Darcy–Forchheimer flow and heat-mass transfer of Carreau fluids with soret and dufour effects: A numerical approach

In this work, the unsteady natural convection flow of a non-Newtonian Carreau fluid across an oscillating inclined vertical plate embedded in a Darcy–Forchheimer porous medium is thoroughly investigated numerically. The issue is modeled by utilizing the Boussinesq approximation, and the Rosseland diffusion approximation is used to simulate radiative heat transmission. This study presents a mathematical analysis of non-Newtonian fluids by incorporating viscous dissipation, chemical reaction, heat source or sink, Soret and Dufour effects. Carreau fluid models, in particular, can describe the shear-thinning behavior that is usual in industrial fluids, although nothing has been discovered about how they interact with several simultaneous transport circumstances. The governing partial differential equations transformed into a computationally convenient form and solved using the Crank–Nicolson method. The effects of emerging quantities on velocity, temperature, and concentration profiles are examined. According to parametric analysis, the velocity field is reduced by increasing the Forchheimer number and Darcy resistance, but temperature distributions are enhanced by radiation, heat sources, and viscous dissipation. Soret and Dufour effects significantly influence coupled heat and mass transfer mechanisms by enhancing both fields. Extensive numerical analysis provides valuable insights into thermo-solutal behavior. The findings have practical application in polymer processing, geothermal systems, and porous medium transport.