The growing demand for energy worldwide requires that attention be given to designing and operating heat exchangers and thermal devices to utilise and save thermal energy. There is a need to find new heat transport fluids with better heat transfer properties to increase convective heat transfer, and nanofluids have been shown to be good alternatives to conventional heat transport fluids. Although extensive research has been done on the properties of nanofluids in recent decades, there is still a lack of research on convection heat transfer involving nanofluids, particularly in the transitional flow regime. This study investigated the convective heat transfer of a one-step prepared alumina-water nanofluid. A uniformly heated rectangular channel was experimentally investigated. Nanofluids with volume concentrations of 0.3, 0.5, and 1% were used, and a Reynolds number range of 200–7000 was considered, which included laminar and turbulent flows, as well as the transition regime from laminar to turbulent flow. The temperatures and pressure drops were measured to evaluate the heat transfer coefficients, Nusselt numbers, and pressure drop coefficients. The results showed enhancements of the heat transfer coefficients for the nanofluids used. The 1.0% nanofluid showed the maximum enhancements, with values of 54% in the transition flow regime and 11% in the turbulent regime. The convective heat transfer efficiency in the transition flow regime was observed to be better than those in the turbulent and laminar flow regimes.