An analysis is carried out of the steady spread of a flame with infinitely
fast kinetics over a thermally thin solid rod in the absence of gravity. Du
e to the radial convergence on the solid surface of the heat flux heating a
nd vaporizing the fuel, the spread rate is found to be higher than for a fl
ame spreading over a slab, and the region of the gas around the flame which
is affected by molecular transport is large compared with the radius of th
e rod. The effects of radiation, of a buoyancy force opposing flame propaga
tion and of axial heat conduction in the solid are discussed briefly.