Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Explicit solutions to phase change problems


Authors: A. D. Solomon, D. G. Wilson and V. Alexiades
Journal: Quart. Appl. Math. 41 (1983), 237-243
MSC: Primary 80A20
DOI: https://doi.org/10.1090/qam/719507
MathSciNet review: 719507
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Abstract: We examine two heat transfer and phase change problems having explicit solutions. The first involves melting of an initially cold material and clarifies the meaning of a recent result of Tarzia [5]. The second concerns a model of binary alloy solidification which, in some cases, is seen to be incorrect.


References [Enhancements On Off] (What's this?)

  • [1] H. Carslaw and J. Jaeger, Conduction of heat in solids, 2nd edition, Oxford University Press, 1959 MR 0022294
  • [2] A. B. Crowley and J. Ockendon, On the numerical solution of an alloy solidification problem, International Journal of Heat and Mass Transfer, 22, 941-947 (1979)
  • [3] L. Rubinstein, The Stefan problem, American Mathematical Society Translations, 1967 MR 0222436
  • [4] L. Rubinstein, Solidification of a binary alloy, Free Boundary Problems, Vol. 1, Proceedings of a seminar held in Pavia, Sept.-Oct., 1979, Instituto Nazionale di Alta Matematica F. Severi, Rome, 399-416, 1980
  • [5] D. Tarzia, An inequality for the coefficient $ \sigma $ of the free boundary $ s\left( t \right) = 2\sigma \sqrt t $ of the Neumann solution for the two-phase Stefan problem, Quarterly of Applied Math, 39, 491-497 (1982) MR 644103
  • [6] D. G. Wilson, Existence and uniqueness for similarity solutions of one dimensional multi-phase Stefan problems, SIAM Journal of Applied Mathematics 5, 135-147 (1979) MR 0473521

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DOI: https://doi.org/10.1090/qam/719507
Article copyright: © Copyright 1983 American Mathematical Society

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