As the demand for clean and reliable energy sources grows, solar energy has emerged as a pivotal solution due to its abundance and sustainability. Photovoltaic systems, which convert solar radiation into electricity through the photovoltaic effect, are widely deployed in regions with high solar insolation. However, the efficiency of solar panels is significantly influenced by temperature; as photovoltaic cells heat up, their electrical conversion efficiency declines, typically by 0.4% to 0.65% per degree Celsius above 25°C. This thermal management challenge necessitates accurate modeling of solar radiation and heat transfer in photovoltaic systems. Traditional computational fluid dynamics (CFD) approaches often simplify solar radiation models, failing to capture the dynamic variations in solar intensity caused by seasonal changes in solar altitude angles. In this study, I developed a high-fidelity simulation framework on the FLUENT platform by integrating a Discrete Ordinates (DO) radiation model with User-Defined Functions (UDFs) to analyze the heat transfer characteristics of solar panels under winter and summer conditions. My approach enables real-time computation of solar radiation intensity, accounting for direct, diffuse, and reflected components, and provides insights into temperature distributions that impact the performance and longevity of photovoltaic systems.
The core of my research involves constructing a three-dimensional model of a silicon-based solar panel, which comprises multiple layers: glass, ethylene-vinyl acetate (EVA) encapsulation, photovoltaic cells, a metal backplate, and a polyvinylidene fluoride (PVF) protective layer. The panel dimensions are 1640 mm × 993 mm × 8.5 mm, tilted at 35 degrees to the ground, and situated within an external flow field to simulate environmental conditions. The optical absorption coefficient of the photovoltaic surface is set to 0.85, based on industry standards, to reflect the portion of solar radiation converted to heat. To address the limitations of constant heat flux assumptions in traditional models, I implemented UDFs that dynamically calculate solar radiation intensity by fitting empirical data for typical winter and summer days. For instance, the direct solar radiation intensity for summer follows a polynomial equation: $$ I_{\text{summer}} = -0.0014t^6 + 0.1046t^5 – 2.9961t^4 + 38.545t^3 – 216.77t^2 + 492.87t – 336.01 $$ where \( t \) represents time, with an R² value of 0.9963. Similarly, the diffuse component is modeled as: $$ I_{\text{diffuse, summer}} = -8 \times 10^{-6}t^6 + 0.0009t^5 – 0.0261t^4 + 0.1543t^3 + 1.9295t^2 – 7.9406t $$ These equations, derived from meteorological data, are incorporated into the UDF to simulate temporal variations in radiation, enhancing the accuracy of heat transfer analyses for photovoltaic applications.
In my numerical setup, I employed the RNG k-ε turbulence model to resolve near-wall flow characteristics, as low wind speeds dominate the environmental conditions. The solver uses the SIMPLEC algorithm for pressure-velocity coupling, with convergence criteria set to a residual of 10⁻⁶. A grid independence study was conducted using mesh densities ranging from 100,000 to 5.5 million cells; results indicated that a mesh of 2.41 million polyhedral cells achieved temperature errors below 2%, balancing computational efficiency and precision. The boundary conditions include an inlet air velocity of 1 m/s, with turbulence intensity calculated as: $$ I = 0.16 \left( \frac{\rho v D}{\mu} \right)^{-1/8} $$ where \( \rho \) is air density, \( \mu \) is dynamic viscosity, \( v \) is velocity, and \( D \) is the characteristic length. For material properties, I defined the thermophysical parameters of each layer in the solar panel, as summarized in the table below. This comprehensive model allows me to simulate the transient behavior of photovoltaic systems under varying solar radiation, providing a foundation for analyzing temperature distributions and their effects on efficiency.
