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One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type

Briozzo A. C., Natale M. F.

Journal of Applied Analysis

2015

Vol. 21, nr 2

89--97

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a boundary condition of Robin type at the fixed face x = 0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of similarity type for t ≥ t0 > 0 with t0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.