Heat Conduction With Melting or Freezing in a Corner

[+] Author and Article Information
Kenneth A. Rathjen

Grumman Aerospace Corporation, Bethpage, N. Y.

Latif M. Jiji

The City University of New York, New York, N. Y.

J. Heat Transfer 93(1), 101-109 (Feb 01, 1971) (9 pages) doi:10.1115/1.3449740 History: Received June 03, 1968; Revised June 29, 1970; Online August 11, 2010


This paper presents an analytical solution to the two-dimensional free boundary problem of solidification of a liquid, initially at a uniform temperature and filling the quarter-space x, y > 0, subject to a constant wall temperature. The problem is the two-dimensional analog of Neumann’s freezing problem. The solution is characterized by similarity in the variables x/t1/2 , y/t1/2 and is obtained by treating the heat of solidification as a moving heat source. A nonlinear, singular, integro-differential equation for the solid-liquid interface is thereby derived and used to establish superhyperbolas to approximate the interface position. Results are presented for a range of the two dimensionless parameters of the problem. The accuracy of the superhyperbolic representation of the interface position is determined by comparison with a finite-difference solution. Equations are given for the calculation of the temperature fields in the solid and liquid regions that are valid for all time (i.e., they are not necessarily short- or long-time solutions).

Copyright © 1971 by ASME
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