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Estimation of transient heat transfer and fluid flow for alloy solidification in a rectangular cavity with an isothermal sidewall

Published online by Cambridge University Press:  14 August 2015

A. Plotkowski ,
K. Fezi  and
M. J. M. Krane
A. Plotkowski*
Affiliation:
Purdue Center for Metal Casting Research, School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
K. Fezi
Affiliation:
Purdue Center for Metal Casting Research, School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
M. J. M. Krane
Affiliation:
Purdue Center for Metal Casting Research, School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA
*
†Email address for correspondence: plotkoal@gmail.com
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Abstract

Transient scaling and integral analyses were performed to predict trends in alloy solidification in a rectangular cavity cooled by an isothermal sidewall. The natural convection fluid flow was approximated by a scaling analysis for a laminar boundary layer at the solidification front, and was coupled to scaling and integral analyses of the energy equation to predict the solidification behaviour of the system. These analyses predicted several relevant aspects of the solidification process, including the time required to extinguish the initial superheat and the maximum local solidification time as a function of the system parameters and material properties. These results were verified by comparison to numerical simulations for an Al–4.5 wt% Cu alloy for various initial and boundary conditions and cavity aspect ratios. The analysis was compared to previous attempts to analyse similar fluid flow and solidification processes, and the limitations of the assumptions used for this analysis were discussed.

JFM classification

Convection: Buoyant boundary layers Convection: Convection Phase change: Solidification/melting
Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 53 - 86
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Copyright
© 2015 Cambridge University Press 

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