Spiral gasless condensed phase combustion

This paper studies combustion fronts propagating on and in a thin disk composed of a solid combustible mixture after ignition in a cylindrical region of radius r₀. A basic solution is constructed that describes an outward propagating circular front of radius R(τ) on the upper surface of the disk. Since the scales of the combustion process (diffusion and reaction) are much smaller than even τ₀, a perturbation analysis is employed for large R. This analysis corresponds to the situation in which the conditions of ignition no longer affect propagation.