Convective and conductive selection criteria of a stable dendritic growth and their stitching. (28th August 2020)

• Record Type: Journal Article
• Authors: Toropova, L.V.; Alexandrov, D.V.; Galenko, P.K.
• Other Names: Nizovtseva Irina guestEditor.; Alexandrov Dmitri guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 16(2021)
• Page Start: 12139
• Page End: 12151
• Publication Date: 2020-08-28
• Subjects: crystalline anisotropy -- dendrites -- dendritic growth -- forced convection -- selection theory; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6830
• Languages: English
• ISSNs: 0170-4214

Abstract

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.