In this paper, effect of a magnetic field on natural convection of non-Newtonian power-law fluids in a partially heated cavity, has been analyzed by using the Finite-Difference Lattice Boltzmann Method (FDLBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 10(4) and 105), Hartmann number (Ha = 0-60), power-law index (n = 0.5-1.5), and length of heated section (H/L = 0.25, 0.5, and 0.75), as the magnetic field is applied horizontally. Results indicate that the augmentation of the power-law index in the absence of the magnetic field causes heat transfer to drop. Generally, the magnetic field decreases heat transfer in different power-law indexes. The increment of the magnetic field power declines the effect of the power-law index on heat transfer. The magnetic field for various Hartmann numbers at Ra = 10(4); has different effects on heat transfer with the enhancement of power-law index. At Ra = 10(5) and for Ha = 0 to 30, heat transfer falls with rise of the power-law index as the effect is weakened by increase in Hartmann number significantly. The influence of power-law index on heat transfer augments with increase in the size of the heated section. (C) 2014 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.