Analytical Solution of Fick's Law of the TRISO-Coated Fuel Particles and Fuel Elements in Pebble-Bed High Temperature Gas-Cooled Reactors

Two kinds of approaches are built to solve the fission products diffusion models (Fick's equation) based on sphere fuel particles and sphere fuel elements exactly. Two models for homogenous TRISO-coated fuel particles and fuel elements used in pebble-bed high temperature gas-cooled reactors are presented, respectively. The analytical solution of Fick's equation for fission products diffusion in fuel particles is derived by variables separation. In the fuel element system, a modification of the diffusion coefficient from D to D/r is made to characterize the difference of diffusion rates in distinct areas and it is shown that the Laplace and Hankel transformations are effective as the diffusion coefficient in Fick's equation is dependant on the radius of the fuel element. Both the solutions are useful for the prediction of the fission product behaviors and could be programmed in the corresponding engineering calculations.