The escalating global energy demand and the pressing need to mitigate climate change have propelled photovoltaic (PV) technology to the forefront of renewable energy solutions. Solar panels, which directly convert sunlight into electricity, are a cornerstone of this transition. However, a critical and persistent challenge that undermines their efficiency and long-term reliability is operational temperature rise. Typically, only a fraction of the incident solar radiation is converted into electrical energy; the majority is transformed into heat, causing the solar cell temperature to increase significantly above the ambient. This temperature elevation has a deleterious effect on the electrical performance of solar panels, as the open-circuit voltage (\(V_{oc}\)) decreases linearly with rising temperature, leading to a notable reduction in power output and conversion efficiency. Furthermore, prolonged exposure to high temperatures accelerates material degradation, such as encapsulant discoloration and solder joint fatigue, shortening the operational lifespan of the solar panels. Therefore, developing effective and sustainable thermal management strategies is paramount for enhancing the energy yield and economic viability of photovoltaic systems.
Among various cooling techniques, passive thermal regulation using Phase Change Materials (PCMs) has emerged as a promising and innovative approach. The fundamental principle involves integrating a layer of PCM at the rear of the solar panel. The PCM absorbs a substantial amount of thermal energy as latent heat during its melting phase at a nearly constant temperature, thereby limiting the temperature rise of the solar cells. This process does not consume external energy, aligning perfectly with the sustainable nature of solar power. This paper presents a comprehensive numerical investigation into the thermal management of solar panels using a PCM-based system. The study employs Computational Fluid Dynamics (CFD) to analyze the transient thermal behavior, evaluating the effectiveness of PCM integration, the influence of PCM thermal conductivity, and the impact of the system’s tilt angle on the cooling performance.
The thermal challenge is visually apparent when observing solar panels under peak insolation. The integrated PCM system aims to counteract this heating by acting as a thermal buffer.
Physical Model and System Configuration
The physical model is based on a standard commercial multicrystalline silicon photovoltaic module. The core PV laminate, excluding the external aluminum frame, has dimensions of 160 mm × 160 mm × 9.4 mm. The PV/PCM system is constructed as a composite multi-layer structure, as illustrated schematically. From the sun-facing side to the back, the layers consist of: a glass cover, an Ethylene-Vinyl Acetate (EVA) encapsulant, the crystalline silicon cell, another layer of EVA encapsulant, a polymer back-sheet (Tedlar), and a protective aluminum plate. For the PCM-integrated system, an aluminum container is rigidly attached to the back of this laminate. This container is filled with the Phase Change Material, ensuring intimate thermal contact with the rear surface of the solar panel to facilitate efficient heat transfer from the hot solar cells into the PCM.
Mathematical Formulation and Governing Equations
The numerical simulation is conducted using a two-dimensional, transient model. To render the problem tractable while capturing the essential physics, the following assumptions are adopted:
- The solar irradiance incident on the front surface is treated as a constant and uniformly distributed heat flux, \(E = 1000 \, \text{W/m}^2\). This front surface exchanges heat with the ambient environment via both convection and radiation. The ambient temperature (\(T_f\)) is set to 293.15 K (20 °C), with a convective heat transfer coefficient (\(h\)) of \(10 \, \text{W/(m}^2 \cdot \text{K)}\). The top, bottom, and back sides (except where the PCM is attached) are considered adiabatic (thermally insulated).
- Thermal contact resistances between different layers within the solar panel and between the panel and the PCM container are neglected.
- The glass cover is assumed to have a transmissivity of 1, and the silicon cell has an absorptivity of 1, meaning the cell surface receives the full \(1000 \, \text{W/m}^2\) irradiance.
Based on these assumptions, the net heat flux at the front surface of the solar panel is governed by:
$$q”_{net} = E – h(T_{surf} – T_f) – \varepsilon \sigma (T_{surf}^4 – T_{sky}^4)$$
where \(T_{surf}\) is the front surface temperature, \(\varepsilon\) is the surface emissivity, \(\sigma\) is the Stefan-Boltzmann constant (\(5.67 \times 10^{-8} \, \text{W/(m}^2 \cdot \text{K}^4)\)), and \(T_{sky}\) is the effective sky temperature.
The energy conservation within the solid layers of the solar panel is described by the heat conduction equation:
$$\rho c_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( k \frac{\partial T}{\partial x} \right) + \frac{\partial}{\partial y} \left( k \frac{\partial T}{\partial y} \right) + \dot{q}_{gen}$$
where \(\rho\) is density, \(c_p\) is specific heat capacity, \(k\) is thermal conductivity, \(T\) is temperature, \(t\) is time, and \(\dot{q}_{gen}\) is the internal heat generation rate per unit volume, which is significant within the silicon cell layer.
