Two-phase Stefan problem with nonlinear thermal coefficients and a convective boundary condition

Abstract

A solidification process for a semi-infinite material is presented through a non-linear two-phase unidimensional Stefan problem, where a convective boundary condition is imposed at the fixed face x=0. The volumetric heat capacity and the thermal conductivity are non-linear functions of the temperature in both solid and liquid phases and they verify a Storm-type relation. A certain inequality on the heat transfer coefficient h is established in order to get an instantaneous phase change process. We determine sufficient conditions on the parameters of the problem in order to prove the existence and uniqueness of a parametric explicit solution for the Stefan problem.