New numerical approach has been selected for simulating magnetic force and radiation influences on alumina transportation within a permeable medium. To enhance characteristics of working fluid, we choose Al2O3–water with various shapes of nanoparticles. Various amounts of radiation, magnetic force and buoyancy have been considered to show their impacts on nanoparticles transportation. Brownian motion influences on working fluid thermal conductivity and viscosity were involved. Outcomes prove that convection decreases with augment of magnetic forces. Considering radiation can increase Nusselt number.