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Natural convection in a mushy layer

Published online by Cambridge University Press:  26 April 2006

M. Grae Worster
M. Grae Worster
Affiliation:
Department of Engineering Sciences & Applied Mathematics and Department of Chemical Engineering, Northwestern University, Evanston, IL 60208, USA
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Abstract

Governing equations for a mushy layer are analysed in the asymptotic regime Rm [Gt ] 1, where Rm is an appropriately defined Rayleigh number. A model is proposed in which there is downward flow everywhere in the mushy layer except in and near localized chimneys, which are characterized by having zero solid fraction. Upward, convective flow within the chimneys is driven by compositional buoyancy. The radius of each chimney is determined locally by thermal balances within a boundary layer that surrounds it. Simple solutions are derived to determine the structure of the mushy layer away from the immediate vicinity of chimneys in order to demonstrate the gross effects of convection upon the solidification within the layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 335 - 359
Copyright
© 1991 Cambridge University Press

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