Coupled Thermo-Physical Processes in Porous Phase-Change Energy Storage Systems with Hybrid Nanofluids

Latent heat thermal energy storage based on phase change materials (PCMs) provides an effective approach for regulating heat transfer and reducing the mismatch between energy supply and demand in systems involving intermittent renewable energy sources [1]. Such storage units are therefore widely regarded as important components in thermal management systems, particularly where transient heat release and absorption must be controlled [2], [3]. In latent heat storage systems, PCMs absorb and release thermal energy during phase transition over a narrow temperature range, which makes them suitable for applications requiring stable thermal regulation [4]. The widespread adoption of PCMs in energy storage applications is facilitated by their availability in various latent heats and melting temperature ranges [5]. Nevertheless, a significant drawback of PCM systems lies in their low thermal conductivity. This characteristic leads to slower rates of both charging and discharging [6]. From a system-level perspective, this limitation is closely related to the interaction among conduction, phase transformation, and boundary-driven heat transfer within the storage domain. To mitigate the drawbacks of poor thermal conductivity, recent advancements have introduced various performance enhancement techniques [7]. These approaches include geometric modification, the use of extended surfaces, porous structures, and nanoadditives, all of which alter the dominant heat transfer pathways during phase change [8]. Yagci et al. [9] examined the phase change behaviour of PCM within a vertical gap. They investigated different fin geometries with varying inlet fluid temperatures.

Sheikholeslami [10] investigated the complete thermal cycle of paraffin behavior enhanced with nanoparticles in an air ventilation setup. His findings revealed that incorporating a paraffin layer increased temperature fluctuations by approximately 8%. Porous foam was utilized by Zhang et al. [11] to enhance the melting process. Their experimental tests revealed that copper foam was the most effective choice among the various types tested. Additionally, they demonstrated that the inclusion of porous foam weakened the buoyancy force. Acır and Canlı [12] investigated the effect of fins on the melting time of paraffin wax under artificial sunlight. Their results showed that increasing the number of fins improved thermal performance, whereas excessive fin thickness reduced the enhancement effect. Tian et al. [13] scrutinized the melting of paraffin in a container with edges to assess its behavior. They experimented with different types of fins and discovered that copper fins exhibited the best performance, reducing the melting period by 41.6%. Wang et al. [14] investigated the melting behaviour of paraffin and reported that the addition of nanomaterials caused a noticeable reduction in melting enthalpy. Although these studies have clarified the separate roles of fins, porous media, and nanoadditives, fewer works have examined their combined influence together with radiative heat transfer in a unified solidification model.

The present work investigates the solidification process in phase-change storage enclosures with circular and square walls by considering the coupled effects of hybrid nanoparticles, porous media, thermal radiation, and fin-assisted boundary cooling. The system is treated as a multiphysics heat transfer problem in which conduction, radiative exchange, porous-domain transport, and phase transformation jointly determine the freezing behaviour. A hybrid nanomaterial is introduced in the liquid phase to modify the effective thermal properties of the PCM, while porous foam is incorporated to strengthen conductive heat transfer within the storage domain. The bottom circular cold wall and attached fins are used to intensify local heat removal and influence the movement of the solidification front. In the numerical formulation, velocity terms with negligible influence on freezing are omitted, and transient source terms are retained to describe the time-dependent evolution of the phase change process. By combining the Galerkin method with adaptive meshing, the study provides a consistent numerical assessment of how material modification, porous structures, and radiation interact to control solidification performance in thermal energy storage systems.

The solidification process is formulated as a coupled multiphysics problem involving conduction, phase transformation, radiation, and transport within a porous domain. The freezing process within an enclosure featuring circular and square walls has been modeled using a combination of the Galerkin method and mesh adaptation techniques. The enclosure is filled with a hybrid nanomaterial in its liquid phase, where the presence of a bottom circular cold wall triggers the phase change to solid. Fins have been strategically jointed to the circular surface to enhance the diffusion of cold energy. The integration of additives shows promise in accelerating the freezing rate, with the domain being filled with porous foam to enhance the conduction mode. In the governing formulation, velocity terms are neglected due to their negligible contribution to the solidification process. This leaves us with two equations, with the addition of the radiation mode as a source term. The freezing process is a time-dependent phenomenon, featuring transient source terms in the mathematical model. The model for analyzing solidification is \cite{15,16}:

