Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-17T19:13:38.666Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Dewynne, J.N., Ph.D. Thesis, University of Wollongong, 1985.Google Scholar
[2]Dewynne, J.N. and Hill, J.M., “On an integral formulation for moving boundary problems”, Quart. Appl. Math. 41 (1984), 443–455.CrossRefGoogle Scholar
[3]Dewynne, J.N. and Hill, J.M., “Simple bounds for the Stefan problem with two chemical reactions”, J. Nonlinear Anal. 9 (1985).CrossRefGoogle Scholar
[4]Dewynne, J.N. and Hill, J.M., “Integral formulation and bounds for two phase Stefan problems initially not at their fusion temperature”, Acta Mechanica 48 (1985).Google Scholar
[5]Dewynne, J.N. and Hill, J.M., “On a multiphase Stefan problem”, Q. Jl. Mech. appl. Math. 38 (1985).Google Scholar
[6]Hill, J.M., “On the pseudo steady state approximation for moving boundary diffusion problems”. Chem. Engng. Sci. 39 (1984), 187–190.CrossRefGoogle Scholar
[7]Hill, J.M., “Some unusual unsolved integral equations for moving boundary diffusion problems”, Mathematical Scientist 9 (1984), 15–23.Google Scholar
[8]Hill, J.M. and Dewynne, J.N., “Improved lower bounds for the motion of moving boundaries”, J. Austral. Math. Soc. Ser. B26 (1984), 165–175.CrossRefGoogle Scholar
[9]Hill, J.M. and Dewynne, J.N., “A note on Langford's cylinder functions cn(z, zo) and en(z, zo)”, Quart, Appl. Math. 43 (1985), 179–185.CrossRefGoogle Scholar
[10]Ockendon, J.R. and Hodgkins, W.R. (eds.), Moving boundary problems in hear flow and diffusion, (Clarendon Press, Oxford, 1975).Google Scholar
[11]Voller, V. and Cross, M., “Accurate solutions of moving boundary problems using the enthalpy method”, Int. J. Heat Moss Transfer 24 (1981), 545–556.CrossRefGoogle Scholar
[12]Wilson, D.G., Solomon, A.D. and Boggs, P.T. (eds.), Moving boundary Problems, (Academic Press, New York, 1978).Google Scholar