Thermal modeling of porous medium integrated in PCM and its application in passive thermal management of electric vehicle battery pack

c

specific heat capacity

c^a

apparent heat capacity

H

volumetric enthalpy

k

thermal conductivity

k^eff

effective thermal conductivity of the composite material

L

specific latent heat of the PCM

{q}

heat flux vector

T

temperature

T_l

liquidus temperature

T_s

solidus temperature

$ν 0(T)$

piecewise linear function of the PCM liquid fraction

$ν(T)$

smooth function of the PCM liquid fraction

ρ

density

EV

electric vehicle

FE

finite element

FEM

finite element method

PCM

phase change material

PM

porous medium

PTMS

passive thermal management systems

RVE

representative volume element

Passive thermal management systems (PTMS) have gained significant attention in recent years due to their potential to enhance energy efficiency and sustainability in various applications. One promising approach involves the integration of porous medium with PCM to exploit their synergistic effects in mitigating temperature fluctuations. PCM can store and release large amounts of thermal energy during phase transitions. Incorporating PCM into passive thermal management systems enhances their ability to regulate temperature effectively, making them particularly suitable for applications in energy systems, electronics cooling, building insulation, and renewable energy systems.^1–5 Porous media, such as metal foams and other structured materials with repeating unit cell, have demonstrated excellent heat transfer characteristics. When integrated with PCM, these materials enhance the overall thermal performance by providing additional surface area for heat transfer within the composite material.^6–9 Moreover, metals employed in thermal management applications exhibit elevated thermal conductivity, resulting in enhanced heat dissipation.^10–16 Anticipating the thermal behavior of the composite structure is crucial, particularly when choosing suitable materials for a specific application. This necessitates the integration of numerical thermal modeling for porous medium within PCM.^17–21 Thermal homogenization simplifies computational efforts for porous medium-PCM composites, consolidating and streamlining thermal properties. This approach reduces the complexity of calculations, making thermal analysis more efficient and feasible, especially in scenarios requiring intricate simulations. It ensures accuracy without overwhelming computational resources.^22–27 The thermal behavior of heterogeneous materials, such as porous medium PCM composites, can be accurately represented through the concept of the RVE, which is a fundamental repetitive unit that encapsulates the microstructural features of the material, allowing for the development of effective macroscopic thermal models. The technique is applied effectively in mechanical and thermal analysis.^28–35 

Thermal homogenization techniques applied to RVEs play a crucial role in predicting the effective thermal properties of the composite material. Various methodologies, such as the FEM and analytical homogenization, have been employed to derive effective, macroscopic thermal properties of porous medium-PCM composites.^{28, 29, 36–38} The integration of porous medium with PCM in EV battery thermal management systems results in superior heat transfer characteristics. The increased surface area and convective pathways within the composite material contribute to efficient heat dissipation, mitigating thermal issues associated with high-power operations.^39–41 This approach addresses challenges associated with rapid charging, high-power discharging, and temperature fluctuations, thereby extending the battery lifespan and enhancing overall performance.^42–45 The combined effects of PCM and porous medium contribute to improved thermal stability in EV battery systems. The latent heat absorption/release during phase transitions in PCM, coupled with the effective heat dissipation provided by the porous structure, help maintain a stable temperature environment within the battery pack.^46–53 Employing methodologies to precisely simulate the comprehensive thermal characteristics of these materials, such as thermal homogenization, enables the optimization of passive thermal management approaches.

