The Exact Solutions of Some Stefan Problems With Prescribed Heat Flux

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

Department of Mechanics and Mech. & Aero. Engineering, Illinois Institute of Technology, Chicago, Ill. 60616

J. Appl. Mech 48(4), 732-736 (Dec 01, 1981) (5 pages) doi:10.1115/1.3157724 History: Received July 01, 1980; Revised April 01, 1981; Online July 21, 2009


The Stefan problem of a semi-infinite material with arbitrarily prescribed initial and flux conditions is studied. When the surface temperature is initially different from the freezing temperature, there exists a presolidification or a premelting period prior to the occurrence of a phase change. The exact solutions for both periods, before and after the appearance of a phase change, are established. This indicates that the initial condition of the Stefan problem with a prescribed heat flux at the surface cannot be assumed to be constant. Possibilities of similarity solutions of the problem are also examined. A similarity solution exists only when the heat flux is proportional to t−1/2 and the initial and boundary conditions satisfy an inequality. The solidification of a supercooled liquid is also investigated. The exact solution is obtained.

Copyright © 1981 by ASME
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