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AbstractA numerical study of the natural convection flow and heat transfer characteristics of different nanofluids within a square enclosure is conducted by using a two-phase Eulerian–Eulerian model. In this study, the Cu-H2O and Al2O3-H2O nanofluids are considered because of their good stability. The Eulerian–Eulerian model considers the governing equations of the liquid and solid phases separately, and the coupling between the phases is done with interfacial interaction forces. Finite difference methods are used to discretize the governing equations. Additionally, sixth-order compact schemes are used to evaluate the non-linear convective terms. The current Fortran-based solver is validated by using experimental and numerical results from the literature. The effect of Grashof number (Gr = 103 to Gr = 106) and volume fraction (1–3%) of nanoparticles on the flow field and heat transfer are discussed in detail through stream function contours, isotherms, velocity and temperature profiles at the midsection of the enclosure, and average Nusselt number values. The results demonstrated that the incorporation of nanoparticles into the base fluid augmented the flow intensity and heat transfer. Moreover, this effect is more significant with Cu nanoparticles than Al2O3 nanoparticles. At Grashof number, Gr = 106 and volume fraction, ϕs = 2% the average Nusselt number values for the Cu-H2O nanofluid and Al2O3-H2O nanofluid are enhanced by 32.04% and 19.47% respectively, compared to the base fluid water. The findings also indicate that increasing the Grashof number and volume fraction leads to a substantial improvement in the heat transfer rate. Finally, a new correlation is developed to predict the average Nusselt number along the heated wall of a square enclosure filled with nanofluids. [ABSTRACT FROM AUTHOR]