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This article presents conservation equations for heat, species, mass, and momentum to predict transport phenomena during solidification processing. It presents transport equations and several examples of their applications to illustrate the physics present in alloy solidification. The examples demonstrate the utility of scaling analysis to explain the fundamental physics in a process and to demonstrate the limitations of simplifying assumptions. The article concludes with information on the solidification behavior of alloys as predicted by full numerical solutions of the transport equations.

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Matthew John M. Krane, Modeling of Transport Phenomena during Solidification Processes, Metals Process Simulation, Vol 22B, ASM Handbook, Edited By D.U. Furrer, S.L. Semiatin, ASM International, 2010, p 157–167,

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