Flame spread along horizontal solid fuel cylinders

The spread of a flame along a thermally thick horizontal solid fuel cylinder in a quiescent atmosphere is analyzed modeling the gas-phase kinetics by means of a single-step irreversible Arrhenius reaction and assuming that vaporization of the solid occurs at a constant temperature. The natural convection flow of the warm gas surrounding the flame is mostly normal to the axis of the cylinder, but a weak flow is also induced along the axis by the axial gradient of the pressure variation that gravity generates in the warm gas. This latter flow aids flame propagation in the lower part of the cylinder. The effects of finite rate kinetics and of radiative losses from the surface of the solid are studied, computing the spread rate as a function of the Damkohler number, the oxygen concentration in the atmosphere and the strength of the radiative losses for a set of material properties chosen to mimic flame spread on PMMA. The effect of a small inclination of the cylinder is also discussed, showing that a continuous transition from upward to downward flame spread occurs when the tilt angle is small of the order of the inverse of the power 1/8 of the Grashof number based on the radius of the cylinder.