  Most studies on nano- and micro- sized aluminum particle ignition have been
focused on the processes occuring inside particles. In the current paper,
thermal ignition of an aluminum particle in the air is simulated with different
heat transfer models: continuum, free-molecular and Fuchs model. A single
parabolic oxidation law is assumed in the particle size range from nano- to
millimeter diameters. A particle is considered ignited when it reaches the
oxide melting point. The criterion defining the limits of validity for each
model is the ratio of continuum and free-molecular heat transfer rates. The
dependence of ignition temperature $T_i$ on particle size is in a qualitative
agreement with the experimental trends: $T_i$ can have values in the range
700--1500 K for nanoparticles due to the dominating contribution of a
free-molecular heat transfer, and sharp growth of $T_i$ with the particle size
in the range of 1-100 $\mu$m diameter is due to the transitional character of
heat transfer. For small values of accommodation coefficient, ignition may
occur in the critical ignition mode with the thermal runaway. The results
suggest the importance of heat transfer and, in particular, energy
accommodation in ignition of nano- and micro- sized particles.
