The fluoride-salt-cooled high-temperature reactor (FHR) is an advanced reactor concept that uses tristructural isotropic (TRISO) high-temperature fuel and low-pressure liquid salt coolant. A test reactor, as the key step in demonstrating the technical feasibility, is currently under design at Massachusetts Institute of Technology. This study focuses on the coupled conduction and convection heat transfer adopting a three-dimensional unit-cell model with one coolant channel and six one-third fuel compacts. The laminar, transitional, and turbulent flows are investigated with the use of computational fluid dynamic (CFD) software, CD-adapco STARCCM+. The model is validated against theory for developing laminar flow in the benchmark study with excellent agreement. The model is also benchmarked for transitional and turbulent flows by Hausen, Gnielinski, Dittus-Boelter, and Sieder-Tate correlations. Azimuthal distributions of temperature, heat flux, and heat transfer coefficient along the coolant-graphite interface were obtained for the asymmetric heat source, graphite materials, and two different types of salt coolant. The results show that the asymmetric power generation has little impact on peak fuel temperature, interface temperature, and heat transfer coefficient for a unit-cell module in laminar flow regime due to effective thermal conduction of the graphite matrix. In the turbulent flow regime, the effect on the azimuthal heat flux and heat transfer coefficient is more pronounced.