This study aims to numerically investigate the conjugate heat transfer (CHT) and the changes in the hydraulic and thermal terms of laminar flow (300 ≤ Re ≤ 800) in a 3-D wavy microchannel heat sink (MCHS). The obtained results from different nanofluid flow simulated models will be compared. The numerical simulation approaches used include single-phase, mixture, Eulerian, DPM, and DDPM. The effect of adding 1%, 3%, and 6% concentration of CuO nanoparticles (100 nm) in deionized water as the base fluid is examined on various parameters such as local and axial temperature, heat transfer convective coefficient, friction factor, Nusselt number (Nu), velocity distribution, and thermal and hydraulic boundary layer parameters. The substrate surface, due to its larger area surface and the amplitude of the sinusoidal wave, has a greater impact on the nanofluid flow as a channel bottom conjugate surface compared to others. The results obtained from the different models show close agreement with each other for various cases. For example, at Re = 304, the average Nu and friction factor for pure water are approximately 10.43 and 0.0260, respectively. For water with 0.01 concentration of CuO nanoparticles, Nu is found to be in the range of 10.43–10.78, and the friction factor ranges from 0.260 to 0.290, depending on the approach used for simulation. This shows a 2% increase in Nusselt number compared to a 0.05% increase in the friction factor. Moreover, these values increase by approximately 5.7% and 11.3% on average with an increase in CuO nanoparticle concentration to 0.06. Additionally, the DPM and DDPM models show a 15% difference in the scattering of CuO nanoparticles compared to the Eulerian-Eulerian models. The single-phase model presented in this study yields similar results to the multiphase approaches. Furthermore, the PEC parameter increases by about 1.9% with the addition of CuO nanoparticles at a concentration of 0.06.