Gegenbauer wavelet approach of a two-phase moving boundary problem with functionally graded phase change material

Over the past few decades, functionally graded phase change materials (FG-PCMs) have been extensively employed in drugs, alloy casting, thermal control, and engineered microstructures. Although FG-PCMs have been extensively studied for their structural properties in a single phase, the modeling and simulations of FG-PMs in two-phase solid–liquid processes are insufficient and are the focus of this study. To simulate the study, a well-structured, spatially varying distribution function for thermal conductivity and thermal diffusivity is considered, which overcomes the limitations for choosing arbitrary distribution functions in solid–liquid phase change processes. Gegenbauer wavelet, based on the collocation method, is employed to carry out the simulations of the current study. The numerical results obtained accurately converge to the established Stefan solution under specific conditions, as well as to the complete model scenario via the known finite-difference method (FDM). Spatially variable thermal conductivity and thermal diffusivity distribution functions significantly influence the solidification rate of FG-PCM. Furthermore, the spatially variable distribution functions of thermal conductivity and thermal diffusivity in solids exhibit lower temperatures, hence enhancing the solid–liquid interface compared to equal or unequal distribution functions of other phases. The quadratic representation of thermal conductivity and thermal diffusivity provides the most rapid solidification rate.