Comment on “Application of Entransy Analysis in Self-Heat

Correspondence pubs.acs.org/IECR

Comment on “Application of Entransy Analysis in Self-Heat Recuperation Technology” Adrian Bejan Department of Mechanical Engineering, Duke University, Durham, North Carolina 27708-0300, United States

Ind. Eng. Chem. Res. 2014, 53, 1274−1285 (DOI: 10.1021/ie4031506) Sir: “Entransy”1 is now an open scandal in thermal sciences. No less than six independent studies in a single year2−7 revealed that the concept of entransy is false: its use simply duplicates ideas and results that were obtained previously based on known methods such as entropy generation minimization, exergy destruction minimization, and constructal law. In brief, refs 2−7 demonstrated, in rigorous thermodynamics terms, that entransy (e.g., eq 1 in the work of Wu and Guo1) is not a “physical quantity”. The entransy formula is based on Guo’s false “analogy” between charging a capacitor and heating a solid body of thermodynamic temperature T.8 Since, during the charging of a capacitor, the work done (u dq) to add the new charge (dq) is proportional to the voltage already sustained by the capacitor (u) (similar to that observed in a linear spring, where the work done (F dx) is proportional to the force F already present inside the spring (cf. Table 1.1 in ref 9), Guo first claimed inexplicably that the internal energy of the solid is a multiple of T, and then claimed that the heat transfer to a solid of temperature T must also be proportional to T. From this followed his entransy, which is a multiple of T2. The physics of heating contradicts Guo, because the rate at which heat can be added to (or subtracted from) the solid body can have any value, which depends on the design (the path) of

Chart 2. Comparison between Figure 8 from the Work of Wu and Guo1 and Figure 8.25 from Ref 9

the process and the system/environment interface. The heat transfer, similar to the work transfer, is path-dependent: it is dependent on the design of the thermodynamic system and its process and interactions. This is why heat transfer and work

Chart 1. Comparison between Figure 6 from the Work of Wu and Guo1 and Figure 8.27 from Ref 9

Published: November 12, 2014 © 2014 American Chemical Society

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Chart 3. Comparison between Figure 12 from the Work of Wu and Guo1 and Figure 8.10 from Ref 9

method in a journal paper in 1977, and in my first textbook in 1982.10

transfer are not thermodynamic properties.9 Guo’s work8 violated thermodynamics by treating heat transfer as a thermodynamic property. The name “entransy” was chosen to sound like “entropy”. It was given the symbol G, which is the same as the symbol for Gibbs free energy. The entransy publishing technique works as follows. One replaces the conventional entropy generation minimization (Sgen) analysis with the minimization of “entransy dissipation”. The results of the latter are identical to the results of the former, which is not surprising, because entransy is proportional to T2, and entropy generation in purely thermal systems (e.g., a solid body) depends monotonically on T. The duplication of classical results (first noted by Grazzini et al.2) goes unnoticed, because the “entransy” terminology makes the entransy paper look “novel”. Manjunath and Kaushik6 concluded on page 359 of their work that entransy papers are “ripof fs of existing publications”. Oliveira and Milanez7 concluded on page 525 of their work that “...the results obtained by the entransy concept are identical to those obtained by the entropy generation minimization technique. These results7 explain, in detail, and validate the conclusion reached in refs 2−4 about entransy.” The designs addressed in the work of Wu and Guo1 were addressed earlier in Chapter 8 in my graduate thermodynamics textbook,9 but were translated into Wu and Guo’s1 own “entransy” treatise. The earlier source9 was not mentioned; yet, a picture is worth a thousand words. Here, I reproduce only Figures 6, 8, and 12 from the Wu and Guo work,1 which are strikingly similar to my original (india ink) figures (Figures 8.27, 8.25, and 8.10 from ref 9. Charts 1−3 show comparisons of these selected figures from the Wu and Guo work1 with those from my textbook.9 The copies and the originals are displayed side by side here. The areas in the originals represent entropy generation rate. The areas in ref 1 are said to represent the “entransy dissipation” rate. Never mind the temperature−heat coordinates of the entransy version, which seem different than the temperature−entropy coordinates in the original version. The temperature−heat graphic method was used earlier in ref 9 (specifically, Figures 3.6 and 3.8 in ref 9, where heat is presented on the abscissa and thermodynamic temperature is presented on the ordinate, just like in ref 1). I first published the temperature−heat graphic

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

REFERENCES

(1) Wu, J.; Guo, Z. Y. Application of entransy analysis in self-heat recuperation technology. Ind. Eng. Chem. Res. 2014, 53, 1274−1285. (2) Grazzini, G.; Borchiellini, R.; Lucia, U. U. Entropy versus entransy. J. Non-Equilib. Thermodyn. 2013, 38, 259−271. (3) Herwig, H. H. Do we really need “entransy”? J. Heat Transfer 2014, 136, 045501. (4) Bejan, A. “Entransy”, and its lack of content in physics. J. Heat Transfer 2014, 136, 055501. (5) Awad, M. M. Entransy is now clear. J. Heat Transfer 2014, 136 DOI: 10.1115/1.4027821. (6) Manjunath, K.; Kaushik, S. C. Second law thermodynamic study of heat exchangers: A review. Renewable Sustainable Energy Rev. 2014, 40, 348−374. (7) Oliveira, S. R.; Milanez, L. F. Equivalence between the application of entransy and entropy generation. Int. J. Heat Mass Transfer 2014, 79, 518−525. (8) Guo, Z. Y.; Zhu, H. Y.; Liang, X. G. EntransyA physical quantity describing heat transfer ability. Int. J. Heat Mass Transfer 2007, 50, 2545−2556. (9) Bejan, A. Advanced Engineering Thermodynamics, 3rd Edition; Wiley: Hoboken, NJ, 2006. (10) Bejan, A. Entropy Generation through Heat and Fluid Flow; Wiley: New York, 1982.

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