Laminar boundary layers with uniform shear cross flow

Laminar boundary layers with fully developed uniform shear cross flows are considered. The first streamwise laminar flow is a Blasius boundary layer flow, the second is uniform shear flow over a semi-infinite plate, and the third is the flow induced by a power-law stretching surface. In the first two cases, the effect of streamwise plate motion is taken into account by the parameter λ. In each case, the similarity solutions reduce the governing boundary layer equations to a primary ordinary differential equation for the streamwise flow and a secondary linear equation coupled to the primary solution for the cross flow. It is found that an infinity of solutions exist in each problem and the unique solution in each case is found by applying the Glauert criterion. In some instances, a simple exact solution for the cross flow is presented. Results for the wall shear stresses and velocity profiles are given in graphical form.