With the increasing demand for high-performance EVs, continued research in this domain holds significance in developing efficient and reliable thermal control mechanisms for EV battery systems.^54–56 The exploration of the thermal characteristics of composite PCM through multiscale analysis has been limited in research, with only a few researchers examining its potential. Additionally, insufficient attention has been given to investigating the 3D anisotropic behavior of these structures. Further research in this domain holds the promise of revealing new insights and improving the design and optimization of porous media and metal foams integrated into PCM for heightened thermal efficiency. This study specifically concentrates on the thermal modeling of an aluminum lattice structure integrated into PCM using the 3D RVE homogenization concept. The ensuing thermal problem is to be addressed through FEM. The objective is to assess the thermal constitutive properties that characterize the thermal behavior of a homogenized medium representative of the actual multiphase body. The resulting effective thermal characteristics, encompassing the thermal conductivity tensor, heat capacity, and density, are attributed to the homogeneous medium to precisely forecast and comprehend the macroscopic transient thermal behavior of the composite. Moreover, material non-linearity is considered in the analysis by incorporating temperature-dependent material characteristics in the model. The apparent heat capacity approach is employed to accommodate the phase transition of the PCM. By integrating the RVE model within the FEM software (ANSYS), we can accurately capture the intricate thermal behavior of the composite structure at the macroscopic level. This structure is subsequently applied in a thermal management strategy for an electric vehicle battery to enhance cooling efficiency.

Porous media, such as metal foams, structured porous materials, or metal lattices, offer several advantages in applications where high thermal conductivity, lightweight combined with structural stability, and enhanced heat transfer are required. The high thermal conductivity is beneficial in applications where heat needs to be dissipated or transferred quickly, such as in heat exchangers, solar panels, batteries, or electronic cooling systems. The light weight and structural integrity make metal porous materials suitable for applications in aerospace or automotive industries. Improved heat transfer is achievable by incorporating a porous structure into PCM. In this setup, the metal's high thermal diffusivity enables the conduction of heat rather than predominantly storing it. Simultaneously, PCM effectively stores heat in latent form without undergoing a significant temperature rise. The synergistic interplay of these elements within the composite material enhances the efficiency of the cooling process. The considered composite material used in this research consists of an aluminum lattice representing the porous medium which is imbedded in the PCM n-octadecane. The lattice has a repeating symmetrical I-WP cell, as displayed in Fig. 1 with the structure of the composite material and the PCM.

The porous medium has a volume fraction of 80% and the thermal properties of aluminum and n-octadecane are given in Tables I and II.^57,58

The material parameters of the PCM within the mushy region are defined as the temperature functions ρ(T), k(T), and c(T) and will be considered in more detail in Sec. III.

In the considered case, the parameter c₂ defines the translation of the function ν₀ along the T-axis and corresponds to the melting temperature, which is placed in the middle of the melting range at a value of 29 °C. The parameter c₁ is used to adjust the behavior of the function to be close to the linear approximation. Maple software is employed to determine the parameter c₁, leading to a curve that closely aligns with the linear function within the temperature range of the phase transition. Figure 2 illustrates the plots depicting the linear volume fraction (ν₀) and the smoothing function (ν) corresponding to a c₁ value of 4.634.

In the last two equations, the indices s and l designate the solid and liquid quantities. The corresponding curves of these functions are displayed in Fig. 3. It is evident that quantities, the thermal conductivity, and the density of the PCM decrease rapidly during the melting process.

Figure 4 depicts the curves of the volumetric enthalpy and apparent specific heat capacity of the PCM across the temperature range, highlighting a significant increase in both quantities during the melting process.

The main objective of employing the composite PCM is to enhance the thermal conductivity of the PCM and improve the heat dissipation of the thermal management system. The metal lattice leads to a significant increase in the thermal conductivity. However, the natural convection in the melted PCM domain is suppressed owing to the large flow resistance in metal lattice. In spite of this suppression caused by metal foams, the overall heat transfer performance is improved when metal foams are embedded into PCM; this implies that the enhancement of heat conduction offsets or exceeds the natural convection loss.⁶² Due to this fact, several authors neglect the effect of natural convection in the liquid PCM domain, which leads to simplified analysis and improved computational efficiency.^63–69 

The thermal behavior of the composite material elucidates the response of its two components, the lattice and PCM, and is governed by a nonlinear mathematical model that encompasses temperature dependency, phase transition effects, and the thermal characteristics of the metallic lattice. Furthermore, solving the thermal problem within the composite domain entails employing a numerical solution method such as the FEM, which involves discretizing the structural geometry into finite elements. The number of elements needed to accurately depict the physical characteristics of the intricate structure is contingent upon the geometric dimensions of the repeating unit cell and the overall size of the analyzed body, which is displayed in Fig. 1. Due to the complexity of the geometry and material behavior, employing a detailed model for computational analysis is impractical. To streamline computational efforts, the homogenization procedure is applied, replacing the detailed model with a uniform and homogeneous medium characterized by effective thermo-physical properties.

