Legendre wavelet based numerical solution of variable latent heat moving boundary problem

Abstract

The major goal of this article is to develop mathematical and numerical analysis of one phase moving boundary problem with conduction and convection effect when variable thermal conductivity depends on time and temperature and also latent heat is presented as the power function of position. In model-1 the temperature at the surface is described while in model-2 the heat flux condition is expressed in terms of power function of time. The numerical algorithms of these two models are obtained by using Legendre Wavelet Galerkin (LWG) and Legendre Wavelet Collocation (LWC) methods. LWG technique is used to obtain the numerical solution in case of constant properties while LWC technique is used for variable thermal conductivity. The effect of both convection term and variability of thermal conductivity with time and temperature on the moving interface is analyzed. Further variability of Stefan numbers, Peclet numbers and other parameters on the location of the moving interface is discussed in detail and is shown graphically.