Friction factors with surface mass transfer

An industrial chemical reacdor is a complex device in which heat transfer, mass transfer, diffusion, and friction may occur along with chemical reaction, and it must be safe and controllable. In large vessels, questions of mixing of reactants, flow distribution, residence time distribution, and efficient utilization of the surface of porous catalysts also arise. A particular process can be dominated by one of these factors or by several of them for example, a reactor may on occasion be predominantly a heat exchanger or a mass-transfer device. A successful commercial unit is an economic balance of all these factors. 

Because pressure drop measurements are much faster and cheaper than mass transfer or heat transfer measurements, it is tempting to try to relate the Sherwood and Nusselt numbers to the friction factor. A relation that has proved successful for smooth circular tubes is obtained from a plausible assumption that is known as the film layer model. The assumption is that for turbulent flow the lateral velocity, temperature, and concentration gradients are located in thin films at the wall of the channel the thickness of the films is indicated with 8/, 87, and 8., respectively. According to the film model, the lateral velocity gradient at the channel surface equals (m)/8/, the lateral temperature gradient equals (T/, - rj/87 and the lateral concentration gradient equals (c. /, - C , )/8,.. From these assumptions, and the theoretical knowledge that 8//8r Pr and 8//8e Sc (for... 

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