Model of heterogeneous combustion of small particles

A steady model of heterogeneous combustion for a spherical particle in the transition heat and mass transfer regime is developed. The model assumes formation of condensed products and reaction rate controlled by the transport of oxidizer to the particle surface. The model is based on the Fuchs' limiting sphere approach. Calculations are performed for combustion of zirconium particles of different sizes. Temperature and oxygen concentration profiles are calculated and compared to those predicted by the continuous medium transfer model. The predictions are compared with available experimental data. For coarse particles, both predicted combustion temperatures and burn rates match respective experimental data when the reaction is assumed to produce zirconium-oxygen solution rather than stoichiometric ZrO₂. A weaker effect of particle size on their burn time is predicted for smaller particles, in qualitative agreement with recent experiments. However, the model underestimates the burn times and overestimates the combustion temperatures for small particles. This discrepancy is likely associated with the finite reaction kinetics at the particle surface that must be accounted for in the future work.