The burning of vertical wooden slabs

Abstract

A theoretical treatment is presented on the laminar, natural convective burning of vertical wooden slabs, coupling both the gas-phase laminar diffusion flame processes and the in-depth wood pyrolysis in the solid phase. The problem considered in this paper is symmetrical with respect to the central plane of the slab. The mechanisms included in the model for transient solid phase pyrolysis are conduction and internal convection with variable thermal properties, and a single Arrhenius decomposition with a heat of decomposition. In the gas phase, the following major assumptions are made: (1) unit Lewis number; (2) a single global chemical reaction; and (3) no radiative emission or absorption by the flame. The radiant heat flux emitted by the slab surface, however, is considered. Comparisons with experimental results are quite favorable. Sample computations show that the maximum burning rate per unit surface area varies very slowly with slab thickness for slabs with half-thicknesses between 0.1 cm and 0.35 cm (approximately as the −0.041 power). For slabs of half-thickness greater than 0.4 cm but smaller than 0.6 cm, the maximum burning rate per unit surface area varies more rapidly (approximately as the −0.324 power of the half-thickness). It is also shown that the maximum total burning rate varies approximately as the 0.625 power of the height for slabs with half-thicknesses between 0.1 cm and 0.4 cm.