Flames with multiple-step chemistry

Let us now consider flames in which more than one chemical reaction occurs. If assumptions 1-7 of Section 5.2 and the isobaric approximation p constant are retained, then the flame equations may be taken as 

T below the ignition temperature and Wj is given by equation (1-8) for T above the ignition temperature, then a reasonable set of boundary conditions [for example, Yi = at t = 0 and all , are specified at t = 0, while Yi = Ci at T = 1 and chemical equilibrium exists (w = 0) at t = 1] is expected to determine a (unique) solution to equations (80) and (81) only for a particular value of the mass burning rate m. 

The normalized temperature t, given by equation (40), is a convenient independent variable only if it varies monotonically with distance through the flame. Although it is conceivable that nonmonotonic behavior of t could occur—for example, for flames in which endothermic reactions become dominant at the highest temperatures—no practical examples of adiabatic flames with temperature peaks or valleys are known the use of t seems appropriate from the viewpoint of monotonicity. The main limitation to the formulation given is assumption 7 to the effect that Cp i = Cp = constant. This assumption can be removed, with t = (T — Tq)I(T — Tq), merely at the expense of complicating the definition of / in equation (82), namely, /=Z7= 1 oo)/Cp(T — To), where each hj is a known function 

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