Soot and Radiation in Combusting Boundary Layers

Classical studies of boundary layer diffusion flames have neglected radiation. As a first step toward a better understanding of radiation heat transfer in fires, a numerical solution is obtained for a steady, laminar, radiating, combusting, boundary layer over a pyrolyzing fuel slab. Two Shvab-Zeldovich coupling functions are needed in the analyses, which treat forced and free flows separately. For these laminar systems, an optically thin approximation for radiation is valid, based on previous measurements of soot volume fraction in combusting boundary layers. As in non-radiating combustion, the mass transfer number, B, and the mass consumption number, r(p), are the dominant parameters controlling the local pyrolysis rate and the excess pyrolyzate, respectively. The dominant role of the dimensionless heat of combustion, D(e), in determining the flame temperature makes it a significant parameter in radiating systems. The surface temperature and emissivity characterize the surface emission, which can dominate flame radiation for solid fuels of small dimension. The flame emission is controlled by the optical thickness and a radiation parameter, which indicates the relative strength of conduction to radiation. A comparison between numerical and experimental pyrolysis rates shows good agreement for a case where surface emission dominates flame radiation [polymethylmethacrylate (PMMA) burning in air]. Values of a mean absorption coefficient and soot generation rates are also obtained from f(v) data using this analysis.