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

A. A. Lacey, L. A. Herraiz

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)153-169
Number of pages17
JournalEuropean Journal of Applied Mathematics
Volume11
Issue number2
Publication statusPublished - 2000

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