In this article, the problem of mixed convection in vertical rectangular microchannels for both regular fluids and nanofluids have been solved, using the CFD technique in the entrance regions of momentum and heat transfer taking in account the influences of viscous heating, inertial force and sleep conditions. In case of nanofluid flow, both the Brownian and thermophoresis molecular transfer mechanisms were considered.The predicted results were validated using fully developed distributions of velocity and temperature. Furthermore, the influences of mixed convection parameter (Gr/Re) and Kn number values on distributions of velocity and temperature through the entrance and fully-developed...