Supercooled Stefan problem with a Neumann type boundary condition

Abstract

We consider a supercooled one-dimensional Stefan problem with a Neumann boundary condition and a variable thermal diffusivity. We establish a necessary and sufficient condition for the heat flux at the fixed face x = 0, in order to obtain existence and uniqueness of a similarity type solution. Moreover we over-specified the fixed face x = 0 by a Dirichlet boundary condition aiming at the simultaneous determination of one or two thermal coefficients.