A survey of the characteristics and predictions of the different theoretical models of the spread of flames over the surface of a solid combustible in opposed or concurrent oxidizing flows shows that, at present, there is a good understanding of what are the controlling mechanisms of the flame spread process andl of what is the necessary formulation to develop a rigorous analysis of the phenomenon. It also shows, however, that the problem is very complicated and difficult to solve mathematically particularly if an analytical solution is sought, and that this complexity is what has prevented so far the development of an analysis capable of describing accurately the flame spread process under realistic conditions where material properties, finite rate kinetics, turbulence and radiation effects can determine the characteristics of the process. Although some of the analyses presently available are capable of predicting quantitatively or at least qualitatively rates of flame spread under certain limiting conditions, it appears that the development of a rigorous numerical analysis will be necessary to predict accurately the flame spread process under varied material and environmental conditions.
INTRODUCTIONThe phenomena of the spread of flames over the surface of a combustible material has received considerable attention during the last few years particularly with regard to the prevention and control of fires. The spread of the flame results from the complex interaction of transport processes in the gas and condensed phases, the vaporization of the fuel and the chemical reaction of the fuel vapors with the gaseous oxidizer. Although much progress has been made primarily through experimental information toward the understanding of the controlling mechanisms of the flame spread process (Fernandez-Pello and Hirano, 1983), the complexity of the problem has so far prevented the development of accurate theoretical models of the process.The formulation of a rigorous mathematical model of the flame spread process would consist of the conservation equations for the reacting gas phase coupled at the interface to the condensed phase conservation equations through the appropriate boundary conditions. This would require the solution of a system of coupled, twodimensional, elliptic, nonlinear partial differential equations that would include variable material properties, appropriated gas phase chemical kinetics and solid phase pyrolysis mechanisms. The solution of this fun problem, even after considerable simplifications, is very difficult. For this reason the analyses developed to date have treated the problem at different levels of complexity. The simpJler models are limited to solid phase energy balances with a priori specified conditions-at the solid-gas interface. More refined models include the analysis of the solid and gas phases, but assume that the rate of the chemical reaction is infinite. The flame spread rate appears in these analyses as an eigenvalue which value is the result sought. These models can be classified as h...