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
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
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.
- H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford, at the Clarendon Press, 1947. MR 0022294
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)
- L. I. Rubinšteĭn, Problema Stefana, Izdat. “Zvaĭgzne”, Riga, 1967 (Russian). Latvian State University Computing Center. MR 0222436
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
- Domingo Alberto Tarzia, An inequality for the coefficient $\sigma $ of the free boundary $s(t)=2\sigma \sqrt {t}$ of the Neumann solution for the two-phase Stefan problem, Quart. Appl. Math. 39 (1981/82), no. 4, 491–497. MR 644103, DOI https://doi.org/10.1090/S0033-569X-1982-0644103-2
- D. G. Wilson, Existence and uniqueness for similarity solutions of one dimensional multi-phase Stefan problems, SIAM J. Appl. Math. 35 (1978), no. 1, 135–147. MR 473521, DOI https://doi.org/10.1137/0135012
H. Carslaw and J. Jaeger, Conduction of heat in solids, 2nd edition, Oxford University Press, 1959
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)
L. Rubinstein, The Stefan problem, American Mathematical Society Translations, 1967
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
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)
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)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
80A20
Retrieve articles in all journals
with MSC:
80A20
Additional Information
Article copyright:
© Copyright 1983
American Mathematical Society
