Insight into the dynamics of ferrohydrodynamic (FHD) and magnetohydrodynamic (MHD) nanofluids inside a hexagonal cavity in the presence of a non-uniform magnetic field

•Buongiorno’s mathematical model is utilized for nanoparticle distribution.•The ferrohydrodynamic and magnetohydrodynamic effects are taken into account.•There are two thick conjugate blocks at the corners of the cavity.•Increase of the magnetic number (Mnf) increases heat and mass transfer rate.•Increasing of the Hartmann number (Ha) decrease the heat and mass transfer rate. The ferrohydrodynamic (FHD) and magnetohydrodynamic (MHD) are two important effects of a magnetic field in a liquid. FHD is the results of Kelvin force while MHD is the effect of a magnetic field due to Lorentz force. The present study aimed to evaluate the heat and mass transfer behavior of nanofluids inside a hexagonal enclosure in the presence of a non-uniform magnetic field considering the effects of Ferro-hydrodynamic (FHD) and Magneto-hydrodynamic (MHD). First, the concentration gradient of nanoparticles was captured due to the nanoscale forces. Then, the governing equations, including the continuity of nanofluid and nanoparticles, and momentum for vertical and horizontal direction were introduced, along with energy equation. Besides, the practical boundary condition of zero mass flux in nanoparticles at the walls was employed. Further, the governing equations were transformed into their non-dimensional form and solved numerically by the Finite Element Method (FEM). Furthermore, a systematic grid check was performed, and the results were compared with those of previous studies. Increasing magnetic number (Mnf) results in an increase in the heat and mass transfer rate. Increasing Lorentz force, in the form of Hartmann number (Ha) leads to a decrease in the rate of heat and mass transfer.