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This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum, energy, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example problems that illustrate how the hierarchy of time and length scales associated with transport leads to the important features of cast microstructures. It includes equations for estimating microsegregation in cast alloys.

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Jonathan A. Dantzig, Transport Phenomena during Solidification, Fundamentals of Modeling for Metals Processing, Vol 22A, ASM Handbook, Edited By D.U. Furrer, S.L. Semiatin, ASM International, 2009, p 70–74,

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