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JOURNALS // Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences // Archive

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 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

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.

UDC: 532.51

MSC: 76F02, 76F45, 76M45, 76R05, 76U05

Original article submitted 13/III/2016
revision submitted – 25/V/2016

Language: English

DOI: 10.14498/vsgtu1483



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