A turbulent convection correlation is developed for use as a surrogate of full three-dimensional (3-D) computational fluid dynamics numerical calculations for helium coolant flow in channels of a prismatic core high-temperature gas-cooled reactor or very-high-temperature reactor. It is developed based on the results of a 3-D thermal-hydraulics numerical analysis of a prismatic core hexagonal fuel module with a central flow channel. The analysis accounts for the changes in material properties with temperature, including the nuclear graphite, helium coolant, and the constituent materials of the fuel compacts, as well as the chopped-cosine axial fission power profile in the reactor core. The heated flow channel is 1.5875 cm in diameter and 8.0 m high. In addition, the flow channel extends 1.2 m and 0.8 m into unheated top and bottom graphite reflector blocks, for a total length of 10 m. Results show that entrance mixing increases the local turbulent heat transfer coefficient, but its effect diminishes after a distance into the heated section equal to 25 channel diameters. The developed correlation is within +/- 2% of the 3-D numerical results for both uniform and chopped-cosine axial power profiles. It is comparable to those reported in the literature based on experimental measurements of the local heat transfer coefficient for gas flows in uniformly heated tubes, including the entrance flow mixing section.