Modelling of stationary flows of a liquid-gas system in an inclined channel subject to evaporation

Two-layer flow of liquid and gas-vapor mixture in an inclined channel is considered. The flow is described by the system of the Oberbeck–Boussinesq convection equations with the effects of evaporation and thermodiffusion. A new exact solution of the problem of evaporative convection is constructed under conditions of non-deformable interface and zero vapour flux on the upper channel wall. The analytical form of the solution is presented for the case when the channel boundaries are heated linearly with respect to the longitudinal coordinate. Calculation of the integration constants are described in detail. Examples of flows are provided for the ethanol-nitrogen fluid system.