Numerical Investigation of Nano-Enhanced Paraffin Combined with Porous Foam for Efficiency Enhancement of Photovoltaic Panels

Photovoltaic (PV) technology is widely recognized as a key renewable energy solution because it enables direct conversion of solar radiation into electrical energy without generating environmental pollution. However, the performance of PV modules is strongly influenced by their operating temperature, where excessive heat buildup during solar exposure can significantly reduce electrical efficiency, decrease power output, and negatively affect long-term system reliability. As a result, the development of effective thermal management and cooling strategies has become essential to ensure stable operation and enhance the overall efficiency of PV systems, particularly under conditions of high solar irradiance [1], [2], [3]. Among the different cooling techniques proposed for PV thermal management, phase change materials (PCMs) have gained significant attention. By exploiting latent heat during phase transition, PCMs help maintain the PV module temperature within an acceptable operating range, thereby improving overall performance. In particular, paraffin-based PCMs are widely adopted in PV cooling systems because of their chemical stability, low cost, and reliable thermal energy storage capacity. However, despite these advantages, the practical use of pure paraffin is still constrained by its low thermal conductivity [4], [5], [6]. The dispersion of nanoparticles within the base PCM has been widely recognized as an efficient approach for developing nano-enhanced phase change material (NEPCM). In particular, ternary hybrid nanoparticles have demonstrated better thermal performance compared with mono- and binary-particle systems, owing to the synergistic combination of their thermo-physical properties. Moreover, incorporating porous metal foam into the PCM domain has been demonstrated to enhance heat transfer by increasing the effective surface area and forming highly conductive pathways within the medium, which together promote faster and more uniform thermal energy distribution throughout the storage medium [5], [7], [8], [9].

Jiang et al. [10] examined the effect of integrating a fractal fin structure with PCM on the thermal behavior of PV cells. The results demonstrated that the proposed fractal fin configuration provided more effective cooling than the conventional straight fin design, resulting in a reduction of approximately 2 ℃ in the PV cell temperature. Kumar et al. [11] improved the thermal performance of a PCM-based cooling system by dispersing TiO$_2$ nanoparticles. They indicated that the NEPCM reduced $T_{PV}$ by nearly 13 ℃, while the daily electrical efficiency increased by approximately 2.1% compared with the conventional system. Li et al. [12] carried out a numerical study on the performance of a solar collector (SC) integrated with PCM. Their study examined the influence of phase change temperature, melting temperature range, and thermal conductivity of the PCM on the thermal behavior and overall performance of the PCM-based SC system. Sathish [13] investigated a hybrid system combining PV–PCM technology with a PEM electrolyzer in the presence of hybrid nanoparticles. They reported that the proposed system achieved an electrical efficiency of approximately 15.5%, while the PEM electrolyzer reached a peak efficiency of about 39.2%. Barthwal and Rakshit [14] examined the melting characteristics of PCM in a PVT equipped with different fin geometries, including triangular, rectangular, and Y-shaped fins. They indicated that the incorporation of fins meaningfully influenced the melting performance of the PCM, with the Y-shaped fin configuration exhibiting the fastest melting process and the shortest melting time among the tested designs.

