A Stefan problem with moving phase change material, variable thermal conductivity and periodic boundary condition

In this paper, we discuss a Stefan problem that includes a moving phase change material and a size-dependent thermal conductivity. This model also includes the time-dependent boundary condition at the first boundary, which later assumed as the periodic nature. The solution to the problem is obtained successfully by using the finite difference scheme. The consistency and stability of the scheme for the problem are also discussed. The calculated results are compared with the exact solution for a particular case, and both are nearly equal. The dependence of the moving boundary and the temperature distribution on various parameters are also analyzed. (C) 2020 Elsevier Inc. All rights reserved.