Correspondence pubs.acs.org/IECR
Reply to “Comment on ‘Application of Entransy Analysis in Self-Heat Recuperation Technology’” Jing Wu* School of Energy and Power Engineering, Huazhong University of Science & Technology, Wuhan 430074, China
Ind. Eng. Chem. Res. 2014, 53, 1274−1285
Zeng-Yuan Guo* Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Ind. Eng. Chem. Res. 2014, 53, 1274−1285 Comment 2: “The physics of heating contradicts Guo, because the rate at which heat can be added to (or subtracted f rom) the solid body can have any value, which depends on the design (the path) of the process and the system/environment interface. The heat transfer, similar to the work transfer, is path-dependent... This is why heat transfer and work transfer are not thermodynamic properties.9 Guo’s work8 violated thermodynamics by treating heat transfer as a thermodynamic property.” [Note that ref 9 in this direct quote corresponds to ref 11 in this reply, and ref 8 in this direct quote again corresponds to ref 10 in this reply.] Response: As explained above, under isometric conditions and in the absence of other forms of work, we have Q = ΔU = U2 − U1, meaning that, during the process from the specified initial state to the end state, the heat transfer is fixed. Therefore, the entransy should be a heat-transfer property, rather than a thermodynamic property. Comment 3: “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 (f irst noted by Grazzini et al.2) goes unnoticed, because the “entransy” terminology makes entransy papers look “novel”.” [Note that ref 2 in this direct quote corresponds to ref 5 in this reply.] Response: The detailed comparisons between entropy analyses and entransy analyses in definition, physical meaning, optimization principle and application have been explored in refs 8, 9, and 12. Here, Table A is a reproduction of Table 2 in ref 12; it is provided to highlight the differences between entransy and entropy. Comment 4: “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.” ” [Note that ref 6 in this direct quote corresponds to ref 13 in this reply, and ref 7 in this direct quote corresponds to ref 14 in this reply.]
Sir: The following is our rebuttal to the Comment by Bejan1 on our published paper, “Application of Entransy Analysis in SelfHeat Recuperation Technology” (Ind. Eng. Chem. Res. 2014, 53, 1274−1285).2 In his Comment, Bejan only cited papers by Herwig,3 Bejan,4 Grazzini et al.,5 and Awad6 that questioned the concept of entransy, but ignored the corresponding response papers published in the same issues of the respective journals.7,8,9 We sincerely hope that next time he would at least acknowledge the existing exchanges between us, so that we, and the readers, do not have to start each time from scratch. Also, we hope, just for self-respect, that Bejan would refrain from using such terms as “scandal”1 too hastily, which is an obvious deviation from the spirit of academic discussions. Now, we start our responses to the accusations. To facilitate our discussion, the italicized texts below are directly quoted from Bejan’s comment.1 Comment 1: “...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... Guo f irst claimed inexplicably that the internal energy of the solid is a multiple of T, and then claimed that the heat transfer to the solid of temperature T must also be proportional to T. From this followed his entransy, which is a multiple of T2.” [Note that ref 1 in this direct quote corresponds to ref 2 in this reply, and ref 8 in this direct quote corresponds to ref 10 in this reply.] Response: Regarding the definition of entransy and analogy between charging a capacitor and heating a solid body, Guo has already explained them in sections 2 and 4 of ref 9. Here, what is worth further mention is that the entransy of a system is defined under the isometric condition, because the volume variation is usually negligible in heat-transfer processes. Under this condition, there is no moving boundary work (p dV work) between the system and its surroundings. In the absence of other forms of work, the principle of energy conservation gives δQ = dU (internal energy) = CV dT, which indicates that the heat transfer δQ to the solid of temperature T is proportional to dT for the constant heat capacity CV. This is just analogous to δQe = dQe = Ce dVe for a charging process of a capacitor, where Qe, Ce, and Ve are the electrical charge, electrical capacity, and voltage, respectively. © 2014 American Chemical Society
Published: November 17, 2014 18354
dx.doi.org/10.1021/ie5040978 | Ind. Eng. Chem. Res. 2014, 53, 18354−18356
Industrial & Engineering Chemistry Research
Correspondence
Table A. Major Differences between the Entransy and Entropy Theories for Heat-Transfer Optimization (From Table 2 in Ref 12) entransy theory heat-transfer purpose optimization objective optimization principle optimization criterion
entropy theory
object heating or cooling maximum heat-transfer coefficient minimum entransy dissipation-based thermal resistance uniformity of temperature gradient for heat conduction; field synergy degree for heat convection; uniform thermal potential for thermal radiation
heat-work conversion maximum heat-work conversion efficiency minimum entropy generation none
Figure 2. Temperature−energy (T−E) diagram for a heat engine cycle. (From Figure 3.6 in ref 11.)
