Mathematical modeling of stationary convective flows with evaporation at an interface is carried out with the help of the exact solutions of the Boussinesq approximation of the Navier- Stokes equations for the two-dimensional case. The effects of thermodiffusion and diffusive heat conductivity in the gas-vapor layer are taken into consideration. The gas flow rate in the upper layer of the system is considered as a given. At the fixed impermeable walls of the channel the no-slip conditions for the velocity vector are fulfilled. The lower rigid boundary is assumed to be a heat insulated boundary. The constant heat flux is defined at the upper boundary of the channel. On the straight interface, being a thermocapillary boundary, the kinematic and dynamic conditions, the condition of heat transfer and the mass balance equations are satisfied. The vapor concentration saturation is defined as a sequence of the Clapeyron- Clausius equation, and a condition of zero vapor flux is assumed to be fulfilled at the upper rigid boundary. The constructed exact solutions can be applied for modeling of flows in two-layer gasliquid system for the case when a liquid has a property of the anomalous thermocapillary effect.