Preliminary assumptions and equations

In order to analyze the structure of a combustion wave, it will obviously be expedient to adopt a coordinate system which is at rest with respect to the wave. The following assumptions will then be made  

The flow is steady, plane, and one-dimensional in the adopted frame of reference. 

The approximate validity of these assumptions and of others to be made subsequently can be justified by order-of-magnitude considerations for many systems. 

In view of assumptions 1-6, if x is the coordinate normal to the combustion wave, then equations (1-26), (1-27), (1-31), (1-32), and (1-33) are valid with 2 = 3 = and with the last term in equation (1-32) omitted. Thus 

The boundary conditions for these differential equations are to be applied at x = — oo (where properties will be identified by the subscript 0) and at x = -h oo (where properties will be identified by the subscript oo). At X = — 00, all properties are uniform djdx 0) (see, however, Section 2.1.2) and the values of all variables except Vq are known (compare Section 2.1.3). At x -hoo, properties again become uniform djdx = 0) and chemical equilibrium is reached. In Chapter 2 (Section 2.1) it was shown that these conditions imply that relationships exist between the properties at X = -h 00 and those at x = — oo. 

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