Fundamental burn-up mode in a pebble-bed type reactor

This paper deals with a pebble-bed type reactor, in which the fuel is loaded from one side (top) and discharged from the other side (bottom). A boundary value problem of a single group diffusion equation coupled with simplified burn-up equations is studied, where the natural radioactive decay processes are neglected in the burn-up modelling. An asymptotic burning wave solution is found analytically in the one-dimensional case, which is called as fundamental burn-up mode. Among this solution family there are two particular cases, namely, a classic fundamental solution with a zero burn-up and a partial solitary burn-up wave solution with a highest burn-up. An example of Th–U conversion is considered and the solutions are presented in order to show the mechanism of the burning wave.