An infinity long, flat plate is initially at rest immersed in a liquid pool with properties n, α, T∞,. The plate is also in thermal equilibrium with pool. At a certain instant, t=0, the plate starts moving at constant velocity U along itself. Determine the time dependent velocity distribution in the fluid, for times t>0 in the immediate vicinity of the solid wall.

At time t=t1, the plate temperature is changed to a new temperature T=T0. Determine the time dependent temperature distribution in the fluid in the immediate vicinity of the wall for t>t1. Note that the temperature does not change along the plate; it is only changes with time and perpendicular to the plate.