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Improved lower bounds for the motion of moving boundaries

Published online by Cambridge University Press:  17 February 2009

James M. Hill  and
Jeffrey N. Dewynne
Jeffrey N. Dewynne
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, N.S.W. 2500
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Abstract

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In a recent paper the authors give upper and lower bounds for the motion of the moving boundary for the classical Stefan problem for plane, cylindrical and spherical geometries. On comparison with the exact Neumann solution for the plane geometry and no surface radiation the bounds obtained are seen to be quite adequate for practical purposes except for the lower bound at small Stefan numbers. Here improved lower bounds are obtained which in some measure remove this inadequacy. Time dependent surface conditions are also examined and the new lower bounds obtained for the classical problem are illustrated numerically.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 2 , October 1984 , pp. 165 - 175
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Davis, G. B. and Hill, J. M., “A moving boundary problem for the sphere”, IMA J. Appl. Math. 29 (1982), 99–111.CrossRefGoogle Scholar
[2]Dewynne, J. N. and Hill, J. M., “On an integral formulation for moving boundary problems”, Quart. Appl. Math. 42 (1984), 443–455.CrossRefGoogle Scholar
[3]Glasser, D. and Kern, I., “Bounds and approximate solutions to linear problems with non-linear boundary conditions”, AIChE. J. 24 (1978), 161–170.CrossRefGoogle Scholar
[4]Hill, J. M., “On the pseudo steady state approximation for moving boundary diffusion problems”, Chem. Engrg. Sci. 39 (1984), 187–190.CrossRefGoogle Scholar
[5]Ockendon, J. R. and Hodgkins, W. R. (eds.), Moving boundary problems in heatflow and diffusion (Clarendon Press, Oxford, 1975).Google Scholar
[6]Rubinstein, L. I., The Stefan problem, Translations of Mathematical Monographs 27 (Amer. Math. Soc., Providence, R. I., 1971).Google Scholar
[7]Wilson, D. G., Solomon, A. D. and Boggs, P. T. (eds.), Moving boundary problems (Academic Press, New York, 1978).Google Scholar