Double-diffusive and Soret-induced convection in a shallow horizontal cavity filled with non-Newtonian power-law fluids

The progress of two-dimensional natural convection of non-Newtonian binary fluid confined in a horizontal rectangular layer is studied both analytically and numerically. The horizontal flux density of temperature is applied on the vertical walls of the cavity, whereas the long horizontal ones are considered impermeable and insulated. Solutal gradients are assumed to be induced either by the imposition of constant gradients of concentration on the vertical walls (double-diffusive convection, M = 0) or by the Soret effect (M = 1). The study focuses on the impact of different governing parameters, namely, the cavity aspect ratio A, the Lewis number Le, the buoyancy ratio N, the power-law behavior index n, the parameter M, the generalized Prandtl, Pr, and thermal Rayleigh Ra_T, numbers. The mathematical model, describing the double-diffusive convection phenomenon, is presented by non-linear differential equations, which are solved numerically based on finite volume method and analytically using the parallel flow approximation in the case of a shallow layer (A ≫ 1). Representative results for the central stream function, Nusselt and Sherwood numbers as well as streamlines, isotherms, and isoconcentrations are depicted as functions of the main parameters mentioned above. The onset and the development of convective motion are investigated. The buoyancy ratio, N, is found to strongly alter the flow pattern, heat and mass transfer. It is demonstrated that the Soret effect imposes a reversal of concentration gradient.