This study compares the prediction of two types of Computational Fluid Dynamics (CFD) models to investigate the turbulent forced convection of the Cu-water nanofluid in a tube with a constant heat flux on the tube wall. One of the CFD models is based on a single-phase (or homogeneous) model and the other is the Eulerian–Eulerian (two-fluid) two-phase model. The Reynolds number is between 10,000 and 25,000, whereas the volume fraction of the Cu particles is in the range of 0–1.5%. The results from the CFD models are compared with the results from experimental investigations in the literature. Both the single-phase and two-phase models overpredict the Nusselt number in most of the cases investigated. Unexpectedly, the two-phase model was found to be relatively less accurate than the single-phase model. The present study suggests a correction of the two-phase model in terms of selecting an appropriate effective conductivity of the solidus phase and this has resulted in a significant improvement in the predictions of the accuracy of the model. A correlation describing the effective conductivity of the solidus phase of Cu-water nanofluid as a function of the Reynolds number and particle concentrations is developed for use in the Eulerian–Eulerian two-phase model. To the best of our knowledge, such an improvement to a two-phase model has been presented for the first time.