Analytical and Numerical Study of Hydrodynamical Boundary Conditions effect on Natural Double-Diffusive Convection in a Shallow Horizontal Rectangular cavity uniformly heated and salted from the side

This paper reports an analytical and numerical study of double-diffusive natural convection in a Newtonian fluid contained in a horizontal rectangular enclosure submitted to uniform heat and mass fluxes along its short vertical sides, while the horizontal ones are insulated and impermeable. Rigid–rigid, free–free, rigid–free and free-rigid hydrodynamic boundary conditions are considered. The first part from this study is devoted to the numerical solution of the governing equations, and the effect of the governing parameters, namely, the cavity aspect ratio, A, the Lewis number, Le , the buoyancy ratio, N , and the thermal Rayleigh, RₐT, number, is examined for each of these boundary conditions. In the second part, an analytical solution, based on the parallel flow approximation in the case of a shallow cavity ( A 1 ) is proposed and a good agreement is found between the two types of solutions.