The evaporation by mixed convection of a water film falling down the inner wall of a vertical annulus was studied numerically. The outer wall was assumed to be insulated and dry. A counter-current flow of preheated, dry air was blown between two concentric cylinders. This air flow was preheated at the inlet of the annulus, which allowed for the evaporation phenomenon. The governing equations for the gas flow were solved using the finite volume method. The energy and mass balances for an element of liquid film allowed us to calculate the average temperature of the liquid film and the evaporated average mass flux density. The influence of the air flow and water film parameters on the evaporated average mass flux density was studied. The increase in this density was obtained by either increasing the temperature and the velocity of air flow or by decreasing the vapour mass fraction at the inlet. The decrease of the mass flow rate and the temperature of feedwater caused an increase in the evaporation phenomenon. The curvature and the length also increased the heat and mass transfer for this annular geometry. These parameters are important factors for film evaporation enhancement in a vertical annulus.