n small-time similarity-solution behaviour in the solidification shrinkage of binary alloy

Author(s)

Assuncao, M. ^[1] ; Vynnycky, M. ^[2] ; Mitchell, S. L. ^[2]

Affiliation

^[1] Univ Sao Paulo Sao Carlos, Inst Math & Comp Sci, Dept Appl Math & Stat, POB 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Limerick, Dept Math & Stat, Limerick V94 T9PX - Ireland

• Document type: Journal article
• Source: EUROPEAN JOURNAL OF APPLIED MATHEMATICS; v. 32, n. 2, p. 199-225, APR 2021.
• Web of Science Citations: 2

Abstract

In the one-dimensional solidification of a binary alloy undergoing shrinkage, there is a relative motion between solid and liquid phases in the mushy zone, leading to the possibility of macrosegregation; thus, the problem constitutes an invaluable benchmark for the testing of numerical codes that model these phenomena. Here, we revisit an earlier obtained solution for this problem, that was posed on a semi-infinite spatial domain and valid for the case of flow superheat. with a view to extending it to the more general situation of a finite spatial domain, arbitrarily large superheat and both eutectic and non-eutectic solidification. We find that a similarity solution is available for short tunes which contains a boundary layer on the liquid side of the mush liquid interface; this solution is believed to constitute the correct initial condition for the subsequent numerical solution of the full non-similar problem, which is deferred to future work. (AU)

• FAPESP's process: 18/07643-8 - Industrial mathematics and practical asymptotics
• Grantee: José Alberto Cuminato
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 16/12678-0 - Mathematical modelling of macrosegregation on binary alloys induced by convection
• Grantee: Milton de Oliveira Assunção Junior
• Support Opportunities: Scholarships in Brazil - Doctorate