Multiple steady state solutions for double-diffusive convection in a shallow horizontal rectangular cavity uniformly heated and salted from the side and filled with non-Newtonian power-law fluids

This paper reports on the multiplicity of steady state solutions and the effect of buoyancy ratio due to both heat and mass transfer on natural convection in a horizontal rectangular cavity filled with a power-law non-Newtonian fluid. The short vertical sides of the cavity are submitted to horizontal thermal and solutal flux densities, while its horizontal walls are impermeable and adiabatic. The problem under consideration is governed by the cavity aspect ratio, A, the Lewis number, Le, the buoyancy ratio, N, the power-law behavior index, n, and the generalized Prandtl, Pr, and thermal Rayleigh, Ra-T, numbers. The equations describing the double-diffusion convection phenomenon are solved numerically using a finite volume method. In the case of a shallow cavity A > > 1, the governing equations are significantly simplified by using the parallel flow approximation, which allows an analytical solution that agrees well with the numerical one. Results expressed in terms of streamlines, isotherms, iso-concentrations, central stream function and average Nusselt and Sherwood numbers are obtained for various values of the governing parameters. The onset and the development of double-diffusive convection, for cooperating and opposing flows, are investigated. The existence of multiple steady state solutions, for a given set of the governing parameters, is demonstrated in the case of opposing double diffusive flow.