Comparative analysis of the thermal and hydraulic performance of three-fluid tubular heat exchanger has been carried out numerically. Single-phase and multi-phase approaches for the turbulent flow of CuO–water nanofluids have been applied. The effect of Reynolds number (2500–10,000) and volume concentration of nanoparticles (0–3%) on the overall performance of the selected heat exchanger has been investigated. The numerical simulation has been performed using a finite volume approach in commercial computational fluid dynamics (CFD) software for two flow arrangements (parallel and counter). Nusselt number was found to increase with the growth in Reynolds number as well as volume concentration of nanoparticles in both the flow arrangements. Particularly, for a maximum volume concentration of nanoparticles (φ = 3%), single-phase approach resulted in an increase of 8.94% for parallel and 11.52% for counterflow arrangements. However, multi-phase approach produced a remarkable increase of 30.37% for parallel and 32.04% for counterflow arrangement. Single-phase approach was applied for treating the nanofluids as homogenous fluids with effective thermophysical properties, meaning that the entire suspension is assumed to act as a single unit with the same velocity. However, the multi-phase model was applied to separately treat the two phases with different velocities.