Plots of the results

Here is the tangential velocity

Here is the dimensionless normal velocity.   Note also that it does not go to 0 at the top of the layer.  Fluid is being expelled as the layer thickens!

The second derivative, f'' is related to the stress on the plate.  

Three important results are obtained.  First, the graphs show that the effective boundary layer thickness is about 6 in η.  Second, the vertical velocity is not 0 at the top of the boundary layer -- fluid is being expelled.  It has to be, the fluid inside the boundary layer is being slowed down.
Third, the wall shear stress and other transport properties are related to the value of f''[0] = .332058.