We consider an ascending laminar air flow in a vertical channel formed by two parallel flat plates wetted by a thin water film and under different temperature and concentration conditions. The study includes a numerical finite volume method for the treatment of the double diffusion problem, where the analytical solution is given to the thermal diffusion. The analytical study showed that the reversed flow is observed only under some wall temperature conditions and also for certain values of Re/Gr. The reversed flow is also strongly dependent on the aspect ratio A, which is based on the cross section of the channel. Indeed, the results show than this dependence is very strong for values less than a certain critical one equal to 2.22. In the absence of the mass transfer the results showed that the evaporation rate remains null along the channel, decreases when the mass gradient is favorable and it finally vanishes at x=15. However, the evaporation rate increases in the case of an unfavorable mass gradient, to cancel at position x=20, then merges with the curve representing the forced convection. In the absence of heat transfer the evaporation rate is less important and amounts to fifty percent of the double diffusion. The results obtained by the analytical and numerical methods are compared each other and with those of a similar works and a good agreement was found.