The aim of this paper is to present modelling and numerical simulations of heat and mass transfer by double-diffusive convection and surface condensation or evaporation in a two-dimensional square cavity subjected to a uniform, but time-dependent wall temperature. At initial state, the cavity is filled with quiescent humid air at uniform temperature and density. By decreasing the wall temperature, condensation occurs at the four wall surfaces. The walls are then heated and evaporation of the liquid water is considered. Since the mass of humid air and average pressure experience noticeable changes during the periodic process, a weakly compressible formulation has been used for the modelling of the thermosolutal flow. Local thermodynamic assumption at the liquid-vapor interface and thin liquid film approximation are introduced.

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