This paper examines the natural convection in an open cavity with non uniform thermal boundary condition. The cavity is filled with a water-Al2O3 nanofluid and subjected to a magnetic field in the presence of heat generation or absorption. Lattice Boltzmann method (LBM) is applied to solve the coupled equations of flow and temperature fields. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, Ra = 10(3)-10(6), Hartmann number varied from Ha = 0-60, heat generation/absorption coefficient (q = -10, -5, 0, 5 and 10) and the solid volume fraction of nanoparticles between phi = 0 and 6%. Results show that the heat transfer rate decreases with the rise of the Hartmann number and increases with the augmentation of the Rayleigh number. The nanoparticles effect is more important at a high Rayleigh number. Also, the nanoparticles effect is more important for heat generation condition (q > 0) than absorption generation condition (q < 0). (C) 2014 Elsevier B.V. All rights reserved.