Material design is applied to create the homogenized material and evaluate its effective thermal characteristics. The RVE is used to perform the homogenization process, which is based on the FEM. Details about this concept and its application in thermal analysis can be found in our previous work.²⁹ The depicted RVE, comprising both the aluminum lattice and PCM domains, is illustrated in Fig. 5. It has geometric dimensions of 10 × 10 × 10 mm³, with the material properties defined previously.

In this equation, [I] represents the identity matrix. Since the thermal behavior of the PCM component is temperature dependent, the computed effective material parameters of the homogeneous unit cell are also functions of temperature. The curves in Fig. 6 presenting the thermal conductivity and density as a function of temperature provide insights into the behavior of materials under different thermal conditions. Due to the metallic porous medium, the density and the thermal conductivity increase in the solid as well as in the liquid state compared to the pure PCM behavior.

As expected, the thermal conductivity of the composite is much higher than that of the pure PCM and the variation with temperature has a narrow range of values around 22.33 W/m/°C. In the solid region, the thermal conductivity of the composite has a value close to 22.45 W/m/°C, while in the liquid region it reaches a value of 22.21 W/m/°C. Considering the behavior of the density curve, the solid region exhibits a density of around 1189 kg/m³, while the liquid region has a density of approximately 1117 kg/m³. Figure 7 illustrates the temperature profiles for the effective parameters, namely, the specific heat capacity and enthalpy, of the homogenized composite. Both curves depict a smooth and fast rise within the narrow melting temperature range of the PCM, attributed to heat absorption during the phase change. In general, the thermal behavior of the homogenized medium demonstrates a trend consistent with that of pure PCM, as depicted by the corresponding curves in Figs. 3 and 4.

In addition to the increased thermal conductivity and density, the material has the desired properties for the optimized thermal management process. The homogenized composite material exhibits the capability to absorb and release a substantial amount of heat during the temperature interval of phase transition. This characteristic enables effective temperature regulation in diverse thermal management applications. In the subsequent analysis, the performance of the composite PCM is assessed for its suitability in thermal management of a battery pack designed for electric vehicle use.

For the proposed investigation, a battery pack model has been designed, incorporating prismatic lithium-ion cells, with a combined total of nine cells. The model's geometry is presented in Fig. 8, showcasing the finite element mesh used for thermal analysis. To optimize the computational efficiency, the structure's symmetry is leveraged, focusing on just one half of the model. The geometrical dimensions and materials of the battery are given in Table III.

For the purpose of model validation, one cell is considered in order to compare the thermal response of the generated model with results given in Ref. 58. The boundary conditions are defined in the reference by free convection around all the free surfaces with heat transfer coefficient value of 7 W/m²/°C and ambient temperature of 294.15 K. In addition, volumetric heat generation of 63.97 kW/m³ is assumed. The created one cell battery's geometry and the computational FE mesh are presented in Fig. 9. The mesh is generated with 21 750 elements, which is fine enough to produce the results with a negligible effect on the results.

The temperature profile calculated within the battery is showcased on the left side of Fig. 10, indicating minimum and maximum temperature readings of 315 and 317 K, respectively. The reference temperature distribution is depicted on the right side of the figure, revealing a very good correlation. Notably, the minimum temperature is observed in the terminals, highlighting specific regions where heat is transferred to the ambient air. Conversely, the maximum temperature is concentrated at the bottom of the cell, suggesting localized heating in this particular area. This detailed insight into the temperature distribution across the battery provides valuable information for understanding and optimizing its thermal performance.

