Figure below shows two infinite plates $2$h apart and an initially stagnant fluid of constant properties between them. The upper plate moving with velocity v $=$ U$,$ while lower plate is stationary. Assume $1)$ Steady state conditions, $(2)$ No pressure drop; and $(3)$ the upper plate is held at temperature T and the lower plate at To$.$ Derive the velocity profile, vz$($y$),$ and temperature profile T$($y$).$ Also, find the shear stress.

If a constant pressure drop $(\frac{P}{L}$ is applied between two plates similar to problem $3$ but of length $L,$ derive the velocity profile for this case.