Vorticity is generated any time a fluid contacts a solid surface. The vorticity diffuses from the solid surface and is convected away by the fluid. Consider the heat transfer to a falling film problem of Section 10.3.

a. Write the vorticity transport equation analog of the falling film heat transfer problem.

b. Use the heat transfer solution as a template and derive the corresponding solution for the vorticity problem. The vorticity is zero at the air/water interface and can be found at the solid interface using the velocity profile.

c. How do the penetration depths for the two problems compare?

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FIGURE P10.31 Oil