Significance of thermal radiation and thermo-physical properties on the modeling of sodium droplet explosion with different reaction rates

The temperature of explosive substances (i.e., coolants) in the nuclear industries are necessary to ensure safety. The present study is focused on the analysis of the significance of thermal radiation and variable thermo-physical properties on thermal stability characteristics of sodium droplet use as a coolant in the design of nuclear facilities. It is pertinent to note that the inclusion of heat loss by convection and heat generated by the reaction is based on Newton's law of cooling and Arrhenius kinetic equation, respectively, with the P-1 approximation radiative heat loss model. The emerging mathematical model is a highly nonlinear ordinary differential equation. The model is solved using the classical fourth-order Runge-Kutta scheme. Consequently, the analysis of the results of the present study reveals the quantitative impacts of the thermal radiative model and variable thermo-physical properties on the temperature of the sodium droplet. The results reveal that the combined inclusion of variable thermophysical properties and thermal radiation significantly reduces the droplet temperature. The temperature of the coolant increases with an increase in the reactants' numerical exponent and thermal radiation reduces the temperature of the sodium droplet at the initial temperature with the reverse effect at free stream temperature.