Unsteady-state Bénard–Marangoni convection in layered viscous incompressible flows

Unsteady-state Bénard–Marangoni convection in large-scale liquid flows with a linear temperature distribution at the layer boundaries has been investigated by the boundary element method. Two variants of boundary conditions are considered. In the case of temperature gradient components distributed at both boundaries, the boundary problem cannot be reduced to a one-dimensional one. The structure of layered convective flows has been studied. It has been demonstrated that the initial and boundary value problems considered here describe convective liquid counterflows and the formation of extremum (local and global) values of temperature fields. The existence of stagnant points (in which the liquid velocity is zero) inside the layer of the moving nonisothermal liquid has been discovered.