Mathematical Modeling of Transport Phenomena During Alloy Solidification

[+] Author and Article Information
C. Beckermann

Department of Mechanical Engineering, The University of Iowa, Iowa City IA 52242

R. Viskanta

School of Mechanical Engineering, Purdue University, West Lafayette IN 47907

Appl. Mech. Rev 46(1), 1-27 (Jan 01, 1993) (27 pages) doi:10.1115/1.3120318 History: Online April 29, 2009


Mathematical modeling of mass, momentum, heat, and species transport phenomena occurring during solidification of metal alloys is reviewed. Emphasis is placed on the incorporation of the effects of the solid structure and the interactions between the solid and liquid phases on a microscopic scale into a (macroscopic) model of the transport phenomena occurring at the system scale. Both columnar and equiaxed growth structures, as well as laminar convection of liquid and solid crystals are considered. The macroscopic conservation equations are introduced via a volume averaging approach and commonly made simplifications are examined. Basic constitutive relations for the phase interactions occurring in alloy solidification are presented. Recent progress in including nucleation, microsegregation, undercooling and other microscopic phenomena in the macroscopic equations is reviewed. The specific areas where future theoretical and experimental research is needed are identified.

Copyright © 1993 by American Society of Mechanical Engineers
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