| Component | Density (kg/m³) | Specific Heat (J/(kg·K)) | Thermal Conductivity (W/(m·K)) |
|---|---|---|---|
| Glass (3 mm) | 2450 | 790 | 0.7 |
| EVA (3 mm) | 960 | 2090 | 0.311 |
| Photovoltaic Cell (2 mm) | 2330 | 677 | 130 |
| PVF Backsheet (2 mm) | 1200 | 1250 | 0.15 |
| Metal Plate | 2719 | 871 | 202.4 |
My analysis focuses on comparing the UDF-based dynamic radiation model with traditional constant radiation models for both winter (December 21) and summer (June 21) scenarios. In winter, with an ambient temperature of 5°C, the UDF model captures the gradual increase in solar radiation absorption, peaking at approximately 74.57 W/m² within the first few seconds of simulation. The temperature distribution shows higher values in the lower regions of the solar panel due to the low solar altitude angle, reaching a maximum of 283.1 K (9.6°C). The error between the UDF and traditional models remains below 3%, as the traditional approach incorporates an atmospheric attenuation factor of 0.7 to account for cloud cover and longer atmospheric path lengths. The governing equation for radiative heat transfer in the DO model is expressed as: $$ \nabla \cdot (I(\vec{r}, \vec{s}) \vec{s}) + (\alpha + \sigma_s) I(\vec{r}, \vec{s}) = \alpha n^2 \frac{\sigma T^4}{\pi} + \frac{\sigma_s}{4\pi} \int_0^{4\pi} I(\vec{r}, \vec{s}’) \Phi(\vec{s}, \vec{s}’) d\Omega’ $$ where \( I \) is the radiation intensity, \( \vec{r} \) is the position vector, \( \vec{s} \) is the direction vector, \( \alpha \) is the absorption coefficient, \( \sigma_s \) is the scattering coefficient, \( n \) is the refractive index, \( \sigma \) is the Stefan-Boltzmann constant, and \( \Phi \) is the scattering phase function. This equation, coupled with the CFD solver, enables precise simulation of solar radiation effects on photovoltaic panels.
For summer conditions, with an ambient temperature of 26.85°C, the UDF model reveals significant differences compared to the traditional model. The traditional approach, which assumes a solar constant of 1361 W/m² adjusted for solar altitude, overestimates radiation intensity by about 20-30% due to neglecting atmospheric attenuation. In contrast, the UDF model computes a maximum radiation absorption of 486.3 W/m², leading to a peak photovoltaic temperature of 320.4 K, whereas the traditional model predicts 334.1 K. The temperature distribution in summer shows hotspots on the eastern side of the panel, corresponding to the solar azimuth angle of approximately 75 degrees (east of north) at 10:00 AM. This non-uniform temperature profile, with gradients up to 30°C/m, can induce thermal stresses that compromise the structural integrity of solar panels. To quantify this, I analyzed the temperature variation along a horizontal axis, as shown in the table below, highlighting the need for effective cooling strategies in photovoltaic systems to mitigate efficiency losses and prolong lifespan.
| Position (mm) | 19.2 | 211.2 | 403.2 | 595.2 | 787.2 |
|---|---|---|---|---|---|
| Temperature Gradient (°C/m) | -23.10 | 7.32 | 11.51 | 14.51 | 13.03 |
The velocity and flow characteristics around the solar panels also play a crucial role in heat dissipation. In both seasons, with an inlet velocity of 1 m/s, the airflow accelerates to 1.46 m/s at the outlet, creating vortices behind the panel that enhance convective cooling. The velocity streamlines, similar in winter and summer, indicate that low wind speeds result in minimal impact on temperature distribution, emphasizing the dominance of radiative heat transfer. The energy balance for the photovoltaic system can be described as: $$ \rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + q_{\text{solar}} – q_{\text{conv}} – q_{\text{rad}} $$ where \( \rho \) is density, \( C_p \) is specific heat, \( k \) is thermal conductivity, \( q_{\text{solar}} \) is the absorbed solar radiation, \( q_{\text{conv}} \) is convective heat loss, and \( q_{\text{rad}} \) is radiative heat loss. My simulations show that the UDF model accurately captures these interactions, reducing errors in radiation calculation to below 3% after atmospheric corrections, which is superior to traditional methods. This precision is vital for optimizing the design of photovoltaic arrays and developing integrated cooling solutions, such as passive air channels or phase-change materials, to maintain uniform temperatures and improve overall performance.
In conclusion, my research demonstrates the efficacy of using a DO radiation model coupled with UDFs to simulate solar radiation and heat transfer in photovoltaic systems. The dynamic approach accounts for temporal variations in solar intensity, providing realistic temperature profiles that highlight the risk of hotspots and thermal stress in solar panels. For winter conditions, the UDF and traditional models show close agreement, whereas in summer, the UDF model’s inclusion of atmospheric attenuation leads to more accurate predictions. The findings underscore the importance of considering solar geometry and environmental factors in the thermal management of photovoltaic installations. This methodology not only enhances the reliability of building energy simulations and solar energy applications but also offers a pathway for urban microclimate analysis and low-carbon design. Future work could explore the integration of this model with real-time weather data to further improve the predictive capabilities for solar panel performance across diverse climatic conditions.