Table C. Major Differences between Figures 6, 8, and 12 from Ref 2 and Figures 3.6 and 3.8 from Ref 11 our figures horizontal ordinates problems to be studied physical meanings of shaded area
heat flow rate, Q̇ [J/s] heat transfer entransy dissipation rate
Bejan’s figures heat Q [J] heat−work conversion none
problem is to determine the optimal air velocity distribution to minimize the average temperature in the entire cavity for a given pumping power. The minimum entransy dissipation principle is used to obtain the equations for the optimal velocity distribution by the variation method, which leads to the minimum average temperature being 580 K. However, the minimum average temperature will be 614 K, if the minimum entropy generation principle is applied. Comment 5: “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’s 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 f rom the Wu and Guo work,1 which are strikingly similar to my original (india ink) f igures (Figures 8.27, 8.25, and 8.10 f rom ref 9.” [Note that, again, ref 1 in this direct quote corresponds to ref 2 in this reply, and ref 9 in this direct quote corresponds to ref 11 in this reply.] Response: Our figures (Figures 6, 8, and 12 in ref 2) differ from Bejan’s figures (Figures 8.27, 8.25, and 8.10 in ref 11) mainly at the following three important points:
Figure 1. Comparison between our figures and Bejan’s figures: (a) our Figure 12 in ref 2 and (b) Bejan’s Figure 8.10 in ref 11.
Response: Our theoretical and numerical studies15,16 have shown that the optimization results derived using the principle of minimum entransy-dissipation-based thermal resistance and the principle of minimum entropy generation are quite different. For example, Chen et al.16 studied a two-dimensional stirring process of air in a square cavity with uniform heat sources and the overall heat generation rate of 70 W. The lateral boundary temperatures are T1 = 300 K and T2 = 550 K, while the top and bottom are at adiabatic conditions. The
Table B. Major Differences between Figures 6, 8, and 12 from Ref 2 and Figures 8.27, 8.25, and 8.10 in Ref 11
horizontal ordinates physical meanings of area use method
our figures heat flow rate, Q̇ [J/s] entransy dissipation rate [W·K] areas can be added directly 18355
Bejan’s figures specific entropy, s [J/(g·K)] heat [J] only weighted areas can be added dx.doi.org/10.1021/ie5040978 | Ind. Eng. Chem. Res. 2014, 53, 18354−18356
Industrial & Engineering Chemistry Research
Correspondence
(3) The physical meanings of the shaded area are different. In our figures, the shaded area represents the entransy dissipation rate, but the shaded area in Bejan’s figures (as shown in Figure 2) has no physical meaning. Based on these obvious differences between our figures and Bejan’s, we do not understand why such total different figures can be characterized as “strikingly similar”.1 The major differences between our figures and Bejan’s figures are summarized in Table C.
(1) The horizontal ordinates are completely different. As shown in Figure 1a in this reply, the horizontal ordinate of our figure is heat flow rate Q̇ , the unit of which are J/s, with reference to time, whereas in Bejan’s figure (Figure 1b in this reply), the horizontal ordinate is specific entropy s and has unit of J/(g·K). (2) The physical meanings of the shaded area are different. In our figures, the shaded area enclosed by the two curves of hot and cold fluids is the entransy dissipation rate of heat transfer process and has unit of W·K. In Bejan’s figures, the shaded area represents heat and has unit of joule (J). (3) The use methods of the shaded area are different. In our figures, each area between the hot-stream line and coldstream line of each heat-transfer process can be added directly to obtain the total entransy dissipation rate for a given chemical process. In Bejan’s figures, only the weighted areas can be added. For instance, the areas [area]H and [area]L in Figure 1b in this reply have the following relation:
