It is proposed that extinction of flames near solid surfaces can be effectively investigated by separating the gaseous reactions from the energy and mass balance at the surface. This separation is implemented by simulating the flow of pyrolysis gases from the solid through a controlled supply of flammable gas issuing from a porous burner kept at a fixed surface temperature. The separation simplifies the interpretation of experiments, the analysis of experimental results and applications in determining the material extinction properties. It is founded on the observation that flame extinction on a solid occurs at that rate of mass pyrolysis (or equivalently at that mass supply rate of the fuel in the porous burner) where the convective heat flux to the solid (or the porous burner) takes its maximum value. Convective heat flux is the dominant heat transfer mode at surface extinction conditions because the flame being close to the surface is blue so that radiation from the flames is negligible. The convective heat flux from the flames increases as the mass supply rate decreases until it reaches a maximum value and then decays because the chemical reactions are quenched. Without loss of generality in underpinning the controlling parameters, the analysis makes use of a two-dimensional stagnation flow over a porous burner and assumes a simple one step reaction between the flammable gas and the air. The mass flux and the temperature at the solid surface and the temperature and the oxygen concentration at infinity are chosen as the independent variables so that the flame sheet is located at a fixed value of the conserved scalar. First, it is shown that there is a finite oxygen concentration at the wall and then, that there is a regime where the critical mass now rate, the heat flux and the oxygen concentration at the wall are independent of the Damkohler number at extinction but they depend on the order of the chemical reaction. This result, supported by experimental observations and numerical calculations, has significant importance in determining the extinction properties of materials. (c) 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
Delichatsios, M. A. (2007). Surface extinction of flames on solids: Some interesting results. Proceedings of the Combustion Institute, 31(Part 2), 2749-2756. https://doi.org/10.1016/j.proci.2006.08.032