This work aims to study the combined free and forced convection of an Al2O3/water nanofluid flowing throughout an annulus. A set of three-dimensional elliptic governing equations were solved numerically using the finite volume technique. The effect of the volume fraction of the nanoparticles and the Richardson number on the thermal and hydrodynamic parameters was extensively investigated. The distribution of the axial velocity and temperature at different cross sections is shown. The axial variation of the frictional and heat transfer coefficients is presented. Results indicate that the Richardson number does not influence the frictional coefficient, while the heat transfer coefficient directly depends on the Ri number. The dimensional axial velocity continually increases with greater volume fraction of nanoparticles at the upper and lower sides of the annulus, while this behavior for dimensionless axial velocity is not continuous. The results indicate that any increase in the volume fraction results in secondary flow enhancement and, therefore, a delay in the occurrence of the maximum heat transfer coefficient.