Within the PCM domain, the heat transfer involves conduction and natural convection in the liquid phase. The governing equations for the PCM are the continuity, momentum (Navier-Stokes), and energy equations. The enthalpy-porosity technique is employed to model the solid-liquid phase change. The energy equation is formulated in terms of the total enthalpy \(H\), which is the sum of sensible enthalpy \(h\) and latent heat content \(\Delta H\):
$$H = h + \Delta H$$
$$h = h_{ref} + \int_{T_{ref}}^{T} c_p \, dT$$
The liquid fraction \(\beta\) is defined as:
$$
\beta =
\begin{cases}
0 & \text{if } T < T_{solidus} \\
\frac{T – T_{solidus}}{T_{liquidus} – T_{solidus}} & \text{if } T_{solidus} < T < T_{liquidus} \\
1 & \text{if } T > T_{liquidus}
\end{cases}
$$
The latent heat content is given by \(\Delta H = \beta L\), where \(L\) is the latent heat of fusion. The momentum equation includes a source term \(S\) (the Darcy damping term) to account for the phase change, which forces the velocity to zero in the solid region:
$$S = \frac{C (1-\beta)^2}{\beta^3 + \epsilon} \vec{v}$$
where \(C\) is the mushy zone constant, \(\vec{v}\) is the velocity vector, and \(\epsilon\) is a small number to prevent division by zero.
The complete set of governing equations for the liquid PCM region is:
Continuity:
$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = 0$$
Momentum:
$$\frac{\partial (\rho \vec{v})}{\partial t} + \nabla \cdot (\rho \vec{v} \vec{v}) = -\nabla p + \nabla \cdot (\mu \nabla \vec{v}) + \rho \vec{g} + S$$
Energy:
$$\frac{\partial (\rho H)}{\partial t} + \nabla \cdot (\rho \vec{v} H) = \nabla \cdot (k \nabla T)$$
The Boussinesq approximation is applied to model the buoyancy-driven flow in the molten PCM:
$$\rho = \rho_0 [1 – \beta_T (T – T_0)]$$
where \(\rho_0\) is the reference density at temperature \(T_0\), and \(\beta_T\) is the thermal expansion coefficient.
Numerical Methodology and Solver Setup
The computational domain encompassing both the solar panel layers and the PCM container is discretized using a structured mesh. A grid independence study was conducted by evaluating mesh sizes of 1.0 mm, 0.5 mm, and 0.1 mm. Considering the trade-off between computational accuracy and cost, a mesh size of 0.5 mm was selected for all simulations, ensuring reliable resolution of temperature gradients and flow features within the PCM. The pressure-based transient solver in ANSYS Fluent was utilized. The Solidification/Melting model was activated to handle the phase change process. The Boussinesq model was selected for density variation in the PCM. Gravity was set in the negative y-direction with a magnitude of \(9.81 \, \text{m/s}^2\). The pressure-velocity coupling was handled using the SIMPLE algorithm. Second-order upwind schemes were employed for spatial discretization of momentum and energy equations. A time step of 1 second was used to ensure temporal accuracy. The convergence criteria for the energy equation and continuity equation residuals were set to \(10^{-6}\). The initial temperature for the entire domain was set equal to the ambient temperature, 293.15 K.
Results and Discussion
2.1 Effectiveness of PCM Integration for Temperature Regulation of Solar Panels
The primary objective was to evaluate the cooling potential of PCM for solar panels. A comparative analysis was performed between a standard solar panel and a PV/PCM system. Both systems were subjected to a constant solar irradiance of \(1000 \, \text{W/m}^2\) at a tilt angle (\(\alpha\)) of 45°. The PCM used was paraffin wax with a thickness of 20 mm. Its thermophysical properties are summarized in Table 1.
| Property | Symbol | Value | Unit |
|---|---|---|---|
| Density | \(\rho\) | 800 | kg/m³ |
| Specific Heat (Solid/Liquid) | \(c_p\) | 2000 | J/(kg·K) |
| Thermal Conductivity | \(k\) | 0.20 | W/(m·K) |
| Latent Heat of Fusion | \(L\) | 232,000 | J/kg |
| Thermal Expansion Coefficient | \(\beta_T\) | 0.001 | 1/K |
| Dynamic Viscosity (Liquid) | \(\mu\) | 0.002 | kg/(m·s) |
| Solidus Temperature | \(T_{solidus}\) | 298 | K |
| Liquidus Temperature | \(T_{liquidus}\) | 300 | K |
The simulation results revealed a stark contrast in thermal behavior. The temperature of the standard solar panel increased rapidly, stabilizing around 355 K (82 °C) after approximately one hour of irradiation. In contrast, the temperature rise of the solar panel integrated with PCM was significantly suppressed. The PV/PCM system exhibited a much lower heating rate, and its temperature plateaued around 308-315 K (35-42 °C) for the majority of the 3-hour simulation period. The maximum temperature difference between the two systems reached approximately 50 K. This dramatic cooling effect is attributed to the PCM’s phase change. The PCM adjacent to the hot backsheet of the solar panel absorbs heat and begins to melt. The melting front progresses through the PCM layer, with the latent heat absorption acting as a powerful thermal sink, preventing the solar cells from reaching high temperatures. Furthermore, natural convection currents established in the molten PCM enhance heat distribution within the container, promoting more uniform melting and improving thermal performance. This confirms the high feasibility of using PCMs for continuous, passive temperature control of solar panels, maintaining them at a lower, more efficient operating temperature.
