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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2016, Volume 20, Number 3, Pages 567–577
DOI: https://doi.org/10.14498/vsgtu1483 (Mi vsgtu1483) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Mathematical Modeling, Numerical Methods and Software Complexes

Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border

S. S. Vlasovaa, E. Yu. Prosviryakovb

a Kazan National Research Technical University named after A. N. Tupolev, Kazan, 420111, Russian Federation
b Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation
Full-text PDF (860 kB) Citations (6)
(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu1483
Abstract: The exact stationary solution of the boundary-value problem that describes the convective motion of an incompressible viscous fluid in the two-dimensional layer with the square heating of a free surface in Stokes's approach is found. The linearization of the Oberbeck–Boussinesq equations allows one to describe the flow of fluid in extreme points of pressure and temperature. The condition under which the counter-current flows (two counter flows) in the fluid can be observed, is introduced. If the stagnant point in the fluid exists, six non-closed whirlwinds can be observed.
Keywords: exact solution, Newton–Rikhmann law, thermal convection, Oberbeck–Boussinesq equations, counter-current flow.
Funding agency Grant number
Foundation for Assistance to Small Innovative Enterprises in Science and Technology 8389 ГУ2/2015
This work was supported by the Foundation for Assistance to Small Innovative Enterprises in Science and Technology (the UMNIK program); the agreement no. 8389 GU2/2015.
Original article submitted 13/III/2016
revision submitted – 25/V/2016
Bibliographic databases:
Document Type: Article
UDC: 532.51
MSC: 76F02, 76F45, 76M45, 76R05, 76U05
Language: English
Citation: S. S. Vlasova, E. Yu. Prosviryakov, “Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:3 (2016), 567–577
Citation in format AMSBIB
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\yr 2016
\vol 20
\issue 3
\pages 567--577
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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