Numerical studies on heat transfer to supercritical water in an internally ribbed tube were performed and compared with those in a smooth tube. The Shear-Stress Transport k-omega model was adopted and validated against experimental data from tubes with different geometries. Comparisons between upward and downward flows show that the Jackson buoyancy criterion, which was proposed based on analysis and experiments in smooth tubes, can be used to evaluate effect of buoyancy in internally ribbed tubes. Radial profiles of turbulence and property reveal that in both smooth tube and internally ribbed tube, forced convection heat transfer is mainly influenced by specific heat, and effects of thermal conductivity and viscosity cancel each other out. As heat flux and bulk temperature increased, changes in the integral effect of specific heat resulted in variation in the heat transfer coefficient. The Jackson Nusselt correlation for smooth tubes can also accurately predict heat transfer coefficients of forced convection in an internally ribbed tube. Under conditions of mixed convection, buoyancy had a weaker impact on heat transfer in the internally ribbed tube. Detailed velocities and turbulence explained this weaker effect: the sharp drops in axial velocity gradient and turbulent kinetic energy, which occurred in a heated smooth tube at a radial position similar to the law of the wall region for isothermal flow, did not occur in a heated internally ribbed tube. Moreover, friction factors for internally ribbed tubes were always higher than that for smooth tubes in both forced convection and mixed convection. (C) 2015 Elsevier Ltd. All rights reserved.