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Germany; Russia Jena; Yekaterinburg
Year
2016
Volume
26
Issue
3
Pages
379-387
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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 Universitya, University of Jenab
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 three-dimensional 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. 379-387.
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