Solution of a one-dimensional phase change problem with non-uniform initial temperature

Abstract

The variable time step methods, proposed earlier by the authors with regard to phase change problems, are applied with some improvements to a problem having a non-uniform initial temperature distribution. A comparison between the numerical results from the present methods and those due to authors, who solve the problem with different techniques, shows a very good agreement. Approximate analytical expressions are also obtained for the temperature distribution as well as for the movement of the interface using the integral method. The computed values from these expressions are found to be very close to those obtained from the numerical methods.