Ignition of carbon particle suspension

There has been a growing interest in the conditions under which a reactive two-phase mixture can thermally ignite. In this paper, we consider radiative ignition of carbon particles suspended in air and contained between two parallel walls at different temperatures. Although the air is considered transparent to radiation, the carbon particles actively absorb, emit, and scatter the radiation. A similar study was done by Baek [1] where the numerical models did not include the scattering term. Inclusion of the scattering process leads to a set of simultaneous integro-differential equations where the integral term contains the singular exponential function E1(x). The coupled equations are solved numerically to study the effects of different physical and radiative parameters on the ignition times of the carbon particles. Our results compare very well with Baek [1] when there is no scattering. The main objective of this paper is to present an efficient numerical scheme to solve the coupled equations with the singular kernel when the scattering process is included.