Thermal Structure in the Gas Phase

Similar to the expression for the condensed phase, the thermal diffusivity in the gas phase is given by g = Xg/pgCg and is assumed to be independent of temperature. The thermal wave thickness in the gas phase 6g is defined according to 6g = Og/Mg. Then, Eq. (3.46a) can be written as  

When the term in the exponent Xg/6g 1, a simplified expression for the heat flux feedback from the gas phase to the solid phase is obtained  

This asymptote occurs whenever the heat transferred back to the burning surface is small compared to the heat released in the gas phase, which implies that Xg/bg is sufficiently large. Though Eq. (3.48) is not precise, it indicates the burning rate behavior without introducing mathematical complexities and reaction parameters. 

If one can assume that the chemical reaction represented by a step function starts at %i = 0, i. e. the burning surface, and ends at x = Xgin the gas phase, as shown in Fig. 3.14, Eq. (3.46d) can be rewritten as 

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