In this article, laminar flow and convection heat transfer of water–alumina nanofluid in a rectangular microchannel have been investigated numerically. Because of the existence of slip velocity between nanoparticles and base fluid, the mixture model is used and results are compared with the single-phase model. The results indicate that using nanofluids can enhance convective heat transfer and pressure drop in a microchannel in comparison with pure water. Also, the enhancement of convection heat transfer is higher in the developing region and the difference of the mixture model and single-phase model is slightly great in this region, but in fully developed region the differences are very low.