Burning on a vertical fuel surface with finite chemical reaction rate

The problem of a natural convection, diffusion flame burning on a vertical fuel surface is analyzed. The fuel sample is assumed to be thermally thick and sufficiently small that the flow is laminar. The flame chemistry is approximated by a one-step reaction with Arrhenius kinetics. The analysis also includes the phenomena of gas phase and surface radiation. The boundary layer equations are transformed to a set of ordinary differential equations using a local similarity approximation. Numerical solutions are obtained by a finite difference procedure. Results are presented for a fuel having the properties of PMMA burning in O₂/N₂ mixtures. For this system, it is found that the effects of gas phase radiation are not significant. The surface burning rate is shown to have a strong dependence on surface radiation, but only a weak dependence on chemical reaction rate. Predicted extinction limits are found to depend on both the chemical reaction rate and the surface heat loss rate. The calculated results are compared with experiments using N₂ and CF₃Br, which show the same effect of these additives on burning rate, but give different extinction limits. This qualitative behavior is reproduced by the theoretical results when the "chemical effect" of CF₃Br is modeled by reducing the overall reaction rate.