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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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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, Volume 20, Number 3, Pages 567–577 (Mi vsgtu1483)  
This article is cited in 4 scientific papers (total in 4 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

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.

† Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1483

Full text: PDF file (860 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 532.51
MSC: 76F02, 76F45, 76M45, 76R05, 76U05
Original article submitted 13/III/2016
revision submitted – 25/V/2016
Language:

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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\crossref{https://doi.org/10.14498/vsgtu1483}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Fomin, L. N. Fomina, “On the solution of fluid flow and heat transfer problem in a 2D channel with backward-facing step”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:2 (2017), 362–375  mathnet  crossref  zmath  elib
    2. V. V. Privalova, E. Yu. Prosviryakov, “Couette-Hiemenz exact solutions for the steady creeping convective flow of a viscous incompressible fluid with allowance made for heat recovery”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 22:3 (2018), 532–548  mathnet  crossref  zmath  isi  elib
    3. G. I. Kelbaliev, S. R. Rasulov, “Matematicheskoe modelirovanie protsessov koalestsentsii i drobleniya kapel i puzyrei v izotropnom turbulentnom potoke (obzor)”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:3 (2019), 541–581  mathnet  crossref
    4. A. A. Domnich, E. S. Baranovskii, M. A. Artemov, “On a mathematical model of non-isothermal creeping flows of a fluid through a given domain”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 23:3 (2019), 417–429  crossref  zmath  isi  scopus
    		• Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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