Double-diffusive convection of non-newtonian power-law fluids in an inclined porous layer

Abstract

This paper presents a numerical study of Double-Diffusive convection within an inclined porous medium saturated by a non-Newtonian fluid. The power-law model is utilized for modelling the behavior of the flow in the porous layer. The given statement implies that the long side of the cavity experience thermal and solutal flux rates, whereas the other walls are impermeable and thermally isolated. The issue is characterized by a set of tightly linked non-linear differential equations, termed governing equations, encompassing the mass conservation equation (known as the continuity equation), the momentum equation, the energy equation, and the species equation. The relevant factors that govern the problem being investigated are the Rayleigh number, R_T, the power-law index, n, the angle of inclination, Φ, the cavity aspect ratio, A, the Lewis number, Le, the normalized porosity, ξ, and the buoyancy ratio, N, two types of cavity configuration have been studied: inclined cavity (i.e. Φ≠0°), then we have studied the case of a vertical cavity (i.e. Φ=90°) where the buoyancy forces induced by the thermal and solutal effects are opposing each other and of equal intensity (N=-1). A semi-analytical solution, valid for an infinite layer (A>>1), is derived on the basis of the parallel flow approximation, A numerical approach utilizing the finite differences method was utilized to resolve the governing equations within the porous medium. It is demonstrated that both the inclination of the layer, Φ, and the power-law index, n, have a strong influence on the strength of the intensity of flow, Ψ_0, the heat transfer rate, Nu, and the mass transfer rate, Sh, within the enclosure. A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations.