Geodesic
Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 3, pp. 567-577

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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: Newton–Rikhmann law, thermal convection, Oberbeck–Boussinesq equations, counter-current flow.
Mots-clés : exact solution 
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     title = {Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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S. S. Vlasova; E. Yu. Prosviryakov. Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 3, pp. 567-577. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_3_a10/