The Exact Solution to an Ablation Problem With Arbitrary Initial and Boundary Conditions

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

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

J. Appl. Mech 51(4), 821-826 (Dec 01, 1984) (6 pages) doi:10.1115/1.3167731 History: Received December 01, 1983; Revised February 01, 1984; Online July 21, 2009


The problem of ablation by frictional heating in a semi-infinite solid with arbitrarily prescribed initial and boundary conditions is investigated. The study includes all convective motions caused by the density differences of various phases of the materials. It is found that there are two cases: (i) ablation appears immediately and (ii) there is a waiting period of redistribution prior to ablation. The exact solutions of velocities and temperatures of both cases are derived. The solutions of the interfacial positions are also established. Existence and uniqueness of the solutions are examined and proved. The conditions for the occurrence of these two cases are expressed by an inequality. Physical interpretation of the inequality is explored. Its implication coincides with one’s expectation. Ablation appears only when the surface temperature is at or above the melting temperature.

Copyright © 1984 by ASME
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