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One-Dimensional Nonlinear Stefan Problems in Storm’s Materials

Author

Listed:
  • Adriana C. Briozzo

    (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)

  • María F. Natale

    (Departmant of Mathematics, Faculty of Business, University of Austral, Paraguay 1950, Rosario S2000FZF, Argentina)

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.

Suggested Citation

  • Adriana C. Briozzo & María F. Natale, 2013. "One-Dimensional Nonlinear Stefan Problems in Storm’s Materials," Mathematics, MDPI, vol. 2(1), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:2:y:2013:i:1:p:1-11:d:31723
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