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An Extended Similarity Solution for One-Dimensional Multicomponent Alloy Solidification in the Presence of Shrinkage-Induced Flow
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 Title & Authors
An Extended Similarity Solution for One-Dimensional Multicomponent Alloy Solidification in the Presence of Shrinkage-Induced Flow
Chung, Jae-Dong; Yoo, Ho-Seon; Choi, Man-Soo; Lee, Joon-Sik;
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This paper deals with a generalized similarity solution for the one-dimensional solidification of ternary or higher-order multicomponent alloys. The present approach not only retains the existing features of binary systems such as temperature- solute coupling, shrinkage-induced flow, solid-liquid property differences, and finite back diffusion, but also is capable of handling a multicomponent alloy without restrictions on the partition coefficient and microsegregation parameter. For an alloy of N-solute species, governing equations in the mushy region reduce to (N+2) nonlinear ordinary differential equations via similarity transformation, which are to be solved along with the closed-form solutions for the solid and liquid regions. A linearized correction scheme adopted in the solution procedure facilitates to determine the solidus and liquidus positions stably. The result for a sample ternary alloy agrees excellently with the numerical prediction as well as the reported similarity solution. Additional calculations are also presented to show the utility of this study. Finally, it is concluded that the present analysis includes the previous analytical approaches as subsets.
Multicomponent Alloy;Solidification;Similarity Solution;Microsegregation Parameter;Partition Coefficient;
 Cited by
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