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Macroscopic models for melting derived from averaging microscopic Stefan problems II: Effect of varying geometry and composition

Published online by Cambridge University Press:  16 July 2002

A. A. LACEY  and
L. A. HERRAIZ
A. A. LACEY
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK
L. A. HERRAIZ
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK Present address: Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
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Abstract

A mushy region is assumed to consist of a fine mixture of two distinct phases separated by free boundaries. A method of multiple scales, with restrictions on the form of the microscopic free boundaries, is used to derive a macroscopic model for the mushy region. The final model depends both on the microscopic structure and on how the free-boundary temperature varies with curvature (Gibbs–Thomson effect), kinetic undercooling, or, for an alloy, composition.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 3 , June 2002 , pp. 261 - 282
Copyright
2002 Cambridge University Press

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