Maximization of the Heat Transfer Irreversibility

Abstract The function of a heat exchanger is to transfer heat. In this paper, a 2nd law-based hypothesis is advanced that the entropy generated as a result of heat transfer alone, termed productive entropy, is the desired irreversibility and should be maximized while the entropy generated (irreversibilities) by other factors like friction and mixing that do not contribute to this function should be minimized or eliminated to reduce the needed heat transfer area. The hypothesis is proven mathematically for heat transfer between two fluids in a heat exchanger and between one hot and two cold fluids in a network of up to four heat exchangers. There currently are two approaches for minimizing the total area (minimum initial cost) of a heat exchanger network (HEN). One uses some empirically based best practices that are generally rooted in the second law, and the other uses optimization algorithms. This paper provides a third approach for HEN optimization, outlining a systematic approach to minimize the area, based on the maximization of productive entropy. The approach identifies the global minimum area for networks with any number of hot and cold streams. It constitutes another method for HEN optimization and an improvement over the existing methods that provide approximate solutions. The methodology is applied to two test cases, and it is shown that this approach improves on the results obtained using the traditional approaches. The approach can be applied to networks using any type of heat exchanger or a combination of different types of heat exchangers.