Gas-Phase Ignition of a Solid with In-Depth Absorption of Radiation

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Abstract
In an earlier paper an asymptotic analysis was presented for the radiant ignition of a solid fuel that gasifies endothermically then reacts exothermically in the gas phase through a one-step Arrhenius process. The theory was restricted to surface absorption of the incoming radiation and to ignitions occurring during the stage of transport-controlled gasification which follows the stage of transition to gasification. These two restrictions are removed in the present paper. Emphasis is placed on determining the ignition time, defined as the interval between initiation of irradiation and thermal runaway. It is shown that if the gas is sufficiently reactive then ignition can occur early in the stage of transition to gasification and that decreasing the absorptivity of the solid increases the ignition time. Comparisons are made with results of earlier numerical integrations, demonstrating the existence of regimes in which the ignition time depends strongly on the ignition criterion adopted. Graphs are given containing results of a parametric study for the ignition time.

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