Moreover, Fig. 11 illustrates the temperature distribution across the battery's thickness at specified height positions, as indicated in Fig. 10(b). The curves representing the temperature field in the thickness direction demonstrate symmetry around the central line. It is worth mentioning that the temperature profile along the length direction, depicted in Fig. 10 through the contour plot, also displays symmetry. The temperature profiles in both length and thickness orientations display a well-balanced and symmetrical distribution around the respective central planes of the battery, providing deeper insights into the overall thermal dynamics of the system. This insight is further supported by the three-dimensional plot of the temperature surface, T(x, y), across the cell domain with the corresponding contour lines plot in Fig. 12.

Notably, the observed shift in the temperature surface maximum toward the lower edge of the cell is indicative of an existing heat source within the system. This localized heat generation contributes to the overall temperature distribution, leading to variations across the domain. Furthermore, the influence of free convection at the boundaries and terminals becomes evident in the contours and patterns displayed in the plots. Increased thermal diffusivity facilitates a more rapid dispersion of heat through the terminals, resulting in reduced temperatures within this specific area.

Figure 13 illustrates the temperature curve along the vertical centerline of the cell, showing an asymmetrical temperature profile in the height direction. The asymmetry observed in the temperature field along the vertical axis is a result of the particular boundary conditions employed in the analysis. It is noteworthy that this asymmetrical temperature profile bears a resemblance to the thermal response observed in the entire battery pack, which is considered in Sec. V B. The thermal behavior of the battery pack, much like the behavior of an individual cell, is influenced by the specific boundary conditions applied during analysis. This parallelism underscores the interconnected nature of thermal dynamics within the cell and the broader battery pack system, reinforcing the significance of accurate boundary condition considerations in predicting and optimizing the overall thermal performance.

Following the presentation of the validation results for the one cell battery model, the focus of the inquiry turns toward investigating the thermal performance of the battery pack. In this scenario, a transient analysis is undertaken for a time interval of 10 000 s, maintaining identical convection boundary conditions at the free faces, with a volumetric internal heat source of 22.8 kW/m³. In Fig. 14, the three-dimensional temperature field within the battery pack is depicted at the 10 000 s time point. The right-hand side of the figure showcases a symmetrical half model. Notably, the minimum and maximum temperatures are noted at approximately 49 and 54 °C, respectively, which are much higher than in the previously considered case of one cell. Moreover, the highest temperature is observed in the bottom part of the symmetry plane within the battery pack, highlighting a critical region that requires attention for thermal management. Conversely, the minimum temperature is identified at the external connectors, emphasizing the significance of monitoring and optimizing thermal conditions at different components for the overall performance and safety of the battery back.

Figure 15 presents the plot of the temperature surface T(x,y) and the plot of the contour lines over the symmetry plane at the final time step of the analysis. Notably, it reveals that the maximum temperature within the cell is concentrated in the bottom area. Additionally, the analysis discerns that the predominant temperature gradient occurs primarily in the height (vertical) direction. This insight is crucial for comprehending the thermal dynamics along the vertical axis of the battery cell. Recognizing the direction of the temperature gradient aids in identifying potential areas of concern and implementing effective thermal control measures. The detailed visualization provided by the figures serves as a valuable resource for optimizing the design and operational considerations of the battery system, ensuring efficient thermal performance and prolonged durability in practical applications.

Furthermore, Fig. 16 illustrates the changing trends of minimum and maximum temperatures within the battery pack throughout the specified time interval of analysis, indicating a gradual rise in both functions over time. Additionally, the graph depicts the increasing difference between the two temperature functions. By the end of the analysis period, this difference approaches a value near 5 °C. The observed increase in temperature discrepancy gives rise to concerns regarding the expanding thermal gradient within the structure, which is intertwined with the thermal and structural stability of the battery pack.

