This research is about modeling the influence of Lorentz forces on Fe3O4-water nanofluid heat transfer enhancement in a permeable cavity. Shape factor influence on thermal conductivity of nanofluid is taken into consideration. Voracity stream function formulation is utilized. The solutions of final equations are obtained by Control Volume based Finite Element Method. Graphs are shown for different values of radiation parameter (Rd), Darcy number (Da), nanofluid volume fraction (phi), Rayleigh number (Re) and Hartmann number (Ha). Results indicate that heat transfer rate enhances with augment of Hartmann number. Selecting Platelet shaped nanoparticles leads to greatest heat transfer rate. (C) 2017 Elsevier Ltd. All rights reserved.