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Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension

Published online by Cambridge University Press:  01 April 2000

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. For simplicity, the fine structure is here taken to be periodic, first in one dimension, and then a lattice of squares in two dimensions. A method of multiple scales is employed, with a classical free-boundary problem being used to model the evolution of the two-phase microstructure. Then a macroscopic model for the mush is obtained by an averaging procedure. The free-boundary temperature is taken to vary according to Gibbs–Thomson and/or kinetic-undercooling effects.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 2 , April 2000 , pp. 153 - 169
Copyright
2000 Cambridge University Press

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