Behavior of the Solution of the Two-phase Stefan Problem with Regard to the Changing of Thermal Coefficients of the Substance

We consider one-dimensional two-phase Stefan problems for a finite substance with different boundary conditions at the fixed faces. The goal of this paper is to determine the behavior of the free boundary and the temperature when the thermal coefficients of the material change. We obtain properties of monotony with respect to the latent heat, the common mass density, the specific heat of each phase and the thermal conductivity of the liquid phase. We show that the solution is not monotone with respect to the thermal conductivity of solid phase, in some cases, by computing a numerical solution through a finite difference scheme. The results obtained are important in technological applications as the climate of buildings, the storage of energy in satellites and clothes and the transport of biological substances and telecommunications. Keywords— Phase change material, Two phase Stefan problem, Finite difference method