Nonstationary laminar Bénard-Marangoni convection for Newton-Richmann heat exchange

The paper presents a mathematical modeling of nonstationary laminar Bénard-Marangoni convection of a viscous incompressible fluid moving in an infinite band. The main attention is paid to the study of the position and displacement of the stagnation point of the solution with time, the appearance and disappearance of counterflows. It is shown that the overdetermined initial boundary value problem within the here presented class of exact solutions of the Oberbeck-Boussinesq equations is reducible to the Sturm-Liouville problem. The hydrodynamic fields indicating the presence of counterflows in the fluid and their change during fluid acceleration are analyzed with the use of a computational experiment.