Effects of radiation on the burning of vertical fuel surfaces

An analysis of laminar, free convective burning of a thermally thick, vertical fuel surface is presented. The analysis differs from previous work on this problem by including the effects of gas phase and surface radiation. Schvab-Zeldovich variables are used and the thin flame assumption is made. The boundary layer equations are transformed to a set of ordinary differential equations by use of a local similarity approximation. Numerical solutions are obtained using a finite difference procedure. Results are presented for PMMA burning in O₂/N₂ mixtures. It is found that gas phase radiation has a neglible effect on burning rate (for this laminar, vertical configuration). Surface radiation is found to strongly affect the results. Whereas adiabatic solutions exist at all oxygen concentrations in the thin flame formulation (i.e., for infinite chemical reaction rates), the inclusion of surface radiation leads to predictions of extinction at Y_{O, ∞}=0.12 for complete combustion and up to Y_{O, ∞}=0.18 for incomplete combustion. At oxygen concentrations above these limits surface radiation increases the convective heat flux and decreases the burning rate relative to the adiabatic results.