Exact Solution for the Rate of Creeping Flame Spread over Thermally Thin Materials

Abstract

In this work we present the exact solution for the rate of creeping flame spread over thermally thin materials based on de Ris' (1969) formulation of the problem. The publication of the present work was prompted by a recent paper by Wichman and Williams (1984). These authors noted that de Ris (1969) obtained theoretical values for flame spread rates which are by a factor of two larger than recent experimental data (Fernandez-Pello et at., 1981). Wichman and Williams (1984) correctly suggested that this discrepancy between the theory and the experiment may have resulted from an approximation by de Ris(1969) of an irrational kernel by a rational function. The substitute kernel used by de Ris (1969) allowed him to obtain an analytical solution of the flame spread rates; however, this approximation may have introduced errors in the calculation of proportionality constants. The exact solution for creeping flame spread rates, which we present in the final analysis, agrees with the experimental data.

In this work, we use essentially the same formulation of the flame spread problem as de Ris (1969) presented earlier. Specifically, we consider flame spread over a thermally thin material in an opposing air flow; flame spread occurs by thermal djffusion of heat upstream of the fire origin.