A theoretical description is presented for a laminar diffusion flame spreading against an
air stream over a solid- or liquid-fuel bed. Both a thin sheet and a semi-infinite fuel bed are
considered. The burning process is described as follows: The hot flame heats the unburned
fuel bed, which subsequently vaporizes. The resulting fuel vapor reacts with the oxygen
supplied by the incoming air, thereby producing the heat that maintains the flame-spread
process.
The formulated model treats the combustion as a diffusion flame, for which the details
of the reaction kinetics can be ignored by assuming infinite reaction rates. The model includes
the chemical stoichiometry, heat of combustion, gas-phase conductive heat transfer,
radiation, mass transfer, fuel vaporization, and fuel-bed thermal properties. The radiation
is mathematically treated as a heat loss at the flame sheet and a heat gain at the fuel-bed
surface.
The calculated flame-spread formulas are not inconsistent with available experimental
data. These results reveal much of the physics involved in a spreading flame. For instance, the
flame-spread rate is strongly influenced by (1) the adiabatic stoichiometric flame temperature,
and (2) the fuel-bed thermal properties, except for the fuel-bed conductivity parallel
to the propagation direction.