Singular Perturbation Theory for Melting or Freezing in Finite Domains Initially Not at the Fusion Temperature

[+] Author and Article Information
S. Weinbaum, L. M. Jiji

Department of Mechanical Engineering, The City College of the City University of New York, New York, N. Y.

J. Appl. Mech 44(1), 25-30 (Mar 01, 1977) (6 pages) doi:10.1115/1.3424008 History: Received January 01, 1976; Revised August 01, 1976; Online July 12, 2010


This paper treats the problem of the inward solidification at large Stefan number 1/ε, ε = CP (Ti − Tf )/L , of a finite slab which is initially at an arbitrary temperature Ti above the melting point. The face at which the heat is removed is maintained at a constant temperature below fusion while the opposite face is either (a) insulated or (b) kept at the initial temperature. Perturbation series solutions in ε are obtained for both the short-time scale characterizing the transient diffusion in the liquid phase and the long-time scale characterizing the interface motion. The asymptotic matching of the two series solutions shows that to O(ε1/2 ) the short-time series solution for interface motion for the insulated Case (a) is uniformly valid for all time. A singular perturbation theory is, however, required for the isothermal Case (b) since the interface motion is affected to this order by the inhomogeneous temperature distribution in the liquid phase.

Copyright © 1977 by ASME
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