This paper presents a numerical study of heat transfer to turbulent and laminar Cu/water flow over a backward-facing step. Mathematical model based on finite volume method with a FORTRAN code is used to solve the continuity, momentum, energy and turbulence equations. Turbulence was modeled by the shear stress transport (SST) K-ω Model. In this simulation, three volume fractions of nanofluid (0%, 2% and 4%), a varying Reynolds number from 50 to 200 for the laminar range and 5000 to 20,000 for the turbulent range, an expansion ratio of 2 and constant heat flux of 4000 W/m2 were considered. The results show the effect of nanofluid volume fraction on enhancing the Nusselt number in the laminar and turbulent ranges. The effect of expansion ratio was clearly observed at the downstream inlet region where the peak of the Nusselt number profile was referred to as enhanced heat transfer due to the generated recirculation flow. An increase of pressure drop was evident with an increasing Reynolds number and decreasing nanofluid volume fraction, while the maximum pressure drop was detected in the downstream inlet region. A rising Reynolds number caused an increasing Nusselt number, and the highest heat transfer augmentation in the present investigation was about 26% and 36% for turbulent and laminar range, respectively compared with pure water.