The Concept of Entropy and Its Application in Thermal Engineering

Today, 156 years after the invention of entropy by Clausius, there remains disagreement among the scientific community on what entropy and the phenomenon of entropy increase mean. One can find a variety of interpretations, such as arrow of time, disorder, wastefulness, and energy dispersal. As described by Clausius, entropy represents the transformational content of a body, and entropy increase in a process is a measure of uncompensated transformation. Despite disagreements, entropy-based analysis has been employed as a design tool in a wide range of applications. A majority of second law-based studies published in scientific journals present merely entropy calculations without demonstrating how such calculations may be useful. One major drawback of a large volume of entropy-based studies is the lack of a correct interpretation of entropy calculations. In some extreme cases, misguided claims have been made about the superiority of entropy-based analysis over first law analysis, claiming, erroneously, that results obtained from the latter would be “misleading”.

The objective of this Special Issue was to invite pioneers and original thinkers to share their critical perspectives on the challenging subject of entropy and its application in thermal processes. Some of the key issues that one may encounter in today’s literature include (i) incorrect methods of calculating entropy generation in thermal systems, (ii) misinterpretation of entropy generation in processes where work is absent, and (iii) entropy-based studies that offer incorrect explanations of entropy-related calculations. This Special Issue contains five submissions that all contribute on some level to a better understanding of the concept of entropy and the correct use of entropy-based methods in thermal processes. Contributions have been made by six authors from five different universities: A. Bejan (Duke University), G. Tsatsaronis (Technical University of Berlin), D. W. MacPhee and M. Erguvan (University of Alabama), M. H. Peters (Virginia Commonwealth University), and Y. Haseli (Central Michigan University).

The first contribution is by Professor Adrian Bejan, who kindly accepted to write a perspective [1] for this Special Issue. Bejan points out the numerous confusions and misconceptions that exist in today’s literature about entropy and the second law that is perceived by many scholars as probabilistic, as well as the fact that entropy was originally invented by Clausius [2] and should be distinguished from the probability of state distribution; this is a concept brought to light by Boltzmann [3]. Bejan also examines misunderstandings that are still in circulation today, such as “the arrow of time is the second law”, “disorder is increasing”, and the “analogy between heat and work”, where the contentious property “entransy” has been criticized specifically.

The next article is by MacPhee and Erguvan [4], who numerically studied a latent heat thermal energy storage system, which is essentially a shell-and-tube heat exchanger. The phase-change material (PCM) and the heat transfer fluid (HTF) are hydroquinone and Therminol VP1, respectively. The article reports an entropy analysis of the specified thermal energy storage system and its entropy generation calculations. The results show that the entropy generation rate decreases by reducing the volume ratio of PCM-to-HTF and decreasing the heat transfer rate. The authors conclude that a minimization of entropy generation does not lead to a practically optimal system. This finding is in-line with the conclusions of earlier studies [5,6,7,8] that note that a decreasing entropy production rate in a heat exchanger with a fixed surface area yields a reduction in the heat transfer rate.

The third contribution is a review article by Bejan and Tsatsaronis [9]. The authors describe the concepts of purpose, modelling methodologies, analysis, and optimization in thermodynamics. The methods reviewed range from traditional exergy analysis and entropy generation minimization to constructal law, which was introduced by Bejan [10,11]. In the next article, Peters [12] presents the molecular approach of Irving and Kirkwood [13] for the derivation of transport equations (mass, momentum, and energy conservation). He then employs a similar methodology to derive an entropy balance equation for open systems. Transport equations are subsequently presented for local equilibrium and reversible flows.

The last article is authored by the guest editor [14] and it highlights the importance of design constraints and the conditional applicability of entropy-based methods by analyzing four different energy systems: a biomass torrefaction plant, a cryogenic air separation unit, a cogeneration process, and a hydrogen production plant. In each case, the relation between the total entropy production and the performance indicator is examined, and the conditions at which minimization of irreversibility could lead to an improved performance are discussed. From these exemplary systems, it is shown that the minimization of irreversibility does not necessarily correspond to enhancing the performance of energy systems. A priority task is to examine whether minimizing entropy production is equivalent to an improvement in performance indicators in an energy system.