An exact solution of the convective Couette flow under the parabolic heating condition at the lower boundary of a fluid layer

Abstract

A new exact solution of the Navier-Stokes equation for the convective flow of an infinite horizontal layer of a viscous incompressible fluid is obtained. Parabolic heating is specified at one of the layer boundaries. The other boundary of the fluid layer is permeable. The obtained exact solution generalizes the isothermal Couette flow and the Ostroumov- Binkh convective analogues. The proposed class of exact solutions takes mto account the horizontal change in hydrodynamic fields. The obtained solution analysis for the velocity and temperature fields is presented. The possibility of the existence of stagnation points and counterflow areas in a moving layer of a non-isothermal viscous incompressible fluid is demonstrated. © 2020 American Institute of Physics Inc.. All rights reserved.