Consider the steady-state laminar flow of an incompressible and constant property fluid parallel to a horizontal, infinitely large flat plate. Away from the surface the velocity of the fluid is U ∞ ,...

Consider the steady-state laminar flow of an incompressible and constant property fluid parallel to a horizontal, infinitely large flat plate. Away from the surface the velocity of the fluid is U_∞, and its temperature is T_∞. Assume that the plate is porous, and fluid with a constant velocity of v_s
is sucked into the plate.

a. Prove that the velocity profile in the direction parallel to the plate is given by

b. Assume that a boundary layer can be defined, at the edge of which u/U_∞
= 0.999. Find the boundary layer thickness for water and air at room temperature and atmospheric pressure.

c. Repeat Parts a and b, this time assuming that fluid is blown into the flow field through the porous plate with a constant velocity vs.

d. Assume that the plate is at a constant temperature Ts. Find the temperature profile in the fluid.