Despite the considerable progress achieved in PV thermal management technologies, excessive temperature rise in PV panels during peak solar irradiation remains one of the major challenges limiting electrical efficiency and long-term operational stability. Numerous investigations have been conducted to reduce panel temperature through the application of conventional cooling methods, PCMs, nanofluids, porous structures, and hybrid thermal management systems. Among these approaches, PCM-based cooling systems have gained significant attention due to their capability to absorb large amounts of thermal energy through latent heat storage, without the need for external energy input. To improve the melting rate, several studies have attempted to enhance the thermo-physical properties of PCM through the addition of nanoparticles or the incorporation of porous media. Although noticeable improvements have been reported, the majority of previous investigations focused on the use of single nanoparticles, mono-enhanced PCM, or standalone porous structures. In addition, relatively few studies have investigated the simultaneous incorporation of tri-hybrid nanoparticles and porous metal foam within PCM for PV cooling applications. Furthermore, the transient melting behavior and thermal response of such integrated systems under realistic peak operating conditions around solar noon have not been comprehensively investigated in the available literature. The novelty of the present work lies in the development of an integrated passive cooling configuration employing paraffin RT-25 enhanced with Ag-Al$_2$O$_3$-TiO$_2$ tri-hybrid nanoparticles and porous foam simultaneously. The proposed approach aims to improve thermal conductivity and accelerate energy transport in order to maintain the PV panel at lower operating temperatures. In addition, the transient thermo-fluid characteristics of the system are numerically analyzed using the Galerkin finite element method with an adaptive mesh technique to ensure accurate prediction of phase transition and heat transfer behavior during severe thermal operating conditions. Compared with previously published studies, the present work provides a more comprehensive thermal management strategy by combining multiple advanced heat transfer enhancement techniques within a single cooling system. The simultaneous utilization of porous foam and tri-hybrid nanoparticles inside PCM is expected to provide superior thermal stability, faster heat dissipation, and improved temperature uniformity relative to conventional PCM-based cooling methods. Consequently, the proposed system offers significant potential for enhancing PV electrical efficiency, improving system reliability, and supporting the development of sustainable and high-performance solar energy technologies.

To address the significant temperature rise in PV panels and its adverse impact on electrical efficiency, an advanced passive cooling configuration is proposed in this study. A thermal management system is integrated beneath the PV module in the form of a cooling container filled with PCM, specifically paraffin RT-25. This arrangement is designed to absorb and store excess thermal energy generated during solar irradiation, thereby regulating the PV surface temperature and improving overall system performance. The hybrid enhancement strategy is implemented by dispersing ternary nanoparticles (Ag, Al$_2$O$_3$, and TiO$_2$) within the PCM and embedding metal foam into the storage domain. This combined approach significantly improves thermal conductivity, increases heat transfer surface area, and accelerates the melting dynamics of the PCM, leading to enhanced thermal regulation of the PV panel. The transient heat transfer and phase change process are numerically modeled using the Galerkin method. The simulation is performed over a critical three-hour period around solar noon, when solar irradiance and thermal loading are at their maximum levels. This operating window provides a realistic assessment of the cooling performance under severe environmental conditions. Figure 1 illustrates the schematic configuration of the PV panel integrated with the bottom-mounted cooling container, highlighting the proposed thermal management design and its structural arrangement.

By modeling the PV layer as a single domain, heat loss occurs from the upper surface while thermal interaction is established with the underlying PCM layer. Accordingly, the system consists of two coupled regions, namely the PV zone and the PCM zone, and is analyzed using the governing equations [15], [16], [17].

The working PCM is paraffin RT-25, and its thermophysical properties are provided in the study [18]. To further enhance its thermal performance, ternary nanoparticles are dispersed within the PCM. The formulation used for the ternary NEPCM is based on previous studies [19], [20].

The solar irradiation intensity, ambient temperature, and convective heat transfer coefficient due to wind are specified as 600 W/m$^2$, 25 ℃, and 10 W/m$^2$·K, respectively. All side boundaries of the system are considered thermally insulated, except for the top surface of the PV panel, where convective and radiative heat losses are taken into account. The numerical simulation is performed over duration of three hours to assess the transient thermal behavior of the system under realistic operating conditions. In this work, the melting process of the PCM has been simulated to regulate the panel temperature. The numerical modeling is carried out using FLEX PDE software, where an adaptive mesh strategy is employed to accurately capture the transient behavior. The governing equations are solved based on the Galerkin finite element formulation to ensure high numerical accuracy and stability. Further details regarding the implementation and capabilities of this software can be found in the previous study [16].

