One-Dimensional Nonlinear Stefan Problems in Storm’s Materials

Adriana C. Briozzo and María F. Natale
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Adriana C. Briozzo: National Scientific and Technical Research Council, Rivadavia 1917, Buenos Aires C1033AAJ, Argentina
María F. Natale: Departmant of Mathematics, Faculty of Business, University of Austral, Paraguay 1950, Rosario S2000FZF, Argentina

Mathematics, 2013, vol. 2, issue 1, 1-11

Abstract: We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x > 0; with phase change temperature T f : 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 = T s < T f 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2013
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