Uniqueness in a melting slab with space- and time-dependent heating-Reference-Cited by-同舟云学术

Uniqueness in a melting slab with space- and time-dependent heating

Published:1970 Issue:4 Volume:27 Page:481-487
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Boley Bruno A.

Abstract

Conditions for uniqueness of solution are derived for a slab which melts under an applied heat input dependent both on time and on the melted depth, the melted material being instantaneously removed. Some examples are constructed in which more than one solution is exhibited as well as one in which no melting solution exists. A theorem demonstrating monotonic dependence of solution on boundary data under certain conditions is proved.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/1970-27-04/S0033-569X-1970-0254434-3/S0033-569X-1970-0254434-3.pdf

Reference11 articles.

1. A method of heat conduction analysis of melting and solidification problems;Boley, Bruno A.;J. Math. and Phys.,1961

2. Upper and lower bounds in problems of melting or solidifying slabs;Boley, Bruno A.;Quart. J. Mech. Appl. Math.,1964

3. Bounds in melting problems with arbitrary rates of liquid removal;Wu, Ting-shu;SIAM J. Appl. Math.,1966

4. S. J. Citron, Heat conduction in melting slab, J. Aero. Sci. 27, 219–228 (1960)

5. G. W. Sutton, The hydrodynamics and heat conduction of a melting surface, J. Aero. Sci. 25, 29–32, 36 (1958)

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