A Simplified Model of Flame Spread in an Opposed Flow along a Flat Surface of a Semi-infinite Solid

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Abstract
A flame-spread model is analyzed in which heat release occurs at the planar interface of two media, each of which moves with a different but constant velocity. The steady-state, two-dimensional equations for conservation of energy in each medium are solved subject to a prescribed temperature distribution on the downstream half of the interface and continuity of the normal heat flux on the upstream half. Differing thermal conductivities in normal and streamwise directions are allowed in each medium. The approach involves introduction of Fourier transforms in the streamwise coordinate and use of the Wiener-Hopf technique. The model is shown to be equivalent to that of de Ris with radiant transfer neglected and also may be interpreted in terms of distributed electrical or radiant heating without combustion. Parametric results are obtained for various heat fluxes and for spread rates. The study helps to improve understanding of mechanisms of flame spread under conditions controlled by heat transfer.

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