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Extended Stefan problem for the solidification of binary alloys in a sphere
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Brosa Planella, Ferran, Please, Colin P. and Van Gorder, Robert A. (2021) Extended Stefan problem for the solidification of binary alloys in a sphere. European Journal of Applied Mathematics, 32 (2). pp. 242-279. doi:10.1017/S095679252000011X ISSN 0956-7925.
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WRAP-Extended-Stefan-problem-for-the-solidification-of-binary-alloys-in-a-sphere-Brosa-Planella-2021.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (1399Kb) | Preview |
Official URL: http://dx.doi.org/10.1017/S095679252000011X
Abstract
We study the extended Stefan problem which includes constitutional supercooling for the solidification of a binary alloy in a finite spherical domain. We perform an asymptotic analysis in the limits of large Lewis number and small Stefan number which allows us to identify a number of spatio-temporal regimes signifying distinct behaviours in the solidification process, resulting in an intricate boundary layer structure. Our results generalise those present in the literature by considering all time regimes for the Stefan problem while also accounting for impurities and constitutional supercooling. These results also generalise recent work on the extended Stefan problem for finite planar domains to spherical domains, and we shall highlight key differences in the asymptotic solutions and the underlying boundary layer structure which result from this change in geometry. We compare our asymptotic solutions with both numerical simulations and real experimental data arising from the casting of molten metallurgical grade silicon through the water granulation process, with our analysis highlighting the role played by supercooling in the solidification of binary alloys appearing in such applications.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics T Technology > TN Mining engineering. Metallurgy |
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Divisions: | Faculty of Science, Engineering and Medicine > Engineering > WMG (Formerly the Warwick Manufacturing Group) | |||||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial , Perturbation (Mathematics) , Phase transformations (Statistical physics) -- Mathematical models, Solidification , Binary systems (Metallurgy) | |||||||||
Journal or Publication Title: | European Journal of Applied Mathematics | |||||||||
Publisher: | Cambridge University Press | |||||||||
ISSN: | 0956-7925 | |||||||||
Official Date: | April 2021 | |||||||||
Dates: |
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Volume: | 32 | |||||||||
Number: | 2 | |||||||||
Page Range: | pp. 242-279 | |||||||||
DOI: | 10.1017/S095679252000011X | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 20 March 2023 | |||||||||
Date of first compliant Open Access: | 20 March 2023 | |||||||||
RIOXX Funder/Project Grant: |
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