In this study, the flow of Cu/oil nanofluids over an impermeable semi-infinite plate was investigated. A complete single-phase modeling of nanofluids flowing over a semi-infinite plate was performed, bringing into account, real experimental data of oil-based nanofluids. The empirical correlations revealed that the viscosity and thermal conductivity of the pure oil and oil-based nanofluids strongly depend on temperature. The similarity transformation method was utilized to transform governing partial differential equations into coupled nonlinear ordinary differential equations solved by employing the standard Runge-Kutta. The results showed that even low volumetric fraction of copper/oil nanofluids noticeably enhanced the heat transfer; however, such behavior was not predicted accounting the classic modeling of nanofluids. Furthermore, both hydrodynamics and thermal characteristics were reliant on the thermal boundary conditions, which this seems to have received a marginal focus in the existing literature. K E Y W O R D S Cu/oil nanofluids, heat transfer characteristics, hydrodynamics, low volumetric nanofluid, nanofluids flow over a semi-infinite plate, Runge-Kutta, thermal conductivity, viscosity