Nuclear fuel materials are those that are capable of undergoing fission reactions along with the liberation of enormous quantitiy of energy. The fuel cycle costs are 20% of nuclear electricity generation cost. This new book evaluates the use of the damped wave diffusion and relaxation equation to nuclear fuels processes. Simultaneous diffusion and autocatalytic reactions and the wave diffusion phenomena may have a combined effect of subcritical damped oscillations in concentration under certain conditions. Closed form analytical solutions are developed from the hyperbolic partial differential equations that govern the phenomena.