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Appearance of mushy regions in a symmetrical Stefan problem with vanishing heat capacity†

Published online by Cambridge University Press:  16 July 2009

Pedro R. Marangunic  and
Mirta B. Stampella
Pedro R. Marangunic
Affiliation:
Instituto de Matemática ‘B. Levi’, Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario, Argentina
Mirta B. Stampella
Affiliation:
Instituto de Matemática ‘B. Levi’, Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario, Argentina
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Abstract

We prove that in the Stefan problem with planar, cylindrical or spherical symmetry, with vanishing heat capacity and constant boundary temperature, no mushy region can appear, even in the presence of constant volumetric heat sources, if the initial data are consistent with the presence of just two pure phases. If the boundary temperature is not constant, a mushy region may or may not appear; we find some general conditions ensuring one case or the other and we give a specific example illustrating the appearance of a mushy region.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 2 , June 1990 , pp. 177 - 187
Copyright
Copyright © Cambridge University Press 1990

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