The paper contains the results of heat transfer regimes analysis in the case of forced turbulent flow of water and modeling fluids in channels of various configurations (round tubes, annular gaps, rod bundles) at supercritical pressures. Two new complex criteria were proposed to describe heat transfer in the pseudo-phase transition region. These criteria take into account the specific features of the influence of inertial and viscous forces on heat and mass transfer processes under conditions of a strong change in fluid properties and when thermally-induced currents arise in the flow. A system of equations suitable for the engineering calculation of heat transfer in fuel assemblies of nuclear supercritical water reactors and in channels of other installations, where coolants are used at supercritical parameters, is presented. The comparison of the calculations of heat transfer coefficient by the proposed method and the predictions of other known correlations with experimental data for the regimes of normal, deteriorated and mixed heat transfer is given.