Furthermore, the data depicted in Fig. 16 underscore the importance of adopting a comprehensive thermal management approach for the battery pack to mitigate elevated temperatures. Such a strategy is instrumental in optimizing the performance, safety, and durability of the battery system in real-world applications. The three-dimensional temperature field plots in the battery pack at time instants 1000 and 5000 s are depicted in Fig. 17. The plots illustrate that the contour plot consistently preserves its distinctive shape, remaining stable across different temperature values. This suggests an almost constant spatial distribution of temperature, even as the temperature undergoes variations over time.

For further analysis, the temperature functions along the lines Lx, Ly, and Lz are considered. These lines are parallel to the corresponding coordinate axis and are displayed in Fig. 18. The lines Lx and Ly are placed in the symmetrical plane of the battery pack while the line Lz is orthogonal to both lines and passes through their cross point, which at the same time, defines the location of maximum temperature in the body. Due to the symmetry of the temperature profile in both x-directions, Ly is located in the middle of the plane of symmetry. In order to localize this point, the normalized temperature distribution is plotted along Ly for different time instants as displayed by the curve chart in Fig. 18. The resulting point is obtained around the height of 50 mm and this is used to locate the other two lines, Lx and Lz.

The temperature distribution at the final time step along lines Lx, Ly, and Lz is depicted in Fig. 19. The curves exhibit behavior similar to the previously examined single-cell case. As a result of the symmetrical boundary conditions, the curve along Lx reaches the peak in the middle of the domain, whereas Lz achieves the maximum temperature at the beginning. In contrast, Ly does not demonstrate symmetrical behavior and reaches the maximum temperature value at a height of approximately 50 mm.

As previously mentioned, temperatures within the battery pack ultimately reach values within a range of approximately 49–54 °C, indicating a significant rise and highlighting the necessity of implementing a thermal management strategy. To address these temperatures, a passive cooling approach is selected, leveraging the composite structure studied earlier in this investigation. Secs. V C and V D investigate the battery pack's thermal response incorporating the modeled composite medium.

Figure 20 illustrates the computational model of the battery pack featuring the composite domain. In this model, an additional layer with a thickness of 10 mm has been incorporated, enveloping the front, back, and side faces of the battery pack. Despite the introduction of this layer, the symmetry of the model remains intact. This strategic placement of material enhances the overall thermal performance of the battery pack to provide efficient temperature regulation. The symmetrical design leads to a uniform distribution of thermal effects and can be used to reduce the computational effort by considering half of the model, as already done in Secs. V A and V B.

The behavior of the numerical model is first checked for the time step size, since it is essential in correctly capturing the phase change behavior of the PCM. This is achieved by comparing the enthalpy values used at each time step during the analysis cycle with the temperature dependent enthalpy function implemented in the FE material model that is presented by the curve in Fig. 21. Evidently, the discrete solution points correctly follow the material model curve, particularly at the beginning and end of the PCM melting zone where the number of time steps is increased, demonstrating that the phase change behavior is accurately captured by the applied time step size.

To examine the outcomes of the analysis, the temperature contour plots within the PCM-pack are evaluated at specific time points: 1000, 5000, 7000, and 10 000 s, as illustrated in Figs. 22 and 23, respectively. These figures describe the outcomes within the half model of the battery pack, maintaining symmetry as previously indicated.

The temperature profile consistently exhibits symmetrical characteristics in the x- and z-directions. However, in the y-direction, it displays an asymmetrical pattern. An interesting observation is that the maximum temperature within the battery pack consistently occurs in the symmetry plane. This consistent location signifies a notable trend in our analysis.

