Modelling ignition temperature and burning time of a single aluminium nanoparticle

A mathematical model is developed for the burning of a single nanosized aluminium particle in air. First, based on thermal definition, the ignition temperature of single Al is obtained. For this purpose, the interpolation method is used for the conduction of heat loss rate in the transition regime; the chemical heat generation rate is described by a single term Arrhenius ignition model; the Gibbs-Thomson equation for an isolated spherical solid particle is utilised for modelling the size dependent melting temperature of nanoparticles; and the size dependent activation energy is also obtained. The theoretical result shows that the ignition temperature is slightly higher than the melting temperature. With the assumption of constant particle size and the use of the `Taffanel and le Floch´ condition, the burning time of a single aluminium particle is achieved. According to the obtained results, as particle size decreases or pressure increases, the reaction rate increases.