Determination of unknown thermal coefficients in a Stefan problem for Storm’s type materials

Abstract

We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x> 0 , with phase change temperature Tf. We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. A convective boundary condition and a heat flux over-specified condition on the fixed face x= 0 are considered. Unknown thermal coefficients are determined for the free boundary problem and for the associate moving boundary problem and we give sufficient conditions to obtain a parametric representation of a similarity type solution. Moreover, we give formulae for the thermal coefficients in both cases.