Couette-Poiseuille flow with a stress-free stationary wall

For $U_0=0$, $U_1=U$, and constant $G=p_x$, zero shear at $y=0$ requiresThe velocity becomes $u=U{y}^2/h^2$, the flux per unit width is $Uh/3$, and the fluid exerts shear $-2\mu U/h$ on the moving upper wall.