A computational model of flame spread over a thermally thick solid fuel in an opposing-flow environment is presented. Unlike thermally thin fuels, for which the effect of fuel surface radiation is negligible for high levels of opposing flow, fuel surface radiation is important for thermally thick fuels for all flow levels. This result is shown to derive from the fact that the ratio of the rate of heat transfer by re-radiation from the surface to that by conduction from the gas to the solid is proportional to the length over which heat can be conducted forward of the flame to sustain spreading. For thin fuels, this length decreases with increasing flow velocity such that while radiation is important at low flow velocities it is not at the higher velocities. For thick fuels at low flow velocities, the conduction length is determined by gas-phase processes and decreases with increasing flow velocity. But at higher flow velocities, the conduction length is determined by solid-phase processes and is rather independent of the gas-phase flow. The result is that over a wide range of flow velocities, the conduction length of importance does not change substantially as it switches from one phase to another so that the ratio of radiation to conduction is of unit order throughout that wide range of flow.

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