Influence of external magnetic source in two-dimensional Fe3O4-water nanomaterial is numerically addressed. Numerical solution is carried out using control based volume finite element method (CVFEM). Combined influences of Lorentz and Kelvin forces are taken into account. Vorticity-stream function forms of equations have been considered. Influences of nanofluid volume fraction, Hartmann, Rayleigh and Magnetic numbers on velocity and temperature distribution are examined. Results demonstrate that temperature gradient augments with rise of Kelvin forces while it reduces for Lorentz forces. Moreover, heat transfer augmentation enhances with augment of Lorentz forces. (C) 2016 Elsevier Ltd. All rights reserved.