Consider the heat transfer to a falling film problem of Section 10.3. The mass transfer analog is the dissolution of a solid wall into the falling film. Assuming the solid wall is composed of salt, \(\mathrm{NaCl}\), use the heat transfer solution as a template, assume dilute solutions, and derive the corresponding mass transfer solution. How do the penetration depths for the two problems compare?

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10.3 ENERGY TRANSPORT In section 10.2.3 we derived the mechanical energy balance considering the kinetic energy of the system. Though not appearing explicitly, the potential energy of the system was treated as a work term against the applied body force, gravity. To derive the full energy balance, we must include the internal energy of the fluid and must also account for heat flows that result due to temperature gradients within the system. Figure 10.11 shows the control volume for deriving the energy equa- tion. We have energy flowing into and out of the control volume by convection and by diffusion due