It is essential that the designer of shell-and-tube exchangers becomes familiar with the principles of the various correlations and methods in numerous publications, their advantages and disadvantages, limitations, and degrees of sophistication versus probable accuracy and other related aspects. All the published methods can be logically divided into several groups:

1. The early developments based on flow over ideal tube banks or even single tubes.
2. The “integral” approach, which recognizes baffled cross flow modified by the presence of a window, but treats the problem on an overall basis without consideration of the modifying effects of leakage and bypass.
3. The “analytical” approach based on Tinker’s multistream model and his simplified method.
4. The “stream analysis method”, which utilizes a rigorous reiterative approach based on Tinker’s model.
5. The Delaware method, which uses the principles of the Tinker model but interprets them on an overall basis, that is, without reiterations.
6. Numerical prediction methods. Here an attempt is made to predict the shell-side flow pattern by solving the flow equations numerically for a mesh suitably selected to describe the shell. Applications of this method are described by Patankar and Spalding (1974) and Butterworth (1978). Once the velocity is specified, the heat transfer coefficient may also be calculated on a local basis. However, although this method is promising, it is difficult to apply to complex cases and, for design purposes, it is not yet a substitute for the other methods listed.

A good review of the state of the art as of 1960 was published by Emerson (1962 and 1963). Only the most pertinent comments to the various correlations and methods of the “early and integral” type are included here, mainly because some are still used in industry. The more recent methods based on Tinker’s flow model will be reviewed in greater detail, as present and foreseeable future developments appear to be best handled by this approach.

A. Early developments

It was recognized in the early 1930s that baffled shell-side flow will behave similarly to flow across ideal tube banks, for which wind tunnel data were emerging. The first heat transfer correlation suggested is due to Colburn (1933) in the form