimum temperatures of the silicon layer and the entire PV panel. The observed drop was largest at 1-2 m/s and decreased (but only positively) with increasing airflow. Overall performance

showed about a 14.5°C reduction in silicon cell temperature between 1 m/s and 5 m/s (around 53.3°C at 1 m/s with mostly mixed convection and a thick boundary layer, or 38.8°C at 5 m/s with dominant forced convection and a thin boundary layer). Low-to-moderate velocity results in a quick downward tendency. When further increase in m/s, the rate of performance decreases to approximately 3 m/s, and the air temperature approaches an asymptote, where performance rates are very high. The maximum PV panel temperature decreased by the same percentage, indicating good heat loss in the panels with or without wind. The mixed convection at low velocities (12 m/s) is indeed dominated by natural convection, and the cooling effectiveness is in a less favorable position than usual. The limit for forced convection is above 3 m/s (higher temperatures in general, better cooling, improved performance). The low panel temperature achieved with high air velocities has been shown to improve electrical efficiency and minimize thermal stress, material degradation, and hotspots. The cooling efficiencies can contribute to both shortterm and long-term power generation of the PV system and system durability.

Figure 11. Chart of air speed (m/s) vs. temperature of the Si cell layer The findings of the ANSYS model, as shown in Fig. 11, can then be interpreted freely considering a physical-intuition viewpoint. The forced-convection component of mixed-convection heat transfer is assuming an increasingly larger role as air velocity increases. This strength effect reduces the thickness of the thermal boundary layer on the PV array surface, allowing it to dissipate heat more easily. It means that the highest point of the front side temperature of the solar cells is. Max) and lowest (Temp.). The minimum temperatures will be lowered, which implies reduced thermal stress on the silicon monocrystalline cells. The distribution of cooling across the panel and the temperature were caused by no longer clumping at the edges. Min drop is astounding. As the data also show, there is some nonlinearity in the response: the largest decrease in temperature. Maximum speeds of 1 and 2 m /s; then the rise in velocity thereafter is comparably smaller with considerably less improvement at the former, which tends towards an asymptotic decrease in Temperature. This upper limit is as close to the minimal possible as possible. The response of a PV cell has been known to be affected by temperature; the higher the cell temperature, the lower the value of open circuit voltage (Voc) and the system’s overall generation. The fact that down-tempering of the cells is also required, therefore,

implies greater electrical efficiency. Thermal mitigation is also used to reduce material degradation, such as solder fatigue, encapsulant brownness, and cell cracking. The trade-offs between increasing airflow and enhancing system efficiency also hold. With a minor variation in the velocity, 1 and 2 m/s, the change in power is positive. The numerical data may provide engineers with a solid foundation for streamlining the system design using ventilation, back-channel cooling, or forced-air models.

Figure 12. Air speed (m/s) vs mixed convection (w/m k) chart Figure 12 presents a chart showing the correlation between air speed on the x-axis and mixed convection on the y-axis for a photovoltaic (PV) panel. Mixed convection: Instead of using temperature gradients as the driver in natural convection, mixed convection involves the simultaneous operation of both natural and forced convection under air movement. Increasing the air speed increases the effectiveness of forced convection. The x-axis shows the three airflow velocities, ranging from 1 m/s to 5 m/s. Conventional heat transfer occurs at air velocities below 5 m/s, thereby reducing cooling capacity. On the other hand, higher speeds generate additional forced convection, thereby enhancing heat transfer. Mixed convection quantifies the heat transfer coefficient, the per-unit-area rate of heat transfer between the surrounding air and the PV panel. Increased values of mixed convection will indicate enhanced cooling. The convective heat transfer value varies gradually with velocity, from 2 2 about 10 W/m K at 1 m/s to 30 W/m K at 5 m/s. At 1 m/s, natural convection dominates with forced convection being an insignificant factor. A large thermal boundary layer of hot air surrounding the PV shutdown surface impedes heat transfer. The faster the air, the more forced convection occurs and the thinner the boundary layer, allowing colder air to reach the panel surface. Due to such close interaction, heat loss is much more effective, as evidenced by a graded increase in the mixed-convection coefficient. Taken together, the increased air velocity, which results in a higher heat-transfer rate, improves convective cooling by expelling warm air and enhances heat-exchange effectiveness, thereby achieving optimal mixed-convection operation [35]. It is typically accompanied by a low air-velocity regime (less than 1 m/s), leading to poor convective heat transfer from the PV panel to the environment. This forms a thick thermal boundary layer on the panel face, hindering heat removal and thereby raising the panel’s operating temperature. This heat, when present by itself, could lead

to cellular fatigue, which could negatively impact electrical performance. When the velocities increase to 4-5 m/s, forced convection prevails, resulting in significantly reduced panel temperatures. The net effect, in turn, allows the cells to operate closer to their optimal temperature, thereby maximizing power output. Optimized mixed convection prevents thermo-stress on the PV panel, reducing material fatigue and prolonging useful life. The ability of effective cooling to keep operating temperatures within acceptable limits is a key requirement for maintaining optimal electrical performance. We have achieved maximum power generation at high mixed-convection values (near 4-5 m/s), at which the cells can operate at lower temperatures, thus producing high voltage and current.

Figure 13. Si cells layer temperature vs mixed convection (w/m .k) chart Figure 13 above shows a clear negative relationship between the Si cell temperature and mixed convection, as indicated by the graph. In that figure, there is an inverse relationship between these variables. The temperature of the Si cell is high at low mixed-convection values 2 (approximately 53 °C at 6 W/m .K). As the degree of mixed convection varies, the temperature of the Si cell progressively decreases until the mixed convection reaches the maximum (approximately

37.72. °C (33.88 °C to 41.55 °C) 37.72 °C (33.88 °C to 41.55 °C). The

variability in the change in temperature per 1 m/s increase in wind speed ranges from 1.6 °C to 5.8 °C. This behavior implies that decreases in temperature diminish as velocity increases, with the greatest decrease in velocity between 1 m/s and 2 m/s and the least at velocities, as shown in Table 9 below.

Table 9. Temperature drop sensitivity according to velocity analysis From Velocity 1 2 3 4

The trends in the temperatures and increase in the efficiency can be associated with the experimental studies mentioned in the manuscript such as the experiments conducted by Ibrahim et al. (2024) [1], Hudiiszteanu et al. (2020), and Hussien et al. (2023) [2,38] which all cite polymerized power output and lower temperatures when forced convection conditions are maintained, i. e. with high wind speeds. The experimental findings, quantitatively, indicate temperature drops of the order 10 - 15 °C as concomitant to proportional drops in panel efficiency due to corresponding wind-speed drops, thus supporting the numerical simulations and the available literature. However, reported values are uncertain due to mesh quality, assumptions about material properties, and idealized boundary conditions. Where there are no repeated measurements of experiments, estimates of errors are thus obtained by the spreading of simulated data and also by comparison with literature values, and not by actual measurement. Sensitivity tests indicate that the major conclusions are robust to changes in wind velocity, but they may become less valuable if material or environmental parameters exhibit considerable variability. Table 10 illustrates the data with error margins.