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One-Dimensional Nonlinear Stefan Problems in Storm’s Materials
National Scientific and Technical Research Council, Rivadavia 1917, Buenos Aires C1033AAJ, Argentina
Departmant of Mathematics, Faculty of Business, University of Austral, Paraguay 1950, Rosario S2000FZF, Argentina
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Received: 17 October 2013; in revised form: 12 December 2013 / Accepted: 20 December 2013 / Published: 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 , 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
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Cite This Article
MDPI and ACS Style
Briozzo, A.C.; Natale, M.F. One-Dimensional Nonlinear Stefan Problems in Storm’s Materials. Mathematics 2014, 2, 1-11.
Briozzo AC, Natale MF. One-Dimensional Nonlinear Stefan Problems in Storm’s Materials. Mathematics. 2014; 2(1):1-11.
Briozzo, Adriana C.; Natale, María F. 2014. "One-Dimensional Nonlinear Stefan Problems in Storm’s Materials." Mathematics 2, no. 1: 1-11.