Entropy Generation Minimization (EGM) first emerged as a thermodynamic optimization method in cryogenic engineering.It spread into the mainstream of heat transfer engineering and energy conversion applications in the 1970s. It was then that EGM was recognized as a self standing method in thermal design, and became a separate course in thermal engineering education (1).

The EGM method is, literally, the minimization of thermodynamic irreversibility, or die minimization of the destruction of useful energy (exergy, work) in actual devices and processes. EGM combines from die start the most basic principles of thermodynamics and heat and mass transfer. Engineering devices and processes are described by "realistic" models that account simultaneously for the thermodynamics and beat transfer features of die system, as well as for materials, shapes, finite-size constraints and finite-time constraints. The minimum entropy generation design is determined for each model, as in the case of the optimal diameter of a heat exchanger passage (Section 127C), and the optimal allocation of a finite heat exchanger inventory among the heat exchangers of a power plant or refrigeration plant (Section 129A and Section 129B). The approach of any other design (S_gen) to the limit of realistic thermodynamic ideality represented by the minimumentropy generation design (S_gen,min) is monitored in terms of the entropy generation number Bejan (1982)

\[\label{eq1} \mbox{N}_{\rm s} = \frac{\mbox{S}_ {\rm gen}}{\mbox{S}_{\rm gen,min}}\tag{1}\]

or alternatives of the same ratio. The vast territory covered by the EGM work that has been published was just reviewed in a new book Bejan (1996). The objective of this Heat Exchanger Design Update is to introduce the practicing heat transfer engineer to the fundamentals of the EGM method. The approach is to illustrate EGM at several levels of complexity, starting from the simple and proceeding toward the complex: differential (infinitesimal) models, elemental features, components, and finally, complete installations.

EGM is a fundamental (combined heat transfer and thermodynamics) method for uncovering die most important thermodynamic trade offs in the design of real devices and processes. These trade offs and the simple models on which they are based "show the way", i.e. identify the optimization opportunities for the more applied work that follows. By itself, EGM is not "design optimization", and certainly not cost minimization. The minimized entropy generation (exergy destruction) is just one component in the overall cost estimation. Important in the calculation of this component is that thermodynamically optimized elemental features work toward decreasing the irreversibility of components, and that optimized components are desirable from the point of view of reducing the irreversibility of the total system. When a component or elemental feature is imagined separately from the larger system,the quantities assumed specified at the points of separation act as constraints on the optimization of die smaller systems. This must be kept in mind when die optimized elements and components are integrated into the total system, which itself is optimized for minimum total cost in the final stage Bejan et al. (1996).