A Stefan problem with variable thermal coefficients and moving phase change material

Abstract

This article describes a one-phase Stefan problem in a semi-infinite domain that involves temperature-dependent thermal coefficients and moving phase change material with a speed in the direction of the positive x-axis. The convective boundary condition at a fixed boundary is also considered in the problem. An approximate approach to the problem is discussed to solve the problem with the aid of spectral tau method. The existence and uniqueness of the analytical solution to the problem are also established for a particular case, and the obtained approximate solution is compared with this analytical solution which shows that the approximate results are sufficiently accurate. The impact of a few parameters on the moving interface is also analysed.