Mathematical modeling of dendrite growth in an Al–Ge alloy with convective flow
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Mathematical modeling of dendrite growth in an Al–Ge alloy with convective flow
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| Автор |
Toropova, L. V.
Rettenmayr, M. Galenko, P. K. Alexandrov, D. V. |
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| Тематика |
CRYSTAL ANISOTROPY
DENDRITES FORCED CONVECTION MATHEMATICAL MODELING PHASE TRANSITION SELECTION THEORY BOUNDARY CONDITIONS FORCED CONVECTION LINEAR STABILITY ANALYSIS MASS TRANSFER CONDITION CONVECTIVE FLOW CRYSTAL ANISOTROPY DENDRITE DENDRITE GROWTH MATHEMATICAL METHOD MATHEMATICAL MODELING SELECTION THEORY TIP VELOCITY UNDERCOOLINGS UNDERCOOLING |
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| Описание |
A theory of stable dendrite growth in an undercooled binary melt is developed for the case of intense convection. Conductive heat and mass transfer boundary conditions are replaced by convective conditions, where the flux of heat (or solute) is proportional to the temperature or concentration difference between the surface of the dendrite and far from it. The marginal mode of perturbation wavelengths is calculated using the linear morphological stability analysis. Combining this analysis with the solvability theory, we have derived a selection criterion that represents the first condition to define a combination of dendrite tip velocity and tip diameter. The second condition—the undercooling balance—is derived for intense convection. The theory under consideration determines the dendrite tip velocity and tip diameter for low undercooling. This convective theory is combined with the classical theory of dendritic growth (conductive boundary conditions), which is valid for moderate and high undercooling. Thus, the entire range of melt undercooling is covered. Our results are in good agreement with experiments on Al–Ge crystallization. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.
Ministry of Education and Science of the Russian Federation, Minobrnauka, (075‐02‐2021‐1387) Russian Science Foundation, RSF, (21‐19‐00279) Foundation for the Advancement of Theoretical Physics and Mathematics, (21‐1‐3‐11‐1) L.V.T. acknowledges financial support from the Ministry of Science and Higher Education of the Russian Federation (project 075‐02‐2021‐1387 for the development of the regional scientific and educational mathematical center “Ural Mathematical Center”) for the linear stability analysis. Moreover, she is grateful to the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (project No. 21‐1‐3‐11‐1) for the development of solvability theory. P.K.G. and D.V.A. acknowledge the Russian Science Foundation (Project No. 21‐19‐00279) for the stitching of selection criteria, computer simulations, and comparison with experimental data. Open Access funding enabled and organized by Projekt DEAL. |
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| Дата |
2024-04-08T11:06:10Z
2024-04-08T11:06:10Z 2022 |
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| Тип |
Conference paper
Conference object (info:eu-repo/semantics/conferenceObject) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Toropova, LV, Rettenmayr, M, Galenko, PK & Alexandrov, DV 2022, 'Mathematical modeling of dendrite growth in an Al–Ge alloy with convective flow', Mathematical Methods in the Applied Sciences, Том. 45, № 13, стр. 8069-8081. https://doi.org/10.1002/mma.7991
Toropova, L. V., Rettenmayr, M., Galenko, P. K., & Alexandrov, D. V. (2022). Mathematical modeling of dendrite growth in an Al–Ge alloy with convective flow. Mathematical Methods in the Applied Sciences, 45(13), 8069-8081. https://doi.org/10.1002/mma.7991 0170-4214 Final All Open Access; Green Open Access; Hybrid Gold Open Access https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/mma.7991 https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/mma.7991 http://elar.urfu.ru/handle/10995/131285 10.1002/mma.7991 85120781296 000728147900001 |
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| Язык |
en
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//21-19-00279
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by-nc https://creativecommons.org/licenses/by-nc/4.0/ |
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| Формат |
application/pdf
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| Издатель |
John Wiley and Sons Ltd
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| Источник |
Mathematical Methods in the Applied Sciences
Mathematical Methods in the Applied Sciences |
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