The low thermal conductivity and viscosity index of conventional lubricants limit their performance. Therefore, it is crucial to achieving a nano-lubricant with suitable thermophysical properties as an alternative for the base-oil. Some investigations have been carried out in the past decade on the anti-frictional and thermal properties of nano-lubricants containing different nanoparticles. Meanwhile, studies on copper oxide nanoparticles are mostly concerned with their effect on thermal conductivity, and only a small number of studies have been carried out on graphene, which is focused on its effect on viscosity. However, rarely investigations have been performed on the simultaneous effect of these nanoparticles on the rheological behavior and thermal properties of engine oil. Also, there are only a few published articles on deriving the thermo-physical properties of nano-lubricants containing these nano-additives from experimental and theoretical approaches. Therefore, current work aims to compare the thermophysical features (dynamic viscosity, shear stress, thermal conductivity, flash point, and pour point) of the engine oil using copper oxide and graphene nano-additives under the influence of the effective variables includes shear rate, temperature, and nanoparticles mass fraction. Also, some correlations are proposed based on the experimental data to predict the rheological behavior and thermal conductivity of the nanofluids.