The equations describing combustion in a flow field are modified for use in laminar flows where the so called boundary layer approximations may be employed. These equations are transformed into a corresponding incompressible flow with the Howarth transformation.
As an example of the use of boundary layer concepts this analysis considers the ignition and combustion in the laminar mixing zone between two parallel moving gas streams. One stream consists of a cool combustible mixture, the second is hot combustion products. The two streams come into contact at a given point and a laminar mixing process follows in which the velocity distribution is modified by viscosity, and the temperature and composition distributions by conduction, diffusion and chemical reaction. The decomposition of the combustible stream is assumed to follow first-order reaction kinetics with temperature dependence according to the Arrhenius law. For a given initial velocity, composition, and temperature distribution, the questions to be answered are: (1) Does the combustible material ignite and (2) How far downstream of the initial contact point does the flame appear and what is the detailed process of development?
Since the hot stream is of infinite extent it is found that ignition always takes place at some point of the stream. However when the temperature of the hot stream drops below a certain value, the distance required for ignition increases so enormously that it essentially does not occur in a physical apparatus of finite dimension. The complete development of the laminar flame front is computed using an approximation similar to the von Karman integral technique in boundary layer theory.
