Analytical and numerical solutions of sodium particle ignition based on the thermal explosion theory with different forms of reaction rates and variable thermal conductivity

Abstract

Analytical and numerical solutions of sodium particle ignition under different forms of reaction rates and variable thermal conductivity were investigated. The solutions of the problem were performed by taking into consideration the convection and convection with radiation heat loss cases for spatially uniform temperature of a sodium particle. Analytical expressions for critical conditions that relates the characteristic thermophysical parameters with environmental temperature and initial particle temperature were obtained. The results showed that the much reduction in the delay time significantly depended on the adding of variable thermal conductivity and heat loss types, which is crucially important for nuclear reactor safety. It was found that, as an ambient temperature (θa) increased the ignition time drastically decreased and the temperature slightly increased for both modes of heat loss. It was significant to note that the explosion occurred in a case of the sensitized reaction rate at a time greater than that of Arrhenius and bimolecular reaction rates, which considers more safe than other reaction types. A notable increased was found in the critical temperature for sensitized reaction rate compared to other reaction rates. As γR (radiation loss parameter) increased above the critical value, the ignition time and ignition temperature decreased. The results showed that the problem could be solved analytically by properly applying the definition of criticality based on the thermal explosion theory in a more straightforward manner without using mathematical approximation solution.