Furthermore, it is noteworthy that the minimum temperature in the battery pack exhibits variation in its location. In the initial three instances (at time points 1000, 5000, and 7000 s), the minimum temperature primarily manifests within the PCM. However, in the final case (at 10 000 s), the minimum temperature is observed in the external connectors. These findings emphasize the dynamic nature of temperature distribution within the battery pack including the effect of the PCM, shedding light on both consistent patterns and noteworthy variations across different time instances. The thermal response discussed becomes more apparent when examining Fig. 24, which depicts the evolution of temperature limits within the battery packs. The curves for the initial case without PCM are included for comparison. Before the time instant 2000 s, they are relatively similar. Nevertheless, the noted fluctuation is attributed to the introduced PCM layer, leading to the absorption of conducted thermal energy in sensible heat form until this particular moment. Simultaneously, it is noteworthy that the composite exhibits significantly higher thermal conductivity in the z-direction, as evidenced by the comparison between Table III and Fig. 6.

During the time span from 2000 to 7000 s, the curves associated with the PCM case exhibit a plateau, signifying a reduced rate of temperature change over time. This phenomenon arises as a result of latent heat absorption occurring during this specific time period. As mentioned earlier, given that the minimum temperature is situated within the PCM, the curve depicting the minimum temperature aligns with the PCM response. This correspondence implies that the medium remains within the mushy region throughout this temperature interval, a characteristic clearly observed in the corresponding temperature range of 28–30 °C, aligned with this time interval. Following the time instant of 7000 s, the PCM resumes absorbing heat in a sensible form, resulting in an elevated rate of temperature change over time. At the last time point considered, 10 000 s, the temperature limits peak at approximately 39 and 41 °C. These values are considerably lower than the temperatures recorded in the initially examined battery pack without the involvement of PCM. The maximum temperature difference between the two cases reaches a value around 14 °C, which occurs at the time instant 7100 s. The temperature field's behavior at the final time step becomes more apparent in Fig. 25, where plots of the temperature surface and contour lines are displayed over the symmetry plane of the pack. Notably, this visualization highlights a reduction in the hotspot region, indicating a more uniform temperature distribution. This improvement is particularly evident when comparing it to the initial pack, as illustrated in Fig. 15.

In Fig. 26, the temperature fields in the pack models are depicted at the 1000 s time point for both cases, with and without PCM. It is evident from the profiles of the temperature distribution that there are notable differences between the two scenarios. Despite these differences, the actual temperature values exhibit a relatively similar pattern. Notably, at this specific time instant, the temperatures recorded are below the melting point of the PCM. It is noteworthy that the heat is being absorbed solely in sensible form, without triggering the phase transition of the PCM. However, the distinguished temperature profile is due to the thermal conductivity of the composite layer.

Figure 27 illustrates a comparison of temperature fields in the pack models at the 5000 s time point, both with and without PCM. The graph reveals evident differences between the profiles of the temperature distribution and the temperature values in these scenarios. At this specific time instant, the temperatures indicate that a portion of the PCM is in the mushy region, suggesting that the material is in a transitional state between solid and liquid phases. This observation implies that a substantial amount of heat can still be absorbed in latent form, underscoring the importance of considering the PCM's dynamic behavior in the heat absorption process. Furthermore, the composite medium offers enhanced thermal conductivity, resulting in increased thermal diffusivity and improved heat dissipation.

Figure 28 illustrates a comparison of the temperature fields within the two battery packs at the final time step of 10 000 s. In the presented comparison, it is evident that the new model exhibits noteworthy improvements. Obviously, the new model exhibits both minimum and maximum temperatures, approximately 39 and 41 °C, respectively, which are lower than their corresponding values in the initial model. This signifies a positive impact on the overall thermal performance of the battery pack with the incorporation of composite. Moreover, this reduction in temperature differences suggests enhanced thermal uniformity, which is a key factor for improved efficiency and reduced thermal stresses. More significantly, the temperature profile in the new model undergoes a substantial deformation and contraction of the hotspot region to a smaller area, resulting in a diminished thermal gradient. Such thermal equilibrium contributes to a more stable and controlled operating environment, mitigating the risk of localized overheating and potential thermal strains to the battery components.

As displayed in Fig. 29(a), the y-coordinate of the maximum temperature is shifted by over 7 mm compared to the case without PCM. This difference is attributed to the heat dissipation mechanism linked to the composite, which involves increased thermal diffusivity and latent heat absorption.

