Numerical solution

Note that you will want to run this several times changing the value of β over the greatest possible range.  If β=0, the result is the same as a flat plate.    

need to run one time to get a value for the outer f'[infinity]

Again note that this is magnitude of the normal velocity after it has been rescaled to be of order 1.  It is really smaller by the relative thickness of the boundary layer to the distance variable -- as required by the continuity equation.