To control the temperature distribution across the PV panel, an advanced cooling layer was incorporated beneath the system in the present study. Paraffin RT-25 was selected as PCM. Since pure paraffin is characterized by relatively low thermal conductivity, tri-hybrid nanoparticles consisting of (Ag-Al$_2$O$_3$-TiO$_2$) were dispersed within the PCM. Furthermore, porous foam was integrated into the cooling domain in order to improve thermal diffusion and enlarge the effective heat transfer surface area inside the storage medium. The simulation was conducted for a three-hour operating period around solar noon, where the PV panel is subjected to maximum solar irradiation and severe thermal loading conditions. Temperature contours and LF distributions were presented to illustrate the thermal propagation and melting characteristics within the NEPCM and porous structure. In addition, the temporal evolution of $T_{PV}$ was analyzed in detail to evaluate the thermal response of the proposed cooling configuration. The electrical efficiency of the PV panel was calculated for all investigated cases in order to assess the effectiveness of the implemented cooling approaches. The proposed integrated cooling strategy represents a promising and innovative solution for next-generation PV thermal management systems, since the simultaneous incorporation of porous foam and hybrid nanoparticles within PCM has rarely been investigated in previous studies.

To ensure the accuracy of the present numerical model, validation was performed by reproducing a previously published case study [21], and the corresponding results are presented in Figure 2. In the earlier study, a paraffin-based thermal storage container positioned beneath the PV panel was employed. The figure confirms the correctness and robustness of the implemented numerical formulation, as well as the reliability of the adopted modeling approach. In addition, the mesh structure was dynamically adapted during the transient simulation, as illustrated in Figure 3. The grid deformation was updated with time to accurately follow the movement of the melting front within the PCM. This adaptive meshing strategy is essential for capturing the sharp gradients in temperature and phase interface evolution with higher precision. By continuously refining the computational grid in regions of strong thermal variation, the numerical model is able to represent the melting process more effectively and reduce numerical diffusion.

Figure 4, Figure 5 and Figure 6 present the contours of LF and temperature distribution for two investigated configurations, namely pure PCM and NEPCM integrated with metal foam. The inclusion of a paraffin-based thermal storage container beneath the PV panel significantly improves heat transfer from the PV module to the PCM domain. As a result, the PV panel experiences a reduction in operating temperature, which contributes to improved thermal regulation and enhanced electrical performance. The melting process initiates from the upper region of the PCM due to the higher temperature near the PV–PCM interface, and the melting front gradually propagates downward with time. This behavior is strongly influenced by the thermal boundary conditions and the geometric arrangement of the storage unit. Due to the relatively small dimensions of the container and the placement of the heated surface at the top, heat transfer is mainly dominated by conduction. This mechanism becomes increasingly effective as thermal energy is continuously supplied to the PCM domain. In the case of NEPCM integrated with metal foam, the thermal distribution and melting behavior become more intricate owing to the improved heat transfer networks and the enlarged effective surface area provided by the porous structure. The addition of porous foam and nanoparticles significantly intensifies thermal diffusion, resulting in a faster process. This enhanced structure facilitates improved heat conduction and reduces thermal resistance within the system. After three hours of operation, the LF of the base PCM case reaches approximately 0.59, indicating partial melting, whereas the improved NEPCM–foam configuration achieves complete melting with LF = 1. In addition, for the NEPCM–porous foam case, full melting is attained at approximately 8251.93 seconds, demonstrating a considerable acceleration in phase change dynamics. Over the course of the process, the PCM temperature ($T_{PCM}$) increases from 309.99 K to 327.58 K, confirming effective heat absorption and storage capability.

The temporal variations of $T_{PV}$, $T_{PCM}$, LF, and PV electrical efficiency ($\eta_{P V}$) are presented in Figure 7. The results clearly indicate that, in general, $T_{PV}$ increases with time due to continuous solar heat accumulation, which consequently leads to a reduction in electrical efficiency. However, a notable improvement in thermal performance is observed when nanoparticles and porous metal foam are introduced into the PCM domain. In this case, a lower PV temperature is maintained throughout the operation period, which directly contributes to higher electrical efficiency compared with the conventional PCM configuration. In addition, the LF increases progressively with time for all cases, confirming the continuous phase change process within the paraffin-based storage medium. However, the NEPCM–foam configuration exhibits a higher LF compared with the pure PCM case, indicating a faster melting rate and enhanced thermal energy absorption capability. It is also observed that, due to the dominance of conduction-driven heat transfer in the NEPCM–foam system, the $T_{PCM}$ increases more rapidly after a certain time compared with pure paraffin, which reflects more efficient internal heat distribution.

