Magnetohydrodynamic natural convection and sensitivity analysis of heat and mass transfer of non-Newtonian fluid in concentric cylinders with wall heat and mass flux

This study addresses the challenge of understanding natural convection (NC) within a circular concentric cylinder system, specifically focusing on thermal and mass flow interaction effects. The problem involves laminar, non-Newtonian, incompressible flow, where the inner cylinder experiences continuous mass and heating flux while the outer cylinder is maintained at a cold temperature ( \(T_c\) $T_c$ ). The governing equations are formulated using the Galerkin weighted residual finite-element technique (GFEM) to investigate this phenomenon. The research examines the influence of six key parameters: Prandtl number, Pr = 10 to 100, power-law index from n = 0.7 to 1.4, Rayleigh number, Ra = \(10^4\) ${10}^4$ to \(10^6\) ${10}^6$ , Buoyancy ratio, Br = \(-2\) $-2$ to 2, Hartmann number, Ha = 0 to 60, and Lewis number Le = 2. The findings reveal that increasing the power-law index (n) and Hartmann number (Ha) leads to a decrease in the average Nusselt number ( \({\overline{{\text {Nu}}}}\) $\overline{\text{Nu}}$ ) and Sherwood number ( \({\overline{{\text {Sh}}}}\) $\overline{\text{Sh}}$ ). Notably, \({\overline{{\text {Nu}}}}\) $\overline{\text{Nu}}$ decreases by \(36.36 \%\) $36.36\%$ when n increases from 0.7 to 1.4, and ( \({\overline{{\text {Sh}}}}\) $\overline{\text{Sh}}$ ) decreases by \(44.89\%\) $44.89\%$ as Ha rises from 0 to 60 at Ra = \(10^6\) ${10}^6$ . These results highlight the significant impact of fluid rheology and magnetic fields on convective heat and mass transfer, providing valuable insights for engineering applications involving non-Newtonian fluids and magnetohydrodynamic (MHD) flows.