Stretched one-dimensional flames

Counterflow flame geometries. Stretched one-dimensional flames 

For axisymmetric, inviscid, steady state potential flow of an incompressible fluid, the velocity distribution in the neighborhood of the stagnation point 

As remarked in Section 2.2, most flames are essentially constant pressure systems, and if the flow is inviscid it is then not necessary to consider the momentum equation at all. Inviscid flow will be assumed for the purpose of the following discussion. Since the flame lies in the radial direction (Fig. 11), the gradients of all dependent variables except the radial velocity are zero in this direction, and the radial diffusive fluxes also vanish. By use of Eqs. (2.1) and (2.2b), conservation of mass in the steady state axisymmetric flow gives 

Treating the variable density flow in the flame by a procedure parallel to that of Section 4.1, we introduce the transformation [cf. Eq. (4.8)] 

By methods similar to those outlined in Sections 2.3 and 2.4, the species and energy continuity equations for the steady state system become 

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