Using a linear velocity profile for the velocity within the boundary layer, use our boundary integral analysis to derive a new expression for the friction number, \(N_{f}\). How does \(N_{f}\) depend upon the Reynolds number? Assuming your fluid has a Schmidt number \(>1\), derive an expression for the Sherwood number based on your results for \(N_{f}\).

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12.3 BOUNDARY LAYER DEFINITIONS In convective transport, we generally presume that most of the action takes place in a very small region near the surface of an object or phase called the boundary layer. The hydrodynamic bound- ary layer, for example, is shown in Figure 12.2. Within the hydrodynamic boundary layer, vis- cous forces are dominant, and momentum is transported perpendicular to the plate by diffusion. Outside the boundary layer, inertial effects are dominant, and momentum is transported by bulk fluid motion alone. The boundary layer is not a well-defined region of space. We cannot see it easily nor can we truly tell where it ends and the free steam begins. Thus, we define the thickness of the hydrodynamic boundary layer as the distance between the plate's surface and the point where the velocity in the boundary layer is 99% of the free-stream velocity. 8h = f(x) where Vx (8h) = 0.99v (12.17)