Non-Darcy MHD Mixed Convection of Fe₃O₄ nanofluid in a Vertical Cylindrical Annulus with Viscous Dissipation and Arrhenius Activation Energy

Abstract: This study investigates the combined effects of viscous dissipation, Darcy and Forchheimer flow and Arrhenius activation energy on magnetohydrodynamic (MHD) mixed convective heat and mass transfer of Fe₃O₄ nanofluid confined within a vertical cylindrical annulus. The study considers three base fluids ethylene glycol, engine oil, and kerosene in the presence of a non-uniform internal heat source and a porous medium under non-Darcy (Forchheimer) resistance. The governing nonlinear coupled equations for momentum, energy, and nanoparticle concentration are defined using Buongiorno’s nanofluid model and solved numerically via the finite element method with quadratic interpolation functions. The results demonstrate that magnetic field strength, viscous dissipation, Forchheimer inertia, and Prandtl number suppress axial velocity and species transport, while thermal radiation, nanoparticle volume fraction, thermo-diffusion, and activation energy significantly enhance thermal and solutal fields. Joule heating raises temperature but reduces velocity and concentration. Comparative analysis shows that ethylene glycol–based Fe₃O₄ nanofluid consistently exhibits superior velocity and heat transfer performance, whereas engine oil–based nanofluid produces higher nanoparticle concentration levels. Validation of the numerical scheme is gained through close agreement of skin friction, Nusselt number, and Sherwood number with existing literature for limiting Newtonian cases. A detailed comparison between inner and outer annular walls shows that inner-wall transport is shear-dominated, while outer-wall transport is mainly convection-driven. The results provide valuable insight into the design of annular MHD thermal systems involving reactive nanofluids and porous media.