Solution
= Solution
The wall is stationary in the laboratory and moves with velocity $+U\mathbf e_x$ in the sheet frame. Its <no-slip boundary condition> is therefore
$$
\boxed{\psi_y(x,d,t)=U,\qquad \psi_x(x,d,t)=0.}
$$
The first equation prescribes wall tangential velocity; the second imposes zero normal velocity. The streamfunction may have a constant mean value on the wall, set by the fluid transport, and that constant need not equal its value at the sheet.