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Mathematics 2014, 2(1), 111; doi:10.3390/math2010001
Article
OneDimensional Nonlinear Stefan Problems in Storm’s Materials
^{1}
National Scientific and Technical Research Council, Rivadavia 1917, Buenos Aires C1033AAJ, Argentina
^{2}
Departmant of Mathematics, Faculty of Business, University of Austral, Paraguay 1950, Rosario S2000FZF, Argentina
* Author to whom correspondence should be addressed.
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)
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Abstract
We consider two onephase nonlinear onedimensional Stefan problems for a semiinfinite 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 $\text{q(t)=}\frac{{q}_{0}}{\sqrt{t}}$ , 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.
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