Geodesic
On laminar flows of planar free convection
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 651-657.

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New exact steady-state solutions of the Oberbeck–Boussinesq system which describe laminar flows of the Benard–Marangoni convection are constructed. We consider two types of boundary conditions: those specifying a temperature gradient on one of the boundaries and those specifying it on both boundaries simultaneously. It is shown that when the temperature gradient is specified the problem is essentially two-dimensional: there is no linear transformation allowing the flows to be transformed into one-dimensional ones. The resulting solutions are physically interpreted and dimensions of the layers are found for which there is no friction on the solid surface and a change occurs in the direction of velocity on the free surface.
Keywords: laminar flow, analytical solution, decrease in dimension
Mots-clés : polynomial solution, Benard–Marangoni convection. 
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S. N. Aristov; E. Yu. Prosviryakov. On laminar flows of planar free convection. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 651-657. http://geodesic.mathdoc.fr/item/ND_2013_9_4_a3/

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