V. V. Privalova, E. Yu. Prosviryakov

THE EFFECT OF TANGENTIAL BOUNDARY STRESSES ON THE CONVECTIVE UNIDIRECTIONAL FLOW OF A VISCOUS FLUID LAYER UNDER THE LOWER BOUNDARY HEATING CONDITION

An exact solution describing a convective unidirectional flow of a viscous incompressible fluid is obtained. The motion takes place in an infinite layer of some finite thickness. The fields of velocity, temperature, and pressure are time-independent. The resulting exact solution is a polynomial of various orders along the vertical (transverse) coordinate. A boundary value problem is formulated for the exact solution constructed. On the absolutely solid lower boundary of the fluid layer, the Navier slip condition and heating are specified. On the upper (free) surface, nonzero tangential stresses and pressure along the longitudinal coordinate are set. The temperature at the upper boundary is assumed to be zero. The obtained particular exact solution of the boundary value problem for the velocity function is analyzed. It is shown that, in the fluid layer under consideration, the velocity can have up to two stagnation points, which indicates the occurrence of countercurrent zones. The nonzero component of the vorticity vector and the tangential stress are analyzed. It is shown that the vorticity vector can change its sign in the fluid layer up to two times and that the tangential stress can change from tensile to compressive as many times.

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