The effect of interfacial heat transfer energy on a two-layer creeping flow in a flat channel

The study of convective currents in the channel received substantial attention for potential use in numerous engineering and manufacturing processes. The paper considers the two-dimensional motion of an immiscible incompressible binary mixture and a viscous heat-conducting fluid in a flat layer. The fluid system is bounded by solid walls. The solution of the equations of thermal diffusion convection is described in a special form: one of the velocity components linearly depends on the longitudinal coordinate, the temperature and concentration fields have a quadratic dependence on the horizontal coordinate. This velocity field corresponds to the well-known solution of Himenz for a purely viscous fluid. At the interface of liquids, the condition of energy exchange is taken into account. An exact stationary solution of the convective problem is constructed. It allows studying the influence of interfacial heat exchange energy on the dynamics of fluid and mixture flow.