At what ambient temperature can thermal runaway of a burning metal particle occur?

Abstract

A simplified heat and mass transfer model is considered to predict at what ambient temperature can thermal runaway occur for a burning metal particle exposed to an oxidizing gas. The model accounts for transition transport phenomena important for particles with sizes comparable to the mean free path of the gas molecules. The quasi-steady model can be reduced to a set of algebraic equations that can be readily solved numerically if both the reaction kinetics law and the value of thermal accommodation coefficient (TAC) are assumed. Such assumptions are made and the solutions are produced and discussed for particles of different sizes for aluminum, magnesium, and boron burning in air. Different reaction kinetics expressions reported in the literature and different values for the TAC are considered for all three fuels. For aluminum, different reaction kinetics lead to a widely different range of air temperatures, at which the particle thermal runaway is predicted. However, the runaway is expected for particles of all sizes, including nano-particles if the air temperature is sufficiently high. Similarly, thermal runaway is also predicted to occur for boron particles of different sizes, although respective air temperatures must be substantially higher than for aluminum. The effect of TAC on the predicted result is strong; smaller values of TAC lead to a reduced effect of particle size on the gas temperature required for the thermal runaway to occur. It is found that neglecting transition heat and mass transport regimes can be always justified for very large, 200 µm particles. For smaller particles, both higher reaction rates and smaller values of TAC may require considering transition transport when modeling behavior of burning particles.