The Dependence of Flame Propagation on Surface Heat Transfer II. Upward Burning

Abstract

Solutions for the flame propagation rate resulting from a given distribution of surface heat flux are presented for upward burning of finite slabs and rods and for a semi-infinite fuel bed. These results are combined with expressions for heal transfer to burning, vertical surfaces to give approximate formulas for the flame spreading velocity in terms of the properties of the fuel-oxidizer system and an empirical forward heat transfer parameter φ, For slabs of finite thickness, flame propagation is found to be steady for φ < φ_crit and unsteady for φ > φ _crit; for steady propagation, the curve of flame spreading velocity versus slab thickness passes through a minimum. For thermally thick fuel beds, simple relationships are obtained between the flame spreading velocity and the instantaneous height of the pyrolysis region. A comparison with experimental data on thermally thick slabs of PMMA yields a value of φ = 0.13 in the turbulent heat transfer region.