The current study uses a numerical multiphase approach on water-based nano-fluids with Al₂O₃ and CuO. The multi-phase approach was employed using the Mixture-Granular model along with the RNG k-ε turbulent model. The multi-phase approach was found to have better accuracy by about 3-5% as compared to the single-phase approach. A variation in the nano-particle concentration and inlet velocity showcases Al₂O₃ as a better nanoparticle compared to CuO. This was evident from the heat transfer effectiveness ratio whose maximum value was 3.05 and 2.2 for Al₂O₃ and CuO respectively. while a maximum profit index of 3.88 and 2.78 for Al₂O₃ and CuO respectively. at 5% concentration. These figures indicate that the dispersion of nanoparticles into a pure fluid highly enhances the heat transfer while requiring a higher pressure drop. With a higher profit index and heat transfer effectiveness ratio, Al₂O3-water proved to be a better nano-fluid than CuO-water. For both the nano-fluids, both the heat transfer ratio and profit index went on increasing along the axis owing to the reduced temperature difference between the wall and the fluid along the axial length as well as a reduced friction factor with nanoparticle increment. However, for a constant concentration, an increase in velocity reduced the heat transfer effectiveness ratio as well as the profit index.