2.2 Influence of PCM Thermal Conductivity on the Performance of Solar Panels
The thermal conductivity (\(k\)) of the PCM is a critical parameter as it governs the rate at which heat is transferred from the solar panel into the PCM bulk. To isolate its effect, simulations were conducted with PCMs having different thermal conductivities while keeping all other properties identical to the base paraffin wax. Three values were investigated: \(k = 0.15, 0.20, \text{ and } 0.25 \, \text{W/(m·K)}\). The system configuration (45° tilt, 20 mm PCM thickness) remained unchanged.
The results indicated that during the initial few minutes, the temperature profiles of the solar panels were nearly identical, as the heat was primarily absorbed by the PCM layer immediately in contact with the panel. As time progressed, a clear divergence emerged. The solar panel integrated with the higher conductivity PCM (\(k=0.25\)) consistently maintained a lower temperature compared to the one with lower conductivity PCM (\(k=0.15\)). The steady-state temperature difference was approximately 1-2 K. The enhanced thermal conductivity facilitates faster heat diffusion from the interface into the deeper regions of the PCM, allowing more PCM mass to participate in the sensible heating and subsequent phase change process earlier. This reduces the thermal resistance between the hot solar panel and the PCM’s latent heat storage capacity, leading to better thermal regulation. This relationship can be conceptually summarized as:
$$\frac{dT_{panel}}{dt} \propto -\frac{k_{PCM}}{\delta_{PCM}}$$
where \(T_{panel}\) is the average solar panel temperature and \(\delta_{PCM}\) is the PCM layer thickness. Therefore, for a given thickness, selecting a PCM with higher thermal conductivity directly contributes to lower operating temperatures for the solar panels.
2.3 Effect of System Tilt Angle on the Cooling of Solar Panels
The orientation or tilt angle (\(\alpha\)) of a solar panel significantly influences its thermal interaction with the environment and, in the case of a PV/PCM system, the heat transfer dynamics within the molten PCM. Simulations were performed for tilt angles of 0° (horizontal), 15°, 30°, 45°, and 90° (vertical). The solar irradiance remained normal to the panel surface in all cases to isolate the effect of tilt on cooling, not on intercepted radiation.
The results demonstrated a pronounced impact of the tilt angle on the thermal performance of the solar panels. After three hours of simulated operation, the average temperature of the solar panel decreased systematically as the tilt angle increased. The horizontal panel (0°) reached the highest temperature, around 328 K (55 °C), while the vertical panel (90°) remained the coolest, with a temperature approximately 20 K lower. This behavior is primarily due to the role of natural convection within the liquid PCM. At a higher tilt angle, the buoyancy force component parallel to the PCM container’s rear surface is stronger. This drives more vigorous circulatory flows, effectively transporting hot liquid PCM away from the panel interface and replacing it with cooler, denser PCM from the lower sections. This enhanced convective mixing improves the overall heat transfer coefficient between the solar panel and the PCM, leading to more efficient heat extraction and lower panel temperatures. This finding is crucial for system design, suggesting that the cooling benefit of PCMs for solar panels is not constant but varies with installation geometry, offering greater advantage for steeper inclinations.
The key temperature data for different tilt angles at the end of the 3-hour simulation is summarized in Table 2.
| Tilt Angle, \(\alpha\) (degrees) | Average Panel Temperature (K) | Average Panel Temperature (°C) |
|---|---|---|
| 0 | 328.2 | 55.0 |
| 15 | 324.1 | 50.9 |
| 30 | 318.7 | 45.5 |
| 45 | 313.5 | 40.3 |
| 90 | 307.8 | 34.6 |
Conclusion
This numerical simulation study provides a detailed analysis of a passive thermal management system for solar panels using Phase Change Materials. A robust two-dimensional transient model was developed, incorporating heat conduction, convection, radiation, and phase change dynamics. The simulations conclusively demonstrate that integrating a PCM layer at the rear of solar panels is a highly effective strategy for temperature control. Under a constant solar flux of \(1000 \, \text{W/m}^2\), the PCM-integrated solar panel maintained a temperature approximately 40-50 K lower than an identical panel without PCM, significantly mitigating the performance loss associated with heating. Furthermore, the study quantified the influence of key design parameters. It was found that the thermal conductivity of the PCM has a direct positive correlation with cooling performance; higher conductivity PCMs lead to lower operating temperatures for the solar panels. Most notably, the system’s tilt angle was identified as a critical factor governing the effectiveness of the PCM cooling due to its strong influence on natural convection within the molten material. The temperature of the solar panels decreased monotonically with increasing tilt angle, with vertical orientations offering the best cooling performance. These insights are valuable for optimizing the design and deployment of PV/PCM systems, contributing to the development of more efficient, reliable, and durable solar energy harvesting technologies.