Rectangular cavity filled with a non-Newtonian shear-thinning nanofluid was investigated considering varied fin geometry under a vertical magnetic field. Irreversibility and entropy generation mechanisms were investigated by finite element method (FEM). The effect of geometry parameter(a), Hartmann number (Ha), nanoparticles volume fraction (φ) and nanoparticles type (Fe 3 O 4 , CuO and Al 2 O 3 ) on the Nusselt numbers, entropy generations and Bejan numbers were investigated by the Response Surface Methodology (RSM). Increasing a leads to an increase of both local and average Nusselt numbers and increment in different terms of entropy generation, while it reduces the Bejan number. Fe 3 O 4 nanoparticle shows the highest Nusselt number compared to other nanoparticles. RSM analysis revealed that a =0.29 and φ=0.04 are the optimized values for the goal of maximum Nusselt number and minimum Bejan number.

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