Figure 8 presents a comparative analysis of $T_{PCM}$ and LF after 3 hours of operation for different configurations. The outputs reveal that the incorporation of nanoparticles and porous foam leads to an increase in $T_{PCM}$ by approximately 5.71%, which indicates improved heat absorption and energy storage within the material. At the same time, the LF increases significantly by about 68.95%, confirming a substantial enhancement in the melting process and phase transition rate. Figure 9 illustrates the comparison of $T_{PV}$ and electrical efficiency ($\eta_{P V}$) for three different cases. It is observed that the system equipped with only pure PCM reduces the PV temperature by approximately 7.87% and improves electrical efficiency by about 15.84% compared with the uncooled reference case. When metal foam and ternary nanoparticles are introduced, an additional improvement in PV efficiency of approximately 1.13% is achieved, demonstrating the beneficial effect of enhanced thermal conductivity and improved heat transfer pathways. Overall, when the complete cooling system is applied, the electrical efficiency increases by about 17.16%, while the PV temperature decreases by approximately 8.53% compared with the uncooled system. These results clearly confirm the strong capability of the proposed hybrid cooling strategy in enhancing thermal regulation, accelerating PCM melting, and improving PV performance under transient operating conditions.

In the present study, an advanced thermal management approach was proposed to control the temperature distribution of the PV panel through the incorporation of a cooling layer beneath the system. Paraffin RT-25 was utilized as PCM owing to its favorable latent heat storage capability, while its thermal performance was further enhanced by dispersing tri-hybrid nanoparticles composed of Ag, Al$_2$O$_3$, and TiO$_2$ within the PCM. In addition, porous foam was integrated into the cooling domain to improve thermal diffusion and accelerate heat transfer throughout the melting process. The transient thermo-physical behavior of the proposed system was numerically analyzed using the Galerkin finite element method with an adaptive mesh technique under peak operating conditions for three hours around solar noon. The obtained temperature contours and LF distributions demonstrated the effectiveness of the combined porous structure and NEPCM in reducing the panel temperature and improving thermal uniformity. Furthermore, the electrical efficiency results confirmed that the proposed cooling configuration provided a significant enhancement in PV performance compared with conventional cooling approaches. The presented integrated cooling methodology highlights a promising and innovative pathway for improving the thermal regulation. The integration of PCM container beneath the PV significantly improves the performance. As a result, the PV panel operates at a lower temperature, which directly contributes to an improvement in electrical performance. The presence of the PCM layer enables the absorption and storage of excess thermal energy during the melting process, thereby reducing the thermal stress imposed on the PV surface. The numerical results clearly demonstrate the effectiveness of the proposed configurations under transient operating conditions. After a period of three hours, the LF in the base case reaches approximately 0.59, indicating incomplete melting of the PCM. In contrast, the improved configuration achieves full melting (LF equal to 1), confirming a significantly enhanced thermal response. For the NEPCM combined with porous metal foam, complete melting is achieved at approximately 8251.93 seconds, highlighting a faster phase transition process. Over the course of the melting process, the $T_{PCM}$ increases from 309.99 K to 327.58 K, reflecting efficient energy absorption and storage. In terms of PV performance, the integration of the cooling system leads to a considerable enhancement in electrical efficiency, with an increase of approximately 17.16%, while the PV temperature is reduced by about 8.53% compared with the uncooled reference system. Furthermore, the addition of metal foam and ternary nanoparticles results in an additional improvement in efficiency of around 1.13%, demonstrating the beneficial synergistic effect of enhanced thermal conductivity and increased surface area. The incorporation of nanoparticles and porous structures also contributes to a 5.71% increase in $T_{PCM}$ evolution and a 68.95% increase in LF, indicating accelerated melting and improved thermal energy distribution within the storage medium. When compared with a configuration using only pure PCM, the PV temperature is reduced by approximately 7.87%, while the electrical efficiency is improved by about 15.84%. These results confirm that even passive PCM cooling provides a noticeable enhancement in system performance; however, the combined use of PCM, ternary nanoparticles, and metal foam yields a much more effective thermal management strategy. Overall, the findings clearly indicate that the proposed hybrid cooling system significantly enhances heat transfer, accelerates phase change behavior, and improves thermal stability.