Time-dependent laser ignition of a combustible stagnant boundary layer

A spatially one-dimensional model for the ignition of a combustiblegas layer adjacent to a plane solid surface is considered. Theeffect of an incident laser beam from the gas side is to raisethe surface temperature; the other boundary is taken to be apoor thermal conductor in the form of an inert gaseous medium.It is assumed that the exothermic chemical reaction within thelayer has a negligible reactant consumption. Three examplesfor the effect of the laser on the solid surface are considered:(a) a large instantaneous temperature rise, (b) a temperaturejump at t=0 which is a linear funtion of time t>0, (c) asurface temperature variation which is a linear function oftime. For (a) and (b) conditions for criticality are obtained.For appropriate states of the system, times to ignition for(a), (b), and (c) have been determined. It is shown that thetheoretical results are in reasonably good agreement with experiment.The kind of physical situation envisaged might occur in a mineshaftwhen a stagnant combustible layer is subject to intense transientlight. Although an idealization, our analysis determines conditionsunder which thermal runaway and subsequent explosion could takeplace.