Exact solution of the convective flow of a viscous fluid layer with a heated lower boundary

Abstract

A new exact solution of the layered convection problem is considered. The obtained solution describes the flow layer of a viscous incompressible fluid with nonzero gradients of temperature and pressure. The horizontal velocity components depend only on the vertical transverse coordinate of the fluid layer. At the lower layer boundary, nonzero temperature gradients and the Navier slip condition are specified, tangential stresses and longitudinal pressure gradients being specified at the upper boundary. The possibility of the occurrence of counterflow areas and the corresponding changes in the tangential stresses and the vorticity vector are shown for the obtained particular exact solution. © 2019 Author(s).