In this paper, we consider the flow of a nanofluid in an enclosed lid-driven cavity using a single-phase model. Two cases are considered: one in which the top and bottom walls are kept at adiabatic conditions, and a second case in which the left- and right-side walls are kept in adiabatic conditions. The impact of different viscosity models on the mixed convection heat transfer is examined, and numerical methods are used to obtain solutions for the Navier–Stokes equations for various parameter ranges. Using our robust methods, we are able to obtain novel solutions for large Reynolds numbers and very small Richardson numbers. Using water as the base fluid and aluminium oxide nanoparticles, our results suggest that heat transfer enhancement occurs with increasing particle concentration and decreasing Richardson numbers. There are also significant differences depending on the viscosity model used in terms of the impact of reducing corner recirculation regions in the cavity.