A computational solution of a phase-change material in the presence of convection under the most generalized boundary condition

Abstract

This article presents a mathematical model describing inward melting process of a phase change material in the presence of convection under the most generalized boundary condition. It is assumed that the material within a container have different geometrical configuration like circular cylinder or sphere. All thermophysical properties of the solid and liquid regions are assumed to be homogeneous. Initially, we convert the mathematical model into an initial value problem in the form of vector matrix representation using a finite difference technique. Two numerical methods; the operational matrix of integration for Bessel functions and finite element Legendre wavelet Galerkin method, are applied to solve the initial value problem. Thus, the obtained results from both methods analyzed for constant (or time depending) temperature or constant (or time depending) heat flux. The whole study is presented in dimensionless form. The effect of Stefan number, Peclet number, Kirpichev number and Biot number on dimensionless temperature profile and dimensionless moving front are illustrated graphically.