In this paper, laminar mixed convection of non-Newtonian nanofluids in a two sided lid-driven enclosure in the presence of a horizontal magnetic field has been analyzed by finite difference Lattice Boltzmann method (FDLBM). The cavity is filled with water and nanoparticles of Alumina (Al2O3) while the mixture shows shear-thinning behavior. This study has been conducted for the certain pertinent parameters of Richardson number (Ri = 0.001-1), power-law index (n = 0.2-1), and Hartmann numbers (Ha = 0-60) and volume fraction has been studied from phi = 0 to 0.09. Results indicate that the augmentation of Richardson number decreases heat transfer. The fall of the power law index declines heat transfer for different studied Richardson numbers. The addition of nanoparticle augments heat transfer for multifarious studied parameters. The increase in Hartmann number drops heat transfer generally and also affects the power-law index and nanoparticle influences on heat transfer. (C) 2015 Elsevier B.V. All rights reserved.