One-Dimensional Nonlinear Stefan Problems in Storm’s Materials

Mathematics

María F. Natale¹  Adriana C. Briozzo² 

[1] Departmant of Mathematics, Faculty of Business, University of Austral, Paraguay 1950, Rosario S2000FZF, Argentina;National Scientific and Technical Research Council, Rivadavia 1917, Buenos Aires C1033AAJ, Argentina;

关键词: Stefan problem;    free boundary problem;    phase-change process;    similarity solution;   

DOI  :  10.3390/math2010001

来源: DOAJ

【 摘 要 】

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 [PLEASE CHECK FORMULA IN THE PDF], 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.

【 授权许可】

Unknown