On the spreading of unsteady cylindrical diffusion flames

The unsteady outwardly spreading motion of a diffusion flame supported by fuel injected from a cylindrical porous burner is theoretically analyzed. The classical technique of Laplace inversion with large or small values of time is used, which enables us to obtain the general asymptotic expressions of the leading order terms of temperature, species concentration, and flame radius. Results show that the flame spreading rate is mainly controlled by the ambient oxidizer concentration relative to the fuel concentration, modified by the flow rate from the burner, and that the characteristic diffusion length can be significantly larger or smaller than the flame radius, with their ratio being related to the quasi-steady assumption. An adiabatic diffusion flame temperature with no heat loss to the burner is obtained, as the flame is situated far away from the burner.