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## Model of Transport of Fuel Gases in a Charring Solid and Its Application to Opposed-Flow Flame Spread.

Model of Transport of Fuel Gases in a Charring Solid and Its Application to Opposed-Flow Flame Spread. (377 K)
Baum, H. R.; Atreya, A.

Volume 31; Part 2;

Combustion Institute, Symposium (International) on Combustion, 31st. Proceedings. Volume 31. Part 2. August 5-11, 2006, Heidelberg, Germany, Combustion Institute, Pittsburgh, PA, Barlow, R. S.; Sick, V.; Glarborg, P.; Yetter, R. A., Editor(s)(s), 2633-2641 pp, 2007.

### Keywords:

combustion; fire research; flame spread; fuels; mathematical models; charring; solids; degradation; char; pressure differential; equations; mass transfer

### Abstract:

This paper outlines the development of a mathematical model for the transport of gases through the char matrix of a burning solid. Two basic assumptions are made. First, the gases evolved by the degradation of the virgin material are transported by pressure differences through a network of narrow passageways created in the char by the conversion of material from the solid to the gas phase. This process is treated as flow through a porous medium, with the mass flux related to the pressure gradient by Darcy's law. Second, the gas temperature is the same as the local char temperature. This model is first used to study the time-dependent thermal degradation of a semi-infinite charring solid heated above the charring temperature. Then, the opposed flow flame spread treated by Atreya and Baum is revisited. It was found that the solution to the condensed phase flame spread problem is identical to the initial transient problem. Weak dependence of the solution on the accumulation parameter ss validates the assumption made in and completes the flame spread solution. Fuel mass flux follows the heat flux lines and is normal to the isobars. Calculations using representative values for wood show that the pressure generation at the char-virgin material interface is considerable and equal to 13.27 kPa. Finally, in view of the fact that the nonlinear pressure equation poses considerable numerical difficulties, this analytical solution may help in determining the stability and accuracy of the numerical scheme used for more complicated problems.