The Stefan problem with a convective boundary condition
Authors:
A. D. Solomon, V. Alexiades and D. G. Wilson
Journal:
Quart. Appl. Math. 40 (1982), 203-217
MSC:
Primary 35R35; Secondary 35B30, 80A20
DOI:
https://doi.org/10.1090/qam/666675
MathSciNet review:
666675
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Abstract: We study the one-phase Stefan problem on a semi-infinite strip $x \ge 0$, with the convective boundary condition $- K{T_x}\left ( {0, t} \right ) = h\left [ {{T_L} - T(0, t)} \right ]$. Points of interest include: a) behavior of the surface temperature $T\left ( {0, t} \right )$; b) asymptotic behavior as $h \to \infty$; c) uniqueness, and d) bounds on the phase change front and total system energy.
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A. Solomon, A relation between surface temperature and time for a phase change process with a convective boundary condition, Letters in Heat and Mass Transfer 6, 189–197 (1979)
A. Solomon, On surface effects in heat transfer calculations, Computers and Chem. Eng. 5, 1–5 (1981)
A. Solomon, On the melting time of a simple body with a convective boundary condition, Letters in Heat and Mass Transfer 7, 183–188 (1980)
A. Solomon, A note on the Stefan number in slab melting and solidification, Letters in Heat and Mass Transfer 8, 229–235 (1981)
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H. Carslaw and J. Jaeger, Conduction of heat in solids (2nd edition), Oxford University Press, London, 1959
J. Douglas, Jr., A uniqueness theorem for the solution of a Stefan problem, Proc. Amer. Math. Soc. 8, 402–408 (1957)
A. Fasano and M. Primicerio, General free-boundary problems for the heat equation, II, J. Math. Anal. Applics. 58, 202–231 (1977)
A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, 1964
P. Hrycak, Problem of solidification with Newton’s cooling at the surface, AICHE Journal 9, 585–589 (1963)
W. McAdams, Heat transmission (3rd edition), McGraw-Hill, New York, 1954
L. Rubenstein, The Stefan problem, American Mathematical Society, Translations of Mathematical Monographs 27, Providence, 1971
A. Solomon, A relation between surface temperature and time for a phase change process with a convective boundary condition, Letters in Heat and Mass Transfer 6, 189–197 (1979)
A. Solomon, On surface effects in heat transfer calculations, Computers and Chem. Eng. 5, 1–5 (1981)
A. Solomon, On the melting time of a simple body with a convective boundary condition, Letters in Heat and Mass Transfer 7, 183–188 (1980)
A. Solomon, A note on the Stefan number in slab melting and solidification, Letters in Heat and Mass Transfer 8, 229–235 (1981)
L. Tao, Free boundary problems with radiation boundary conditions, Quart. Appl. Math. 37, 1–10 (1979)
R. Vyborny, On a certain extension of the maximum principle, pp. 223–228 in Differential equations and their applications, Academic Press, New York, 1963
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Article copyright:
© Copyright 1982
American Mathematical Society
