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The rapid advance and slow retreat of a mushy zone

Published online by Cambridge University Press:  25 March 2011

NICHOLAS R. GEWECKE  and
TIM P. SCHULZE
NICHOLAS R. GEWECKE*
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-0614, USA
TIM P. SCHULZE
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-0614, USA
*
†Email address for correspondence: gewecke@math.utk.edu
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Abstract

We discuss a model for the evolution of a mushy zone which forms during the solidification of a binary alloy cooled from below in a tank with finite height. Our focus is on behaviours of the system that do not appear when either a semi-infinite domain or negligible solute diffusion is assumed. The problem is simplified through an assumption of negligible latent heat, and we develop a numerical scheme that will permit insights that are critical for developing a more general procedure. We demonstrate that a mushy zone initially grows rapidly, then slows down and eventually retreats slowly. The mushy zone vanishes after a long time, as it is overtaken by a slowly growing solid region at the base of the tank.

JFM classification

Phase change: Solidification/melting
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 227 - 243
Copyright
Copyright © Cambridge University Press 2011

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References

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