Reactive-diffusive zones

For steady-state diffusion flames with thin reaction sheets, it is evident that outside the reaction zone there must be a balance between diffusion and convection, since no other terms occur in the equation for species conservation. Thus these flames consist of convective-diffusive zones separated by thin reaction zones. Since the stretching needed to describe the reaction zone by activation-energy asymptotics increases the magnitude of the diffusion terms with respect to the (less highly differentiated) convection terms, in the first approximation these reaction zones maintain a balance between diffusion and reaction and may be more descriptively termed reactive-diffusive zones. Thus the Burke-Schumann flame consists of two convective-diffusive zones separated by a reactive-diffusive zone. 

So long as the finite-rate chemistry occurs in a single reactive-diffusive zone extending to the surface of the condensed phase, the analysis need not be restricted to a one-step reaction. Known mechanisms of homogeneous polymer degradation may be taken into account—for example, [45]. The results continue to be expressible in formulas that resemble equation (29) but that usually are somewhat more complicated. 

The second way in which the derivation of equation (5-75) can fail is for the thickness of the reactive-diffusive zone in the gas to become comparable in size with the thickness of the convective-diffusive zone. This occurs if (T — 7])/T becomes of order which would be favored by low overall... 

With few exceptions [177]-[180], [223]-[225], recent analyses of diffusive-thermal phenomena in wrinkled flames have employed approximations [208] of nearly constant density and constant transport coefficients, thereby excluding the gas-expansion effects discussed above. Although results obtained with these approximations are quantitatively inaccurate, the approach greatly simplifies the analysis and thereby enables qualitative diffusive-thermal features shared by real flames to be studied without being obscured by the complexity of variations in density and in other properties. In particular, with this approximation it becomes feasible to admit disturbances with wavelengths less than the thickness of the preheat zone (but still large compared with the thickness of the reactive-diffusive zone). In this approach it is usual to set v = 0 equations (87)-(90) are no longer needed, and equations (93) and (95) are simplified somewhat. It... 

Nonadiabaticity and Lewis numbers differing from unity modify the rate of heat release per unit area. Let us rule out distributed heat loss and consider nonadiabaticity associated with the temperature of the product stream at infinity,, differing from the adiabatic flame temperature, T j-. If the product stream is hotter (a superadiabatic condition), then by enhancing heat conduction (through reducing distances over which heat conduction occurs) and by bringing the reactive-diffusive zone closer to the product side of the stagnation point, an increase in k results in an increase in the flame temperature at the reactive-diffusive zone and thereby increases... 

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