ANALOGIES AMONG MOLECULAR TRANSFER PHENOMENA

Your objectives in studying this section are to be able to  

Identify the analogies among molecular momentum, heat, and mass transfer for the simple case of fluid flow past a flat plate. 

Define and interpret the following dimensionless numbers Schmidt, Prandtl, and Lewis. 

In the flow of a fluid past a phase boundary, there will be a velocity gradient within the fluid which results in a transfer of momentum through it. In some cases, there is also a transfer of heat by virtue of a temperature gradient. The processes of momentum, heat, and mass transfer under these conditions are intimately related, and it is useful at this point to consider the analogies among them. 

Consider the velocity profile for the case of a fluid flowing past a stationary flat plate. Since the velocity at the solid surface is zero, there must necessarily be a sublayer adjacent to the surface where the flow is predominantly laminar. Within this region, the shearing stress T required to maintain the velocity gradient is given by 

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