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|Title:||Convective and Conductive Selection Criteria of a Stable Dendritic Growth and Their Stitching|
|Authors:||Toropova, L. V.|
Alexandrov, D. V.
Galenko, P. K.
|Publisher:||John Wiley and Sons Ltd|
|Citation:||Toropova L. V. Convective and Conductive Selection Criteria of a Stable Dendritic Growth and Their Stitching / L. V. Toropova, D. V. Alexandrov, P. K. Galenko // Mathematical Methods in the Applied Sciences. — 2021. — Vol. 44. — Iss. 16. — P. 12139-12151.|
|Abstract:||The paper deals with the analysis of stable thermo-solutal dendritic growth in the presence of intense convection. The n-fold symmetry of crystalline anisotropy as well as the two- and three-dimensional growth geometries are considered. The steady-state analytical solutions are found with allowance for the convective-type heat and mass exchange boundary conditions at the dendritic surface. A linear morphological stability analysis determining the marginal wavenumber is carried out. The new stability criterion is derived from the solvability theory and stability analysis. This selection criterion takes place in the regions of small undercooling. To describe a broader undercooling diapason, the obtained selection criterion, which describes the case of intense convection, is stitched together with the previously known selection criterion for the conductive-type boundary conditions. It is demonstrated that the stitched selection criterion well describes a broad diapason of experimental undercoolings. © 2020 John Wiley & Sons, Ltd.|
|metadata.dc.description.sponsorship:||The present work comprises different parts of research studies including (i) the model formulation, stability and solvability analyses, derivation of the selection criterion in the case of intense convection, its sewing with the criterion for the conductive boundary conditions, (ii) numerical simulations, (iii) experiments, and their comparison. Different parts of the present work were supported by different grants and programs. With this in mind, the authors are grateful to the following foundations, programs, and grants. Theoretical part (i) was supported by the Russian Foundation for Basic Research (grant no. 19-32-51009). Numerical part (ii) was made possible due to the financial support of the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center, project no. 075-02-2020-1537/1). The experimental part (iii) was supported by the German Space Center Space Management under contract number 50WM1941.|
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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