A mathematical model of convective flow in a horizontal channel with evaporation at the interface between a binary liquid and a gas-vapor mixture, derived on the basis of the Navier – Stokes equations in the Oberbeck – Boussinesq approximation taking into account thermal diffusion effect is under consideration. Using the constructed exact solution of the governing equations, various types of boundary conditions for the temperature on the walls of the channel, inside which the two-layer system of media with a phase transition is located, are tested. The boundary conditions can be the following: heating of the both walls, thermal insulation of the both walls, or a combination of these conditions. The different nature of the dependence (linear and quadratic) of surface tension on the concentration of one  components is taken into account. It has been studied which of the problem statements under consideration make sense to discuss from the point of view of analyzing the evaporation process. The application of the constructed solution for description of the flow in the system «70% aqueous solution of ethanol — a mixture of ethanol vapor and nitrogen» shows that the solution adequately reflects the main characteristics of the process: the relationship of the evaporation mass flow rate with the thermal load of the channel wall and flow rate of co-current gas. A qualitative comparison with available experimental data is provided.