Wavelet galerkin and wavelet collocation method in moving boundary problem with temperature dependent thermal physical properties

Abstract

In this paper, we have studied the two phase moving boundary problem arising during melting/freezing of a melt in a semi-infinite region. In both solid-liquid regions we assume that the physical properties such as thermal conductivity and specific heat are different and temperature dependent and their densities are also different in both regions. To solve this problem we used wavelet Galerkin and wavelet Collocation method. The results thus obtained are compared with exact solution when thermal conductivity and specific heat are temperature independent and the agreement is excellent. The whole analysis is presented in dimensionless form. The effect of variability of thermal conductivity, specific heat with temperature, ratio of thermal conductivity of two regions, ratio of densities of two regions, Stefan number on solid layer thickness are analyzed and discussed. © 2014, Begell House Inc. All rights reserved.