In this paper, laminar mixed convection of non-Newtonian nanofluids in a square lid-driven cavity in the presence of a vertical magnetic field has been analyzed by Finite Difference Lattice Boltzmann Method (FDLBM). The cavity is filled with water and nanoparticles of copper (Cu) 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 from φ = 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 although the effect of nanoparticle on the enhancement of heat transfer varies in different power-law indexes. The magnetic field declines heat transfer generally and also changes the effect degree of nanoparticles on the increase in heat transfer.
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