Behavior of the solution of a Stefan problem by changing thermal coefficients of the substance

We consider a one-dimensional one-phase Stefan problem for a semi-infinite substance. We suppose that there is a transient heat flux at the fixed face and the thermal coefficients are constant. The goal of this paper is to determine the behavior of the free boundary and the temperature by changing the thermal coefficients. We use the maximum principle in order to obtain properties of monotony with respect to the latent heat of fusion, the specific heat and the mass density. We compute approximate solutions through the quasi-stationary, the Goodman’s heat-balance integral and the Biot’s variational methods and a numerical solution through a finite difference scheme. We show that the solution is not monotone with respect to the thermal conductivity. The results obtained are important in technological applications. 2007 Elsevier Inc. All rights reserved.