Magnetohydrodynamic double diffusive mixed convection of power-law non-Newtonian hybrid nanofluid in rotating eccentric annuli with different positions of inner cylinder

The study numerically analyzes magnetohydrodynamic (MHD) double-diffusive mixed convection in a rotating eccentric annulus filled with a non-Newtonian power-law hybrid nanofluid consisting of $A{l}_2{O}_3$ and $F{e}_3{O}_4$ nanoparticles suspended in water, considering various placements of the inner cylinder. The study utilizes the Galerkin weighted residual finite element method (GFEM) for the analysis. In this structure, the nanofluid fills the gap between the cylinders, keeping the outside circle of the geometry cold and the inner circle hot. In this structure, the nanofluid fills the gap between the cylinders, keeping the outside circle of the geometry cold and the inner circle hot. This study explores the effects of multiple governing parameters, including a power-law index varying between 0.7 and 1.3, nanoparticle concentrations from 0% to 2%, Hartmann numbers between 0 and 30, and buoyancy ratios ranging from −1 to 1. The analysis also considers Reynolds numbers in the range of 200 to 600, Richardson numbers from 0 to 5, Lewis numbers between 1 and 10, and angular velocity between −20 and 20 while maintaining a constant Prandtl number of 6.8377. In addition, heat and mass transfer rates are evaluated in terms of Nusselt and Sherwood numbers, and visualizations such as streamlines, isotherms, and concentration contours are presented. The heat and mass transfer rates remain nearly unchanged regardless of whether the inner cylinder rotates clockwise or counterclockwise. The results show that the heat and mass transfer rates remain nearly unchanged regardless of whether the inner cylinder rotates clockwise or counterclockwise. An increase in the Hartmann number leads to an enhancement in heat transfer, while it simultaneously reduces the mass transfer rate. On the other hand, a higher power-law index results in a decline in both heat and mass transfer rates. Conversely, a rise in the buoyancy ratio contributes to the enhancement of both thermal and mass transport. The novelty of this study is how varying angular velocities (positive and negative) influence heat and mass transport in a power-law non-Newtonian fluid under MHD effects. It offers a new parametric analysis of forced and free convection interactions using Reynolds number, Hartmann number, Richardson number, and angular velocity. For a non-rotating inner cylinder at power-law index = 0.7, the average Nusselt number decreases by 36.89%, while the average Sherwood number decreases by 17.14% as the Hartmann number increases from 0 to 30.