In this paper, laminar mixed convection of non-Newtonian nanofluids in a square two sided lid-driven cavity 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 the volume fraction has been studied from phi = 0-0.09. Results indicate that the augmentation of Richardson number causes the heat transfer to drop. The heat transfer drops for different Richardson numbers as the power-law index falls. The addition of nanoparticle augments heat transfer for multifarious studied parameters. The greatest effect of nanoparticle on the enhancement of heat transfer was observed at power-law index of n = 0.2 for various Richardson numbers. (C) 2015 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.