Abstract: A numerical simulations of single phase fluid flow and natural convective heat transfer is local friction coefficient of wall,and Nusselt number are predicted at the different Rayleigh numbers.Simulated results show that the natural circulation of fluid is formed between the heating wall with up-flow performed presented in pebble bed modular reactor（PBMR） with the consideration of the inertial and viscous forces.Flow behavior and heat transfer caused by inner heat source in a vertical annulus with saturated fuel particles is numerically investigated at the conditions of shutdown.Distributions of velocity,temperature,and the cooling wall with down-flow.The center of the vortex moves up with the increase of Reyleigh number.The extremum of local Nusselt number and friction factor of wall is existed,and the position moves up along axial direction with the increase of Rayleigh number.Comparing with nitrogen as a cooling medium,Helium fluid will give a more uniform distribution of temperature in the reactor core.