Convective Couette-type flows under condition of slip and heating at the lower boundary

Abstract

A Couette type boundary value problem is considered for a new exact solution of the layered convection problem. The obtained solution describes the flow of a viscous incompressible fluid layer with nonzero temperature and pressure gradients along the longitudinal (horizontal) coordinates. The horizontal velocity components depend only on the vertical (transverse) coordinate of the fluid layer. The Navier slip condition and nonzero temperature gradients are specified on the lower absolutely solid boundary of the layer. The tangential stresses and constant (atmospheric) pressure are specified at the upper boundary. The possibility the occurrence of countercurrent regions and the corresponding changes in the tangential stresses and the vorticity vector are shown for the obtained particular exact solution.