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Two-phase Stefan problem with nonlinear thermal coefficients and a convective boundary condition
  • Adriana Briozzo,
  • Maria Natale
Adriana Briozzo
Universidad Austral Buenos Aires - Sede Rosario
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Maria Natale
Universidad Austral Buenos Aires - Sede Rosario
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Abstract

We consider a non-linear two-phase unidimensional Stefan problem, which consists on a solidification process, for a semi-infinite material \(x>0\), with phase change temperature \(T_{1},\) an initial temperature \(T_{2}>T_{1}\) and a convective boundary condition imposed at the fixed face \(x=0\) characterized by a heat transfer coefficient \(h>0\). We assume that the volumetric heat capacity and the thermal conductivity are particular nonlinear functions of the temperature in both solid and liquid phases and they verify a Storm-type relation. A certain inequality on the 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.