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N. V. Burmasheva, E. Yu. Prosviryakov

TEMPERATURE FIELD INVESTIGATION IN LAYERED FLOWS OF A VERTICALLY  SWIRLING VISCOUS INCOMPRESSIBLE FLUID UNDER TWO THERMOCAPILLAR FORCES AT A FREE BOUNDARY

The exact solution of the Oberbeck-Boussinesq equations, which describes the influence of the thermocapillary effect on the convective flows of a viscous incompressible fluid, is discussed. The class of exact solutions is chosen in such a way that it allows one to solve an overdetermined system of equations for the motion of a fluid by identically satisfying the incompressibility condition. Heat sources at both boundaries, which heat (cool) the fluid, are selected as the boundary conditions. The exact solution has been obtained and the temperature field has been studied. It is shown that the structure of the exact solution does not allow one to reduce the dimension of the boundary value problem under study. It is also shown that the obtained exact solution admits the presence of countercurrents in the fluid.

Keywords: layered flow, exact solution, counterflows, Marangoni convection, vertical swirl, vortex flow, system of Oberbeck–Boussinesq equations

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