The Stefan Problem With an Imperfect Thermal Contact at the Interface

[+] Author and Article Information
L. N. Tao

Department of Mechanics, Mechanical, and Aerospace Engineering, Illinois Institute of Technology, Chicago, Ill. 60616

J. Appl. Mech 49(4), 715-720 (Dec 01, 1982) (6 pages) doi:10.1115/1.3162598 History: Received January 01, 1982; Revised April 01, 1982; Online July 21, 2009


The Stefan problem in a semi-infinite region with arbitrarily prescribed initial and boundary conditions, subject to a condition of the mixed type at the interface is investigated. To establish the exact solution of the problem, some new basic solutions of the heat equation are offered. Their mathematical properties are also supplied. The exact solutions of the temperatures in both phases and of the interfacial boundary are derived in infinite series. The existence and uniqueness of these series are considered and proved. It is also shown that these series are absolutely and uniformly convergent. Some concluding remarks about the differences between the present problem and the classical Stefan problem are given. Also the effect of a density discontinuity at the interface is discussed.

Copyright © 1982 by ASME
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