An explicit solution for an instantaneous two-phase Stefan problem with nonlinear thermal coefficients

Abstract

We consider a nonlinear heat conduction problem for a semi-infinite material x > 0, with phase-change temperature T 1 , an initial temperature T 2 (>T 1 ) and a heat flux of the type q(t) = q 0 /√t imposed on the fixed face x = 0. We assume that the volumetric heat capacity and the thermal conductivity are particular nonlinear functions of the temperature in both solid and liquid phases. We determine necessary and/or sufficient conditions on the parameters of the problem in order to obtain the existence of an explicit solution for an instantaneous nonlinear two-phase Stefan problem (solidification process).