The curves in Figs. 30–32 illustrate a comparison of temperature distributions along the lines Lx, Ly, and Lz for the two examined scenarios at the final time step. Notably, the curves exhibit similar behavior in both cases, indicating consistent trends. However, a distinct disparity emerges, particularly in the PCM case, where the curves consistently register temperatures more than 12 °C lower than their counterparts in the first case. The maximum difference between these two sets of curves reaches approximately the 14 °C threshold at the time instant of 7100 s, underscoring the significant temperature variation between the two scenarios.

The temperature profiles in Figs. 33–35 depict the evolving physical states of the PCM at various time instants within the composite region surrounding the battery cells. The legend's temperature contour values are configured to depict the three phases of the PCM: solid, mushy, and liquid. Below 28 °C, the material is in a solid state, within the temperature range of 28–30 °C, the PCM is in a mushy state, and at temperatures exceeding 30 °C, the material transitions to the liquid phase. However, at the time instant of 1000 s, the entire domain registers a temperature below the transition threshold of 28 °C, rendering it solid. However, by 1700 s, a segment of the domain surpasses this temperature value and a transition to the mushy region takes place. This particular zone is situated near the battery pack's center, where temperatures reach their maximum. At 2000 s, the temperature of the PCM domain falls within the range of 28–30 °C, placing it squarely within the mushy region. As time progresses, the dynamics of the composite undergo significant changes. By 5000 s, a portion of the composite exhibits temperatures exceeding 30 °C, transitioning into a liquid state, originating from the central region of the battery pack. The liquid region expands further and by 6900 s, a small area is still in the mushy state, with the majority of the PCM existing in the liquid phase. Finally, at 7000 s, the entire PCM domain attains a temperature surpassing 30 °C and clearly reaches the liquid state.

The findings discussed correspond with the temporal evolution of the minimum temperature curve within the composite CM domain, as illustrated in Fig. 36.

The integration of a porous medium with PCM presents a promising solution for enhancing heat transfer efficiency and addressing thermal regulation challenges in various applications such as EV battery packs. Despite its advantages, predicting the thermal behavior of composite materials is challenging, necessitating the development of computational tools to anticipate their response under different conditions. In this study, a computational tool is developed, which is tailored to evaluate constitutive parameters of composite materials, providing a comprehensive description of their thermal behavior. The RVE homogenization approach is employed to assess the composite's effective thermophysical material properties, enabling accurate predictions of thermal conductivity and phase transition dynamics. The FEM was utilized to solve the three-dimensional thermal homogenization problem, yielding an orthotropic effective thermal conductivity tensor, while the apparent heat capacity method effectively managed phase transition within the PCM domain. Integration of the composite into battery pack thermal management was thoroughly examined, demonstrating a notable reduction in the highest temperatures of the battery pack, with a reduction of about 14 °C observed at the specific moment when the PCM fully transitioned into its liquid form. The proposed thermal management strategy was found to be efficient and practical, highlighting the potential of composite materials in improving thermal performance in real-world applications. The modeling approach presented in this study provides a robust tool with significant efficiency in reducing computational time for analyzing the thermal behavior of large models, demonstrating the practical feasibility of employing the homogenization technique to decrease computational effort. In general, the integration of porous medium with PCM holds significant promise for advancing passive thermal management systems. The use of RVE thermal homogenization techniques for metal foam and porous medium PCM composites enables accurate prediction of macroscopic thermal properties, facilitating the design and optimization of efficient PTMS. As research in this field continues to progress, it is essential to refine these models for real-world applications, further establishing the viability and impact of this technology on energy-efficient thermal management systems.

The authors have no conflicts to disclose.

Ali Al-Masri: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Khalil Khanafer: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Kambiz Vafai: Conceptualization (equal); Investigation (supporting); Methodology (supporting); Project administration (equal); Supervision (equal); Writing – original draft (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.