In this study, a numerical study of MHD mixed convection nanofluid filled lid driven square enclosure was performed. The bottom wall of the cavity is heated and the top wall is kept at constant temperature lower than that of the heater. Other walls of the square enclosure and cylinder surface are assumed to be adiabatic. The governing equations are solved with finite element method. The influence of the Richardson number (0.001 <= Ri <= 10), Hartmann number (0 <= Ha <= 50), angular rotational speed of the cylinder (-10 <= Omega <= 10) and solid volume fraction of the nanoparticle (0 <= phi <= 0.05) on fluid flow and heat transfer are numerically investigated. It is observed that 17% of heat transfer enhancement is obtained for Ri = 10 when compared to flow at Ri = 1. Averaged heat heat transfer decreases with increasing Hartmann number and 14.2% of heat transfer enhancement is obtained for Omega = -10 compared to motionless cylinder case at Omega = 0. When the solid volume fraction of nanoparticle is increased, heat transfer increases. (c) 2014 Elsevier Ltd. All rights reserved.