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 u = U_∞[1 − exp(−vs ν y)]

(b) Assume 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 the 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.