Downward flame spread along a vertical surface of a thick solid in the thermal regime

An analysis is presented of the steady two-dimensional spread of a flame do wn a vertical surface of a thermally thick solid fuel, under the assumption s that the gas-phase reaction is infinitely fast and that vaporization of t he solid occurs at a constant temperature. A condition of regularity of the solid phase temperature, the gas phase mixture fraction and enthalpy, and the mass vaporization flux at the vaporization front is proposed to determi ne the dame spread rate. Numerical solutions computed using this condition show that the spread rate decreases with decreasing heat of reaction and be comes zero for a certain heat of reaction. An order-of-magnitude analysis i s given for the case when heat conduction in the solid dominates heat condu ction in the gas.