Non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition

Abstract

A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent and a Robin type condition at fixed face x=0 for a semi-infinite material is considered. The source function depends on the evolution the heat flux at the fixed face x=0. Existence of a similarity type solution is obtained and the asymptotic behaviour of free boundary with respect to latent heat fusion is studied. The analysis of several particular cases are given.