Towards wind-aided flame spread along a horizontal charring slab: The steady-flow problem

The spread of fire across the ceiling of a large room (or long corridor) in a structure is modeled as wind-aided flame spread along a horizontal char-forming thick slab, in the presence of significant convective, diffusive, and radiative transport. The goal is to predict the rate of streamwide advance of the site on the solid-gas interface at which the pristine solid undergoes endothermic degradation to a combination of (1) a porous carbonaceous heat retaining matrix, and (2) a mixture of partially combustible vapors that move through the matrix to the outer gas. This rate of advance of the thermal degradation site is sought as a function of normally available data concerning the thermodynamic and physical properties of the solid and the thermodynamic and dynamic state of the hot vitiated bulk gas that flow over the slab. A nonlinear, unsteady, two dimensional, treatment in the Shvab-Zeldovich approximation entails boundary layer simplification in the manner of Prandtl convective transport simplification in the manner of Oseen, and thin flame simplification in the manner of Burke and Schumann. The formulation given here is general and is limited to the steady state problem.