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Mathematics 2014, 2(1), 1-11; doi:10.3390/math2010001
Article

One-Dimensional Nonlinear Stefan Problems in Storm’s Materials

1,2,*  and 2
Received: 17 October 2013 / Revised: 12 December 2013 / Accepted: 20 December 2013 / Published: 27 December 2013
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
Download PDF [224 KB, 30 December 2013; original version 27 December 2013]

Abstract

We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x > 0; with phase change temperature Tf : We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. In the first case, we assume a heat flux boundary condition of the type q(t) = q 0 t , and in the second case, we assume a temperature boundary condition T = Ts < Tf at the fixed face. Solutions of similarity type are obtained in both cases, and the equivalence of the two problems is demonstrated. We also give procedures in order to compute the explicit solution.
Keywords: Stefan problem; free boundary problem; phase-change process; similarity solution Stefan problem; free boundary problem; phase-change process; similarity solution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Briozzo, A.C.; Natale, M.F. One-Dimensional Nonlinear Stefan Problems in Storm’s Materials. Mathematics 2014, 2, 1-11.

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