On fuel rod surface inflammation under the conditions of a coolant-loss accident

The article considers a system of equations describing the growth of fuel rod shell temperature and of oxide film thickness on the surface of the shell. A relaxation-type equation is proposed for oxygen concentration in the oxide film at the interface with the coolant. An equation is obtained, which allows one to investigate the linear-to-parabolic transition of the oxide film growth law under isothermal conditions, and a relation is demonstrated between the linear law rate constant and the relaxation time of the oxygen concentration distribution in the oxide layer. For small and large times in comparison to the relaxation time the problem is reduced to the previously investigated problem on metal particle ignition under linear and parabolic conditions of oxidation. Expressions are cited for the dimensionless parameters determining the conditions materialization of which results in fuel rod surface inflammation. These parameters are studied as functions of internal heat evolution intensity and coolant motion rate. The characteristic times of heating of the fuel rod surface up to inflammation are estimated.