A theoretical model is considered to predict the minimum ambient gas
temperature at which fine iron particles can undergo thermal runaway--the
ignition temperature. The model accounts for Knudsen transition transport
effects, which become significant when the particle size is comparable to, or
smaller than, the molecular mean free path of the surrounding gas. Two kinetic
models for the high-temperature solid-phase oxidation of iron are analyzed. The
first model (parabolic kinetics) considers the inhibiting effect of the iron
oxide layers at the particle surface on the rate of oxidation, and a kinetic
rate independent of the gaseous oxidizer concentration. The ignition
temperature is solved as a function of particle size and initial oxide layer
thickness with an unsteady analysis considering the growth of the oxide layers.
In the small-particle limit, the thermal insulating effect of transition heat
transport can lead to a decrease of ignition temperature with decreasing
particle size. However, the presence of the oxide layer slows the reaction
kinetics and its increasing proportion in the small-particle limit can lead to
an increase of ignition temperature with decreasing particle size. This effect
is observed for sufficiently large initial oxide layer thicknesses. The
continuum transport model is shown to predict the ignition temperature of iron
particles exceeding an initial diameter of 30 μm to a difference of 3% (30
K) or less when compared to the transition transport model. The second kinetic
model (first-order kinetics) considers a porous, non-hindering oxide layer, and
a linear dependence of the kinetic rate of oxidation on the gaseous oxidizer
concentration. The ignition temperature is resolved as a function of particle
size with the transition and continuum transport models, and the differences
between the ignition characteristics predicted by the two models are discussed