  A three-dimensional, steady, laminar shear-layer flow spatially developing
under a boundary-layer approximation with mixing, chemical reaction, and
imposed normal strain is analyzed. The imposed strain creates a counterflow
that stretches the vorticity in the spanwise direction. The equations are
reduced to a two-dimensional form for three velocity components. The
non-reactive and reactive cases of the two-dimensional form of the governing
equations are solved numerically, with consideration of the several of
parameter inputs such as Damk\"ohler number, Prandtl number, chemical
composition, and free-stream velocity ratios. The analysis of the non-reactive
case focuses on the mixing between hotter gaseous oxygen and cooler gaseous
propane. The free-stream strain rate \kappa is predicted by ordinary
differential equations based upon the imposed spanwise pressure variation.
One-step chemical kinetics are used to describe diffusion flames and
multi-flame structures. The imposed normal strain rate has a significant effect
on the width of downstream mixing layers as well as the burning rate.
Asymptotically in the downstream direction, a constant width of the shear layer
is obtained if imposed normal strain rate is constant. A similar solution with
layer width growing with the square root of downstream distance is found when
imposed strain rate decreases as the reciprocal of downstream distance.
