Magnetohydrodynamics mixed convection and sensitivity analysis of non-Newtonian power-law fluid in a ventilated cavity with a rotating heated cylinder

Magnetohydrodynamics (MHD) mixed convection of non-Newtonian power-law fluid for laminar flow inside a ventilated square cavity with an inner rotating heated cylinder is studied numerically using the Galerkin weighted residual finite element method (GFEM). The left vertical wall has an inlet port at its top, while the right vertical wall has an outlet port at its bottom. Several significant parameters, including Hartman number ([Formula: see text]), Prandtl number ([Formula: see text]), Reynolds number ([Formula: see text]), power-law index ([Formula: see text]), angular rotational velocity ([Formula: see text]), and magnetic field inclination angle ([Formula: see text]) on the flow is numerically investigated. Streamlines, isotherms, local Nusselt numbers (Nu), average Nusselt numbers [Formula: see text], sensitivity analysis, and other numerical representations of the results are provided. The research showed that when the magnetic field is aligned parallel to the gravitational field ([Formula: see text]), the heat transfer rate increases, and the buoyancy force leads the heat transfer process. In the clockwise rotational condition of the cylinder [Formula: see text], the local Nusselt number increases by 69.84% while Re rises from 100 to 400. The relation between [Formula: see text] and the power-law index is inversely proportional in all three rotational conditions of the cylinder. In the cylinder's clockwise and anticlockwise rotational directions, [Formula: see text] rises as the Hartmann number rises from 0 to 80. When the Reynolds number increases, [Formula: see text] also increases in all three rotational conditions of the cylinder. A sensitivity analysis using variance analysis (ANOVA) has been performed in this study.