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The solution of Problems Involving the Melting and Freezing of Finite Slabs by a Method due to Portnov

Published online by Cambridge University Press:  20 January 2009

F. Jackson
F. Jackson
Affiliation:
Nova Scotia Technical College, Halifax, Canada
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In a recent paper (1) Portnov used a form of Poisson integral to find the exact solution for the temperature distribution in a freezing semi-infinite slab occupying the region x > 0, and having an arbitrary time dependent temperature applied at the face x = 0. Previously, Boley (2) had used a method based on Duhamel's theorem to find solutions for problems involving melting, in both finite and semi-finite regions, caused by time dependent heat fluxes. Steady-state solutions have been investigated by Landau (3), Masters (4) and others (5).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 2 , December 1964 , pp. 109 - 128
Copyright
Copyright © Edinburgh Mathematical Society 1964

References

REFERENCES

(1)Portnov, I. G., Exact solution of freezing problem with arbitrary temperature variation on fixed boundary, Soviet Physics, Doklady, 7 (1962), pp. 186–189.Google Scholar
(2)Boley, B. A., A method of heat conduction analysis of melting and solidification problems, J. Math. Phys., 40 (1961), pp. 300–313.CrossRefGoogle Scholar
(3)Landau, H. G., Heat conduction in a melting slab, Quart. of Appi. Math., 8 (1950), pp. 81–94.CrossRefGoogle Scholar
(4)Masters, J. I., Problem of intense surface heating of a slab accompanied by a change of phase, J. Appl. Phys., 27 (1956), pp. 477–485.CrossRefGoogle Scholar
(5)Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids (Oxford University Press, London, 1957).Google Scholar