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Some recent results for heat-diffusion moving boundary problems

Published online by Cambridge University Press:  17 April 2009

James M. Hall  and
Jeffrey N. Dewynne
James M. Hall
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, N.S.W.
Jeffrey N. Dewynne
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, N.S.W.
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Abstract

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Integral formulations for the three classical single phase Stefan problems involving the infinite slab and inward solidifying cylinders and spheres are utilized to generate standard analytical approximations. These approximations include the pseudo steady state estimate, large Stefan number expansions, upper and lower bounds, approximations based on integral iteration and related results such as formal series solutions. In order to demonstrate the applicability and limitations of the integral formulations three generalizations of the classical stefan problem are considered briefly. These problems are diffusion with two simultaneous chemical reactions, a Stefan problem with two moving boundaries and the genuine two phase Stefan problem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 3 , December 1985 , pp. 437 - 460
Copyright
Copyright © Australian Mathematical Society 1985

References

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