= Solution
At the upper wall,
$$
\mu u'(h)=\frac{2\mu U}{h}.
$$
This is the shear exerted by the plate on the fluid in the positive $x$-direction. By action and reaction, the flow exerts on the top plate the stress
$$
\boxed{-\frac{2\mu U}{h}e_x}.
$$
The same result follows from a force balance on a rectangle of length $\delta x$ and full height $h$. The <pressure> force is $-G_0h\,\delta x\,e_x$, the bottom shear vanishes, and equilibrium requires the top plate to exert $G_0h\,\delta x\,e_x$ on the fluid. Thus the fluid exerts $-G_0h\,e_x=-2\mu Ue_x/h$ on the plate. These results form the <Couette-Poiseuille flow with a stress-free stationary wall>.
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