A cold liquid film flowing down a vertical solid wall, as shown in the figure, has a considerable cooling effect on the solid surface. Estimate the rate of heat transfer from the wall to the fluid for such short contact times that the fluid temperature changes appreciably only in the immediate vicinity of the wall.

a$.$ Determine the velocity distribution in the falling

film

b$.$ Show that in the vicinity of the wall the velocity is a

linear function of $y$ given by $v_z\frac{g}{}y$

c$.$ Simplify the energy equation and write the

assumptions made along the way