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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: EUROPEAN JOURNAL OF APPLIED MATHEMATICS; v. 32, n. 2, p. 199-225, APR 2021.
• Citações Web of Science: 2

Resumo

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)

• Processo FAPESP: 18/07643-8 - Matemática industrial e técnicas assintóticas
• Beneficiário: José Alberto Cuminato
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 16/12678-0 - Modelagem matemática de macrosegregação em ligas metálicas binárias induzida por convecção
• Beneficiário: Milton de Oliveira Assunção Junior
• Modalidade de apoio: Bolsas no Brasil - Doutorado