Analysis of the constant B-number assumption while modeling flame spread

Recent experimental data show that the B-number of a solid fuel is not a constant, as predicted by classical 2-dimensional theory. Due to conduction and radiation losses that take place along the length of the pyrolysis region of a solid fuel sustaining an upward spreading flame, the mass transfer number changes as one progresses from the leading edge to the trailing edge of the flame. Experimental results on PMMA show that the B  -number follows a power law relationship of the form B=k1tk2B=k1tk2, where k1k1 and k2k2 are constants that can be determined using an experimental set up discussed in this paper. The theory used to obtain a B-number of a solid fuel from the stand-off distance (the distance of the flame sheet from the surface of the fuel) was obtained by Torero et al. [J.L. Torero, T. Vietoris, G. Legros, P. Joulain, Combust. Sci. Technol. 174 (11–12) (2002) 187–203]. The current work extends this theory by obtaining a relationship between the B  -number and the stand-off distance of the form yf=A(B)x1/4yf=A(B)x1/4, where yfyf is the standoff distance along x  , the streamwise direction, and A(B)A(B) is a function that depends only on the B-number. An immediate application of the current experimental and theoretical work is the prediction of flame length of an upward spreading flame.