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.　The　effect　of　geometry　parameter　(a),　Hartmann　number　(Ha),　nanoparticles　volume　fraction　(φ)　and　nanoparticles　type　(Fe3O4,　CuO　and　Al2O3)　on　the　Nusselt　numbers,　entropy　generations　and　Bejan　numbers　were　investigated　by　the　response　surface　methodology　(RSM).　Increasing　a　leads　to　an　increase　in　both　local　and　average　Nusselt　numbers　and　increment　in　different　terms　of　entropy　generation,　while　it　reduces　the　Bejan　number.　Fe3O4　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.　©　2019,　Akadémiai　Kiadó,　Budapest,　Hungary.