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Germany; Russia Jena; Yekaterinburg
Section  Mechanics 
Title  Analytical solution of the problem on inclined viscous flow around a parabolic dendrite within the framework of Oseen's approximation 
Author(s)  Alexandrov D.V.^{a}, Galenko P.K.^{b} 
Affiliations  Ural Federal University^{a}, University of Jena^{b} 
Abstract  A mathematical model of inclined viscous flow around a dendrite in Oseen's hydrodynamic approximation is formulated. The analytical solution of the problem on inclined viscous flow around a parabolic dendrite in two and threedimensional cases is constructed. The components of fluid velocity in the vicinity of the dendritic tip in 2D and 3D flow geometries are determined in the laboratory coordinate system by means of the curvilinear coordinates of parabolic cylinder and paraboloid of revolution. The analytical solutions of Oseen's hydrodynamic equations are rewritten in the coordinate system connected to the dendrite growing with a constant velocity. The obtained solution transforms to the previously known one in the limiting case of zero angle between the fluid velocity direction far from the dendrite and its axis. A scaled component of fluid velocity as a function of parabolic coordinates at different slope coefficients of flow is illustrated. 
Keywords  dendrites, convection, viscous flow, Oseen's approximation 
UDC  532.51 
MSC  76D07, 76M45 
DOI  10.20537/vm160307 
Received  23 May 2016 
Language  Russian 
Citation  Alexandrov D.V., Galenko P.K. Analytical solution of the problem on inclined viscous flow around a parabolic dendrite within the framework of Oseen's approximation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 3, pp. 379387. 
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