A hybrid material was created by combining two types of nanoparticles, namely alumina and CuO, which were mixed in water to produce NEPCM. The characteristics of this new material can be described as follows [15], [16]:

Solving the coupled equations becomes crucial, especially with the presence of a transient source term. It's essential to choose an appropriate technique for discretizing unsteady terms and adopt a suitable approach for mesh generation. The governing equations are discretised using the Galerkin method, as adopted in previous studies [16]. When combined with an adaptive grid and an implicit time integration scheme, this approach provides improved numerical stability and accuracy in capturing the solidification process.

Freezing within a tank characterized by circular and square walls is investigated, employing Galerkin approach and mesh adaption technique (Figure 1). A meticulous exploration of this process is undertaken, with a focus on the dynamics facilitated by a hybrid nanomaterial in its liquid phase. The transformation from liquid to solid phase is catalyzed by the presence of a bottom circular cold wall within the domain. To optimize system efficiency, fins are strategically affixed to the circular wall, facilitating enhanced penetration of cold energy. Additionally, the introduction of additives holds promise in accelerating the rate of freezing, while the combination of porous foam within the region serves to augment the conduction mode. In the derivation of the governing equations, velocity terms are strategically eliminated, recognizing their minimal impact on the freezing process. This simplification yields two equations, with the radiation mode introduced as a crucial source term. Freezing, being inherently a time-dependent phenomenon, necessitates the inclusion of transient source terms in the mathematical model. These terms are discretized using an implicit approach, allowing for a comprehensive examination of the freezing process over time. The meaning of this work lies in its new approach to modeling freezing processes within complex enclosures, offering valuable insights into optimizing energy efficiency and advancing our understanding of phase change dynamics.

The arrangement of denser grid regions shifts over time, as depicted in Figure 2, which illustrates the grid configuration. Employing this technique in mesh generation enhances the correctness of the freezing process simulation. Validation of the present code is demonstrated in Figure 3, showcasing its reliability in modeling. Previous research [16] focused on the solidification process within permeable media, utilizing a similar numerical approach to analyze the system. Assessing the accuracy of the modeling is crucial not only for validating the assumptions made but also for evaluating the modeling methodology itself.

To assess the impacts of various parameters, Figure 4, Figure 5, Figure 6, and Figure 7 should be carefully examined. In this study, three techniques were implemented to enhance the freezing rate. Notably, the most significant effects were observed with changes in $\gamma$ and $\phi$. When $\phi$ increases, the driving force behind the freezing process strengthens, leading to a quicker solidification. This influence is particularly pronounced in the absence of the other two approaches. The incorporation of radiation mode results in a decrease in the domain's temperature and facilitates the attainment of a higher solid phase. On the other hand, a decline in $\gamma$ corresponds to an acceleration in the freezing speed and a decrease in the energy level. In cases where radiation is absent in nonporous media, the conversion of water to ice takes the longest time, occurring after 9810 s. However, when all three techniques are employed, the time required for complete freezing is significantly reduced to 788.96 s. This underscores the efficacy of utilizing multiple approaches simultaneously in optimizing the freezing process.

Two different values of $\gamma$ were tested, and the resulting profiles and ice front movements are depicted in Figure 8 and Figure 9. As $\gamma$ decreases from 1 to 0.9, the presence of porous foam enhances conductive heat transfer, resulting in a reduction in temperature and an accelerated solidification process. The alter in the slope of the profiles is noticeable with varying $\gamma$, particularly evident in the faster reduction of energy when $\gamma$ = 0.9. The speed of the ice front exhibits an inverse relationship with $\gamma$, where the inclusion of porous foam makes solidification time decline. In a scenario where Rd = 1 and $\phi$ = 0.02, a decrease in $\gamma$ causes a decrement in freezing time, transitioning from 6198.09s to 788.96s. This emphasizes the importance of $\gamma$ in influencing the solidification process, particularly when combined with the presence of porous foam.

