A turbulent 3D mixed convective flow of pure water, H2O, and nanofluid, SiO2-H2O, inside a differentially heated moving wall enclosure containing an insulated rotating cylinder over a range of rotational speeds,-5 ≤ Ω ≤ 5, Reynolds numbers, 5000 and 10000, and constant Grashof number, is numerically investigated. A cooled lid-driven top wall and a heated bottom wall are the only thermally uninsulated walls in this domain. A standard k-ε for the Unsteady Reynolds-Averaged Navier-Stokes (URANS) approach is applied to the turbulence calculation. Nusselt number, mean velocity profile, streamline, isothermal and isosurface temperatures are derived and presented in this paper to gain a better understanding of the effects of clockwise and anticlockwise rotating cylinder directions on the heat transfer and flow patterns. Interesting changes in flow structure and heat transfer have been analysed for all rotational speeds and fluid types at both Reynolds number values. Nonlinear increases in Nusselt number have been observed by using nanofluid instead of pure water. The wall shear stress and turbulent kinetic energy profiles are found to be influenced by changing the Reynolds number and rotational speed and direction. Furthermore, incremental heat transfer rates at the walls can be achieved by increasing the cylinder rotation speeds, but these increases have weaker influences on the top wall than on the bottom wall.