Nusselt number drop models

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... 

Equations for Outside Nusselt Number [(ARe)c < 1] Rigid-Drop Model... 

The fundamental principle in scaling models is to keep all dimensionless variables constant. The dimensionless equations, e.g. Equations (4.12)-(4.15), are scale independent, and keeping Re, Pr, Eu, and Fr numbers constant results in dimensionless variables, G, p, f, and C versus t that is the same at all scales. In the simplest case, scaling with a constant Re, i.e. an increase in length scale by a factor of 10, requires that the characteristic velocity decreases by a factor of 10. As a result, assuming no density difference, i.e. Fr = 0, Eu will be constant and the pressure drop is scaled with pU. Keeping Re and Pr constant should also result in the same dimensionless heat transfer coefficient, i.e. the Nusselt number, as obtained in the dimensionless correlations in Example 4.1. 

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