Heat transfer to supercritical water (SCW) flowing upward in a vertical heated tube at low mass fluxes (G ≤ 20 kg/m2 s) has been numerically investigated in COMSOL Multiphysics and validated with experimental data. The turbulence models, essential to describing local turbulence, in COMSOL have been checked under conditions in which empirical heat-transfer correlations are available, and it is concluded that the shear-stress transport (SST) turbulence model gives the most accurate results. The numerical results obtained show a buoyancy induced circulation of the fluid resulting from gravitational force acting on density gradients as well as a thin thermal boundary layer with a steep temperature gradient at the inner wall and a flat temperature profile in the bulk fluid. The heat-transfer coefficient of SCW is enhanced near the pseudocritical temperature (Tpc) and is deteriorated at temperatures above Tpc. A new heat-transfer correlation has been developed and validated with experimental data.