Abstract: To calculate the turbulent heat transfer of liquid lead bismuth (LBE) under different heating conditions in an annulus, a four equation model solver 4eqnFoam was developed based on the open source computational fluid dynamics program OpenFOAM. The prediction results of LBE in a plane and a pipe were compared with the results of direct numerical simulation and experiment, and the effectiveness of the solver was verified. Based on the solver, the turbulent heat transfers of LBE at different Reynolds numbers in an annulus with adiabatic outer wall and heated inner wall and an annulus with equal heat flux on the inner and outer wall were calculated respectively. The results show that with the increase of Reynolds numbers, the dimensionless temperature fluctuation, Reynolds heat flux, and turbulent heat diffusion of LBE in the annulus increase, while the mean turbulent Prandtl number decreases. When the Reynolds number increases to a certain extent, the mean turbulent Prandtl number does not change significantly. Based on the 4eqnFoam solver, more references can be provided for the calculation of LBE thermal hydraulic phenomena.