Study of the Linear and non-Linear Stability of Thermosolutal Convection Within a Porous Medium Saturated by a non-Newtonian Binary Fluid

Abstract

This study, presents a numerical study of the linear and non-linear stability of thermosolutary convection within a porous medium saturated by a non-Newtonian binary fluid. The power-law model is utilized for modeling the behavior of the working medium. The given statement implies that the long side of the cavity experience thermal and solutal flow rates, whereas the others walls are impermeable and thermally isolated. The problem is characterized by a set of tightly linked non-linear differential equations, named governing equations, that include 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, 𝑅𝑇, 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, three types of cavity configuration have been studied: horizontal cavity (i.e. Φ=0°), 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). An analytical solution is obtained for shallow enclosures (𝐴 >> 1) using the parallel flow approximation, and a modified form of the Darcy equation. By solving the entire set of governing equations, a numerical investigation of the same phenomenon was conducted. One of the most intriguing discoveries from this research is that it identifies a bi-stability phenomenon, this particular phenomenon signifies the existence of two stable solutions. Plus, 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, Ψ0, the heat transfer rate, 𝑁𝑢, and the mass transfer rate, 𝑆ℎ, within the enclosure. The results obtained from both methods demonstrate a good level of agreement across a diverse range of these governing parameters