In the present work the natural convective heat and mass transfer in an asymmetric, trapezoidal enclosure is studied numerically. Such a configuration is encountered in greenhouse-type solar stills, where natural convection in the enclosed humid air due to vertical temperature and concentration gradients between the saline water and the transparent cover, plays a decisive role. In this double-diffusion problem, the relative magnitude of the thermal and the concentration (or solutal) Rayleigh numbers, expressed by their ratio N is a key parameter. The two-dimensional flow equations, expressed here in a stream function-vorticity (Psi - Omega) formulation, along with the energy and concentration equations are solved. Due to the large values of the Rayleigh numbers encountered under realistic conditions (10(7) less than or equal to Ra less than or equal to 10(10)), mostly turbulent flow conditions prevail. A two-equation, low-Reynolds number turbulence model has thus been selected and a curvilinear coordinate system is employed, allowing for better matching of the computational grid to the enclosure geometry. The numerical solutions yield a multi-cellular flow field, with the number of cells depending on the Rayleigh number for a fixed Lewis number and geometry. For a positive value of N (N = 1) the solution is qualitatively similar to the case with only thermal buoyancy present (N = 0). However, for negative values (N = - 1), more complex unsteady phenomena arise, having a different nature in the laminar and the turbulent flow regime, which are both investigated. Correlations for the mean convective heat and mass transfer coefficients are obtained for a wide range of Rayleigh numbers, and comparisons are made for the different values of N, showing lower values and different rate of increase with Ra for N = -1. (C) 2004 Elsevier Ltd. All rights reserved.