Abstract
This work presents a scale analysis to explore the role played by forward (longitudinal) solid conduction in the mechanism of opposed-flow flame spread over flat and cylindrical fuels. Closed-form expressions in terms of known parameters and properties are derived for a non-dimensional conduction number, which compares solid phase forward conduction with the gas to solid conduction in the preheat zone. The corresponding expressions for cylindrical fuels are related to the flat fuel expressions using a curvature factor that depends on fuel radius and flow velocity. The results of the analysis are compared to existing experimental data for flame spread over thick flat and cylindrical fuels. For thin fuels, a comprehensive numerical model is used to evaluate the conduction number for comparison with the prediction of the analysis. An energy balance at the leading edge, taking into account the longitudinal conduction through solid, produces a spread rate formula that is related to the well-known thermal limit through the conduction number.
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