Diffusion-flame extinction for a spinning fuel disk in an oxidizer counterflow

Activation-energy asymptotics is applied to predict extinction of a Rat laminar diffusion flame adjacent to a solid fuel disk, which is rotating about its axis with angular velocity b and subjected to an impinging gaseous oxidizer Row having a radial velocity gradient a. By allowing for radiative energy loss from the surface of the disk in the similarity solutions, radiative extinction is obtained for smaller values of the parameter c = (a(2) + b(2))(1/2) as well as diffusive extinction at large values. Flammability boundaries are calculated for a model of poly(methyl methacrylate) burning in oxygen/nitrogen mixtures, showing a minimum ambient oxygen concentration to occur at an intermediate value of c separating radiative and diffusive extinction. The location of the minimum and the flammability boundary; are shown to correlate well with a characteristic flow time. The minimum oxygen index below which combustion is impossible (having spacecraft fire-safety implications) is qualitatively consistent with results of earlier numerical studies, which addressed only the limits in which either a or b is zero and found the lowest value of the limiting index to occur when a = 0. The present generalized theory helps to explain these results.