2. Consider the flow of a finite layer of viscous fluid on an oscillating plate shown in Figure 2. The

plate has an oscillating velocity Uo cos(t) at y = 0. The fluid is of finite thickness h and the surface at

y =h is stress-free.

Consider a constant pressure gradient (

op = -K ) is applied along the flow direction x.

Əx

(a) Solve the equations of motion analytically for this flow. Clearly state the assumptions.

(b) Plot the velocity distribution and discuss the results for the following cases:

(i) K = 0, (ii) K>0, and (iii) K <0.

Uplate = Uo cos(t)

Stress-free

h

Figure 2. Flow over an oscillating plate.

y

x