A numerical study of a moving boundary problem with variable thermal conductivity and temperature-dependent moving PCM under periodic boundary condition

The work in this paper concerns the study of a one-phase moving boundary problem with size-dependent thermal conductivity and moving phase change material. We have considered a time-dependent boundary condition at the surface y=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y=0$$\end{document} and a temperature-dependent moving phase change material which later both assumed in periodic nature. A quadratic profile for temperature distribution is assumed to solve the problem numerically via heat balance integral method. In a particular case, we compared our results with exact solution and found to be closed. The effect of various parameters either on temperature profile or on tracking of melting front are also discussed in detail. The parameters physically interpret that transition process becomes fast for a higher value of Stefan number or/and Peclet number while there is a small delay in the propagation of melting interface for larger value of either amplitude of moving phase change material or amplitude of periodic boundary condition. Furthermore, we discuss a comparative study on temperature profile as well as on moving melting front in case of standard problem, moving boundary problem with constant thermal conductivity and presence of convection, and moving boundary problem with variable thermal conductivity and presence of convection and obtained result shows that the transition process is faster in case of moving boundary problem with constant thermal conductivity and presence of convection and is slower in case of moving boundary problem with variable thermal conductivity and presence of convection while it is between them in case of standard problem.