Method for describing the Zircaloy-4 oxidation using the analytical solution of the oxygen diffusion equation

The oxidation of the Zircaloy-4 fuel element sheath at high temperature transients is treated as a moving boundary one-dimensional diffusion problem. It is usually served by numerical methods. A method is provided in this work to analytically solve the oxygen diffusion equations. The temperature transient has been approximated as a stepwise function of time, {T-i, (t(0i), t(i))}i=1,n. The main assumption was that in the beginning of the ith step of the temperature transient the oxide grown during the previous steps, x(0i), could be considered as being formed at a constant temperature, T-i, but during another time interval, named equivalent time interval Delta t(eq). Calculations have been made with a routine, OXCON, developed using this model. The results approach well the predictions of validated corrosion codes, FROM and PRECIP-II, which solve the diffusion equations using numerical methods.