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The Quarterly Journal of Mechanics and Applied Mathematics 2000 53(3):449-473; doi:10.1093/qjmam/53.3.449
© 2000 by Oxford University Press
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Asymptotic results for the Stefan problem with kinetic undercooling

J. D. EVANS1,+ and J. R. KING2

( 1 Department of Mathematical Sciences, The University of Wales, Aberystwyth, Ceredigion SY23 3BZ 2 Department of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD )

We study the behaviour of the one-phase Stefan problem with kinetic undercooling; moving boundary problems governed by the same formulation also arise in the modelling of silicon oxidation and of solvent diffusion in glassy polymers. The one-phase model is carefully derived from a two-phase formulation in the limit of small thermal diffusivity in the solid. A linear kinetic undercooling law is assumed at the moving boundary and the one-phase model is then studied in a number of asymptotic regimes. In particular, results for small and large Stefan number are presented in one dimension and in a paradigm two-dimensional example.

Received 15 December, 1998. Revised 7 October, 1999.

+ <Andrew.May@tessella.co.uk>


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