Figure 10 and Figure 11 portray the impact of $\phi$ on the freezing phenomena. As the concentration of $\phi$ increases, it leads to a modification in the thermal treatment of the PCM, resulting in stronger conduction. The time required for the process exhibits a reverse relationship with $\phi$. Particularly in the absence of the two other techniques, the influence of $\phi$ becomes more pronounced. A bigger $\phi$ value is observed to increase the slope of the (S) profile, with the maximum value of this scalar achieved at an earlier time. In a scenario where Rd=1 and $\gamma$=0.9, an increase in $\phi$ causes a notable reduction in solidification time, transitioning from 806.73s to 788.96s. This underscores the significance of $\phi$ in expediting the freezing process, particularly when combined with other enhancing techniques.

The impact of Rd on the unit's behavior is examined in Figure 12 and Figure 13. With the insertion of the radiation term in the T equation, there is a notable increase in heat release, consequently leading to a decline in the energy of the domain. Additionally, the temperature exhibits a decreasing trend over time and with increasing Rd. As Rd rises, there is a corresponding increase in the (S) and a rapider movement of the ice front within the domain. In a scenario where $\phi$ = 0.02 and $\gamma$ = 0.9, an augment in Rd results in a notable lessening in freezing time, transitioning from 842.95s to 788.96s.

Figure 14 illustrates the differences in freezing time with changes in variable parameters. The dispersing of hybrid nano-powders allows for the modification of the thermal features of the base PCM. The role of nanoparticle concentration ($\phi$) on the system's behavior is evident across different scenarios. Particularly noteworthy is the maximal impact of $\phi$, which occurs when Rd = 0 and $\gamma$ = 1, resulting in a significant augmentation of the freezing rate by approximately 7.81%. However, the influence of $\phi$ diminishes in the attendance of Rd and metal foam. The inclusion of radiation mode enhances the penetration of cold energy, leading to a reduction in process time.

When combined with the other two techniques, solidification time decreases by approximately 6.4%. In contrast, in the absence of these techniques, an increase in (Rd) corresponds to a substantial decrease in the required time for solidification, reaching about 32.62%. The implementation of foam strengthens conduction within the unit, resulting in a decline in the needed time for full freezing. Specifically, in the absence of radiation, the completion time reduces by about 91.21% with the incorporation of porous foam. Additionally, when $\phi$ = 0.02 and Rd = 0.9, a reduction in $\gamma$ leads to a drop in freezing time by around 87.27%.

The solidification behaviour of a hybrid NEPCM system in enclosures with porous structures has been examined by considering the combined influence of nanoparticle addition, porous media, and thermal radiation. The results indicate that the freezing process is governed by the interaction of conductive transport within the porous matrix, radiative heat transfer, and the modification of effective thermal properties induced by nanoparticles.

Among the investigated factors, the presence of porous foam exerts the most pronounced influence on the solidification process. By enhancing conductive heat transfer, it significantly shortens the freezing time. Under combined conditions ($\gamma$ = 0.9, $\phi$ = 0.02, Rd = 0.9), the total solidification time is reduced by approximately 87.27%, demonstrating the dominant role of porous media in improving heat extraction from the system.

Thermal radiation contributes to further enhancement by increasing the rate of heat release from the domain. In the absence of porous structures, an increase in the radiation parameter leads to a reduction in freezing time of up to 32.62%. When combined with porous media and nanoparticle addition, the contribution of radiation remains noticeable, although its relative effect becomes less pronounced compared with conduction through the porous matrix.

The addition of nanoparticles improves the effective thermal conductivity of the base material and results in a measurable reduction in freezing time. The maximum effect, approximately 7.81%, is observed in configurations without porous media and radiation. When these mechanisms are present, the contribution of nanoparticles diminishes, indicating that their role is secondary in strongly coupled systems.

Overall, the results show that the performance of phase-change thermal storage systems is controlled by the interaction of multiple heat transfer mechanisms. The combined use of porous structures, radiative effects, and nanoparticle enhancement provides an effective means of accelerating solidification, although their relative contributions depend on the operating conditions and system configuration.