Fractal-Based Analysis of Pore Distribution Effects on the Thermal Performance of Phase Change Materials Embedded in Metal Foams

Accurate description of phase change heat transfer in porous media relies on precise characterization of pore structures. In this study, fractal theory is employed to characterize the complex microstructure and pore distribution of metallic foams, and the Weierstrass–Mandelbrot (W–M) function is introduced to describe the stochastic spatial distribution of pores. Based on this fractal description, a transient melting heat transfer model is developed for metallic foam/paraffin composite phase change materials (CPCM). The effects of pore fractal dimension, porosity, and pore density on melting dynamics are systematically investigated. The results indicate that reducing porosity significantly accelerates the melting process and improves thermal energy storage efficiency. Crucially, the random pore distribution induces irregular melting fronts but has only a limited effect on the overall thermal response. Furthermore, even at identical porosities, variations in fractal dimension and pore density distinctly influence heat transfer rates, exhibiting similar evolutionary trends in melting behavior and thermal performance. These findings clarify the respective roles of pore structural parameters and stochastic pore heterogeneity in phase change heat transfer and provide guidance for optimizing composite phase change materials in high-performance thermal energy storage systems.