A Stefan problem with temperature and time dependent thermal conductivity

Abstract

In this paper, a one phase Stefan problem with time and temperature dependent thermal conductivity is investigated. With the help of similarity transformation and tau method based on shifted Chebyshev operational matrix of differentiation, an approximate solution of the problem is discussed. For a particular case, an exact solution of the proposed problem is also discussed and it is used to check the accuracy of the obtained approximate results. The effect of some parameters involved in the model on temperature distribution and movement of phase front is also analysed.