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 | References | Similar Articles | Additional Information

Abstract: We study the one-phase Stefan problem on a semi-infinite strip , with the convective boundary condition . Points of interest include: a) behavior of the surface temperature ; b) asymptotic behavior as ; c) uniqueness, and d) bounds on the phase change front and total system energy.

**[1]**H. S. Carslaw and J. C. Jaeger,*Conduction of Heat in Solids*, Oxford, at the Clarendon Press, 1947. MR**0022294****[2]**Jim Douglas Jr.,*A uniqueness theorem for the solution of a Stefan problem*, Proc. Amer. Math. Soc.**8**(1957), 402–408. MR**0092086**, https://doi.org/10.1090/S0002-9939-1957-0092086-6**[3]**Antonio Fasano and Mario Primicerio,*General free-boundary problems for the heat equation. II*, J. Math. Anal. Appl.**58**(1977), no. 1, 202–231. MR**0487017**, https://doi.org/10.1016/0022-247X(77)90239-6**[4]**Avner Friedman,*Partial differential equations of parabolic type*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR**0181836****[5]**P. Hrycak,*Problem of solidification with Newton's cooling at the surface*, AICHE Journal**9**, 585-589 (1963)**[6]**W. McAdams,*Heat transmission*(3rd edition), McGraw-Hill, New York, 1954**[7]**L. I. Rubenšteĭn,*The Stefan problem*, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by A. D. Solomon; Translations of Mathematical Monographs, Vol. 27. MR**0351348****[8]**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)**[9]**A. Solomon,*On surface effects in heat transfer calculations*, Computers and Chem. Eng.**5**, 1-5 (1981)**[10]**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)**[11]**A. Solomon,*A note on the Stefan number in slab melting and solidification*, Letters in Heat and Mass Transfer**8**, 229-235 (1981)**[12]**L. N. Tao,*Free boundary problems with radiation boundary conditions*, Quart. Appl. Math.**37**(1979/80), no. 1, 1–10. MR**530665**, https://doi.org/10.1090/S0033-569X-1979-0530665-3**[13]**R. Výborný,*On a certain extension of the maximum principle*, Differential Equations and Their Applications (Proc. Conf., Prague, 1962), Publ. House Czechoslovak Acad. Sci., Prague; Academic Press, New York, 1963, pp. 223–228. MR**0173860**

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Additional Information

DOI:
https://doi.org/10.1090/qam/666675

Article copyright:
© Copyright 1982
American Mathematical Society