This paper reports the analytical and numerical results on double diffusive natural convection in a binary fluid contained in a two-dimensional enclosure where horizontal temperature and concentration differences are specified. A numerical code, based on a finite volume procedure, and a scaling law approach are used to analyse the influence of the different parameters which characterize those thermosolutal flows : in this first paper, the mass transfer problem is studied in the steady-stale. A general mass transfer correlation is proposed, which is valid over a nide range of parameters.