A moving boundary problem with variable specific heat and thermal conductivity

Abstract

This article presents a Stefan problem including thermal conductivity and heat capacity as the functions of temperature. At α=β, the exact solutions to the proposed problem are discussed for two different specific cases, i.e. m=n=1 and m=n=2. For the general case, estimation of the solution to the problem is deliberated with the help of shifted Chebyshev tau method. To exhibit the accurateness of the obtained approximate solution, the comparison between exact and approximate solution are depicted through tables which shows that the approximate results are in good agreement with the exact solution. We also present the impact of parameters appeared in the considered problem on temperature profile and location of moving interface. It is found that the melting of the material effectively enhances when we increase either the value m or[spsbacksalsh]and n or Stefan number.