Geodesic
Steady convective Coutte flow for quadratic heating of the lower boundary fluid layer
Russian journal of nonlinear dynamics, Tome 14 (2018) no. 1, pp. 69-79.

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This paper presents an exact solution to the Oberbeck – Boussinesq system which describes the flow of a viscous incompressible fluid in a plane channel heated by a linear point source. The exact solutions obtained generalize the isothermal Couette flow and the convective motions of Birikh – Ostroumov. A characteristic feature of the proposed class of exact solutions is that they integrate the horizontal gradient of the hydrodynamic fields. An analysis of the solutions obtained is presented and thus a criterion is obtained which explains the existence of countercurrents moving in a nonisothermal viscous incompressible fluid.
Mots-clés : Couette flow, exact solution
Keywords: Birikh – Ostroumova flow, planar Rayleigh – Benard convection, quadratic heating, counterflow. 
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V. V. Privalova; E. Yu. Prosviryakov. Steady convective Coutte flow for quadratic heating of the lower boundary fluid layer. Russian journal of nonlinear dynamics, Tome 14 (2018) no. 1, pp. 69-79. http://geodesic.mathdoc.fr/item/ND_2018_14_1_a6/

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