In this paper, natural convection of non-Newtonian nanofluid, using the Buongiorno's mathematical model in a porous cavity has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM) while entropy generations through fluid friction, heat transfer, and mass transfer are analyzed. The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 10(4) and 10(5)), Darcy number (Da = 0.0001,0.001,0.01), Prandtl number (Pr = 0.1, 1, and 10), buoyancy ratio number (N-r = 0.1, 1, and 4), power-law index (n = 0.4-1), Lewis number (Le = 1, 5, and 10), Thermophoresis parameter (N-t = 0.1, 0.5, 1), and Brownian motion parameter (N-b = 0.1, 1, 5). The Prandtl number is fixed at Pr = 0.1. Results indicate that the heat and mass transfer augments as Rayleigh number increases. The increase in Darcy number augments heat transfer and declines the mass transfer at Ra = 10(4). The augmentation of Darcy number enhances heat transfer at Ra = 10(5). The increase in power-law index alters heat and mass transfer. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorate mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer. The increase in Darcy number enhances total entropy generation in different Rayleigh numbers. In addition, the rise of Rayleigh number and Darcy number causes Bejan number to drop in various power-law indexes. The enhancement of the Lewis number provokes the total irreversibility to rise. Further, the total entropy generation increases as the buoyancy ratio number augments. It was shown that the increase in the Brownian motion and Thermophoresis parameters changes the total irreversibility. (C) 2017 Elsevier Ltd. All rights reserved.