A numerical study of laminar mixed convection in a two-sided lid-driven cavity filled with a water–Al 2O 3 nanofluid is presented. The top and bottom walls of the cavity are kept at different temperatures and can slide in the same or opposite direction. The vertical walls are thermally insulated. An Adaptive Network-based Fuzzy Inference System (ANFIS) approach is developed, trained and validated using the results of a Computational Fluid Dynamics (CFD) analysis. The results show that ANFIS can successfully be used to predict the fluid velocity and temperature as well as the heat transfer rate of the cavity, with reduced computation time and without compromising the accuracy. ► Nanofluid laminar mixed convection in a two-sided lid-driven cavity is studied. ► ANFIS and CFD are used to examine the thermal behaviour of cavity. ► Computation time is reduced by using ANFIS without compromising accuracy. ► Higher heat transfer rates at higher values of ϕ and lower values of Ri. ► Heat transfer enhancement is a function of aspect ratio and lid-driven direction.