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Bejan, A. Comment on “Application of Entransy Analysis in SelfHeat Recuperation Technology”. Ind. Eng. Chem. Res. 2014, DOI: 10.1021/ie5037512. (2) Wu, J.; Guo, Z. Y. Application of entransy analysis in self-heat recuperation technology. Ind. Eng. Chem. Res. 2014, 53, 1274−1285. (3) Herwig, H. H. Do we really need “entransy”? A Critical Assessment of a New Quantity in Heat Transfer Analysis. J. Heat Transfer 2014, 136 (4), 045501. (4) Bejan, A. “Entransy”, and Its Lack of Content in Physics. J. Heat Transfer 2014, 136 (5), 055501. (5) Grazzini, G.; Borchiellini, R.; Lucia, U. Entropy versus entransy. J. Non-Equilib. Thermodyn. 2013, 38 (3), 259−271. (6) Awad, M. M. Discussion: “Entransy is now clear”. J. Heat Transfer 2014, 136 (9), 095502. (7) Guo, Z. Y.; Chen, Q.; Liang, X. G. Closure to “Discussion of ‘Do We Really Need “Entransy”?’ ”. J. Heat Transfer 2014, 136 (4), 046001. (8) Guo, Z. Y. Closure to “Discussion of ‘ “Entransy,” and Its Lack of Content in Physics’ ” (2014, ASME J. Heat Transfer, 136(5), p. 055501). J. Heat Transfer 2014, 136 (5), 056001. (9) Chen, Q.; Guo, Z. Y.; Liang, X. G. Closure to “Discussion of ‘Entransy is now clear’ ” (2014, ASME J. Heat Transfer, 136(9), p. 095502). J. Heat Transfer 2014, 136 (9), 096001. (10) 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. (11) Bejan, A. Advanced Engineering Thermodynamics, 3rd Edition; Wiley: Hoboken, NJ, 2006. (12) Chen, Q.; Liang, X. G.; Guo, Z. Y. Entransy Theory for the Optimization of Heat TransferA Review and Update. Int. J. Heat Mass Transfer 2013, 63 (5), 65−81. (13) Manjunath, K.; Kaushik, S. C. Second law thermodynamic study of heat exchangers: A review. Renewable Sustainable Energy Rev. 2014, 40, 348−374. (14) Oliveira, S. R.; Milanez, L. F. Equivalence between the application of entransy and entropy generation. Int. J. Heat Mass Transfer 2014, 79, 518−525. (15) Chen, Q.; Zhu, H. Y.; Pan, N.; Guo, Z. Y. An alternative criterion in heat transfer optimization. Proc. R. Soc. AMath. Phys. Eng. Sci. 2011, 467, 1012−1028. (16) Chen, Q.; Wang, M. R.; Pan, N.; Guo, Z. Y. Optimization principles for convective heat transfer. Energy 2009, 34 (9), 1199− 1206. (17) Bejan, A. Entropy Generation through Heat and Fluid Flow; Wiley: New York, 1982.
Ẇlost T = 0 [area]H + [area]L ṁ Tf
as given in eq 8.39 in ref 11. This indicates that “the low-temperature area is shaded as it is, whereas the upper area had to be reduced by the factor T0/Tf before being shaded. The horizontal and vertical linear dimensions of [area]H were reduced by the factor (T0/Tf)1/2 (p 366).11” Note that, in the Comment,1 the author cited his original Figure 8.10 in ref 11 while intentionally ignoring the graphical representation of T0/Tf [area]H as shown in the upper right corner of Figure 1b in this reply. Table B highlights the major differences between our figures and Bejan’s figures. Comment 6: “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 “entransy dissipation” rate. Never mind the temperature−heat coordinates of the entransy version, which seem dif ferent than the temperature−entropy coordinates in the original version. The temperature−heat graphic method was used earlier in ref 9 (specif ically, Figures 3.6 and 3.8 in ref 9,... just like in ref 1). I f irst published the temperature−heat graphic method in a journal paper in 1977, and in my f irst textbook in 1982.10” [Again, note that refs 1 and 9 in this direct quote respectively correspond to refs 2 and 11 in this reply; ref 10 in this direct quote corresponds to ref 17 in this reply.] Response: Figure 2 in this reply is the original Figure 3.6 from ref 11 mentioned in the comment. (Figure 3.8 is not shown here for simplicity, since it is very similar to Figure 3.6 in ref 11.) There are three essential differences between our figures and Bejan’s figures: (1) The horizontal ordinates are again different. The horizontal ordinates of our figures are heat flow rate Q̇ and, thus, are expressed in unit of J/s, which is related to time. The horizontal ordinates of Bejan’s figures, as shown in Figure 2 in this reply, are heat (given in joule (J)). (2) The problems to be studied are different. The purpose of using our figures is to study the pure heat-transfer problems, while Figures 3.6 and 3.8 in Bejan’s work11 are used for studying the heat-work conversion problems. 18356
dx.doi.org/10.1021/ie5040978 | Ind. Eng. Chem. Res. 2014, 53, 18354−18356
