Heating and Ignition of Metal Particles in the Transition Heat Transfer Regime

This paper considers the heating and ignition of small metallic particles in hot gases for a range of Knudsen numbers, for which the continuum description of heat transfer is not valid. Modified Fuchs’ model for the transition heat transfer analysis was adapted to treat diatomic gas with properties changing as a function of temperature. The dimensionless heat transfer coefficient, Nusselt number, was calculated as a function of the particle diameter for the transition heat transfer regime. Heat transfer rates in the transition regime are somewhat different from one another for the cases of particle heating and cooling while the absolute values of the particle-gas temperature difference are the same. This effect does not exist for the continuum heat transfer model. It is observed that the applicability of the continuum heat transfer model for particles of different sizes depends on pressure and particle-air temperature difference. For example, for particles at $300K$ heated in air at $2000K$⁠, the continuum heat transfer model can be used for particle diameters greater than $10μm$ and $1μm$ at the pressures of $1bar$ and $10bars$⁠, respectively. Transition heat transfer model must be used for the analysis of heat transfer for nanosized particles. For calculating the ignition delay, the continuum model remains useful for particle diameters greater than $18μm$ and $2μm$ for $1bar$ and $10bars$⁠, respectively. The sensitivity of the transition heat transfer model to the accommodation coefficient is evaluated. It is found that for metallic particles, the accommodation coefficient has a relatively weak effect on the heat transfer rate.