The authors study the case of the evaporation of water from a wet plane surface moving with a constant velocity in the same direction as a laminar hot draft. They numerically solve the unsteady transfer equations formulated with vorticity, stream function and constant physical properties, using a finite-difference scheme with an implicit alternating directions method. They determine the space-time distributions of temperatures, humidities and velocity components as well as the local values of their gradients according to the system parameters. In this study, the main results can be summarized as follows: The emission of vapor does not significantly disturb air flow. The velocity of the wall does not affect the hydrodynamic entrance length, that is correctly given by the Schlichting formula, but it increases the mean temperature in a section of the tunnel and the temperature and humidity wall gradients in proportion to the Lewis number. A privileged point exists in a section of the tunnel, at which the longitudinal velocity component is independent of the mobile plane velocity. Finally, the authors study the influence of inner drying with the help of the Luikov model.