Combined Influence of Soret and Dufour Effects on Double-Diffusive Convection and Thermal Stability in an Anisotropic Porous Medium Saturated With a Non-Newtonian Fluid

This study investigates the coupled effects of Soret and Dufour on double-diffusive convection within an anisotropic porous layer saturated by a non-Newtonian fluid governed by the power-law model (Oswald-de Waele). The horizontal walls are subjected to constant heat and mass fluxes, while the vertical boundaries are adiabatic and impermeable. The system is formulated by combining the generalized Darcy law with the Boussinesq approximation and subsequently reduced to a single nonlinear equation through the parallel flow assumption. Numerical resolution was carried out using a Newton iterative scheme implemented in MATLAB. The results reveal that increasing the Soret and Dufour effects lowers the critical Rayleigh number, thereby promoting the earlier onset of convection. The centerline velocity of the fluid decreases slightly with the intensification of these effects, as well as with variations in the Lewis and permeability numbers, with a maximum reduction of 1.86% observed for Du = 1 at Le = 2. In contrast, the Soret effect remains below 0.5% for Ra = 100. Permeability proved to be a key factor, since low values constrain convective motion, whereas higher values facilitate internal circulation and enhance both heat and mass transfer. An increase in the Lewis number shifts the dynamics in favor of solutal diffusion. Heat and mass transfer rates attain a quasi-steady behavior for Ra ≥ 200 or Le ≥ 0.5, indicating saturation regimes dominated by diffusion. These findings highlight the stabilizing influence of thermodiffusive effects on convection and demonstrate how hydrodynamic and diffusive parameters interact to modulate coupled heat and mass transport. The conclusions of this study may serve to guide the optimization of coupled transfer processes in practical applications such as thermal energy storage, industrial processes, and geophysical or biological flows involving non-Newtonian fluids.