Thermal Radiation Effects on Thermal Explosion in Polydisperse Fuel Spray-Probabilistic Model

We investigate the effect of thermal radiation on the dynamics of a thermal explosion of polydisperse fuel spray with a complete description of the chemistry via a single-step two-reactant model of general order. The polydisperse spray is modeled using a Probability Density Function (PDF). The thermal radiation energy exchange between the evaporation surface of the fuel droplets and the burning gas is described using the Marshak boundary conditions. An explicit expression of the critical condition for thermal explosion limit is derived analytically and represents a generalization of the critical parameter of the classical Semenov theory. Because we investigated the model in the range where the temperature is very high, the effect of the thermal radiation is significant