Double-diffusive mixed convection of pseudoplastic fluids between two-square concentric duct annuli has been analyzed by FDLBM. Results indicate that the augmentation of Richardson number decreases heat and mass transfer. The fall of the power law index declines heat and mass transfer at Ri = 0.00062 and 0.01. The increase in the size of the adiabatic body enhances the heat and mass transfer in the lid-driven enclosure generally.