The thermal ignition of a mixture of carbon particles and air contained between two parallel walls is examined. Though the air is assumed to be transparent to radiation, the carbon particles are considered to actively absorb, emit, and scatter the radiation. Therefore the problem is formulated exactly as a set of simultaneous integrodifferential equations. The numerical results reveal that the carbon particles located far away from the hot wall can be heated up faster than the air, for the radiative energy emitted from the hot wall can penetrate deep into a mixture of carbon and air. Therefore the radiation is found to play a significant role of igniting particles earlier. An increase in the particle size also exerts a strong influence on extending the ignition delays. However, the carbon mass loading is known to negligibly affect the ignition delays due to its counterbalancing effects on the particle temperature. An appreciable change given in the lower wall temperature makes no significant difference in ignition delays. © 1990.