On laminar flows of planar free convection

    2013, Vol. 9, No. 4, pp.  651-657

    Author(s): Aristov S. N., Prosviryakov E. Y.

    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, polynomial solution, decrease in dimension, Benard–Marangoni convection
    Citation: Aristov S. N., Prosviryakov E. Y., On laminar flows of planar free convection, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 4, pp.  651-657

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