Impact of the Non-Newtonian Oswald–de Waele Fluid on Heat and Mass Transfer With Soret and Dufour in Anisotropic Porous Media

An analytical and numerical study on the influence of flow indices of a non-Newtonian fluid in the presence of Soret and Dufour effects during heat and mass transfer, in the absence of the thermal Rayleigh number, is conducted in a saturated anisotropic porous layer. The Darcy model, the Boussinesq approximation, and the Oswald-de Waele model were used. Heat and mass fluxes are constant on the horizontal walls, while the vertical walls are assumed to be adiabatic and impermeable. The analytical investigation is based on the parallel flow approximation in the horizontal cavity, while the numerical method involves solving the nonlinear equation using the Newton-Raphson method in MATLAB. We observed that the numerical solution admits real solutions for n < 1 and n > 1 when the thermal Rayleigh number is zero. A parametric study is conducted to show the effect of a non-Newtonian fluid with Soret and Dufour parameters, in the absence of thermal Rayleigh number, on the stream function at the center of gravity, speed, temperature, concentration, as well as the Nusselt and Sherwood numbers. The results highlight the predominant role of Soret and Dufour effects in heat and mass transfer, even in the absence of the thermal Rayleigh number, and emphasize the importance of these mechanisms for the optimal design of systems involving non-Newtonian fluids in anisotropic porous media.