Accession Number : AD0617329

Title :   BOUNDS IN MELTING PROBLEMS WITH ARBITRARY RATES OF LIQUID REMOVAL.

Descriptive Note : Technical rept.,

Corporate Author : COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS

Personal Author(s) : Wu,Ting-Shu ; Boley,Bruno A.

Report Date : APR 1964

Pagination or Media Count : 46

Abstract : A slab, whose material properties are dependent on both temperature and position, is insulated on one face and heated on the other according to either prescribed heat flux or temperature, so that eventually it begins to melt. After melting has started, a portion of the molten material is instantaneously removed at some prescribed rate. It is shown that the solution of this melting problem is unique, and that, under certain conditions, larger rates of heating and/or ablation result in larger rates of melting and in higher temperatures. In order to arrive at these results just stated, it is first necessary to extend the strong maximum principle for parabolic differential equations to the pertinent nonlinear case, and to prove a uniqueness theorem and a comparison theorem for the nonlinear Fourier heat-conduction equation under various boundary conditions. (Author)

Descriptors :   (*MELTING, ABLATION), (*ABLATION, MELTING), THERMAL CONDUCTIVITY, BOUNDARY VALUE PROBLEMS, HEAT TRANSFER, PHASE STUDIES

Distribution Statement : APPROVED FOR PUBLIC RELEASE