A. BACKGROUND

Some historical facts are relevant. Every mathematical analysis of engineering equipment is based on idealizations of reality, and by the mid-1930s those appropriate to heat exchangers were well established as, namely, the following:

• Idealization 1: the heat transferred between fluid streams separated by solids is proportional to an overall heat-transfer coefficient, uniform in value throughout the exchanger
• Idealization 2: the two heat exchanging streams flow in some combination of parallel-flow, counter-flow, or cross-flow patterns relative to one another.

These idealizations allowed analytical expressions to be derived for the total heat transfer effected by an exchanger of given interface area; and these relationships could be expressed in the form of charts. Such expressions are to be found in Section 1.3. Their theoretical foundation is provided in Section 1.1, Section 1.2, and Section 1.3.

As was stated in #%SECTION_1.4.0_%#, the most complex challenge in shell-and-tube heat exchangers is that of prediction of the shell-side heat transfer coefficient and pressure drop. Already, in the 1940s, it was realized that complex factors such as leakage between tube and baffles and baffles and shell and bypass between tube bundle and shell were important (and in some cases dominant). Semi-empirical methods for dealing with these complexities were developed and have been widely applied and are exemplified by the following two methodologies: