A Stefan Problem With Contact Resistance

[+] Author and Article Information
G. W. Barry

Physics Department, Lehigh University, Bethlehem, PA

J. S. Goodling

Mechanical Engineering Department, Auburn University, Auburn, AL

J. Heat Transfer 109(4), 820-825 (Nov 01, 1987) (6 pages) doi:10.1115/1.3248187 History: Received June 16, 1986; Online October 20, 2009


A Stefan problem in which a semi-infinite molten material at the fusion temperature solidifies as a result of imperfect thermal contact with a cooler semi-infinite solid is considered. The contact resistance, due to surface roughness, is modeled by a convective boundary condition. Biot’s variational principle is used to reduce the coupled partial differential equations to a pair of coupled ordinary differential equations that are solved numerically. The position of the moving boundary as a function of time is given for both bismuth and aluminum solidifying on stainless steel.

Copyright © 1987 by ASME
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