Discussion on the application of entropy generation minimization to the optimizations of heat transfer and heat-work conversion

Cheng Xue-Tao; Liang Xin-Gang

doi:10.7498/aps.65.180503

Abstract

The entropy generation minimization is widely used to deal with optimization problems of heat transfer and heat-work conversion. However, it is found that the minimization of entropy generation does not always lead to the optimization of the design objectives in engineering. So, it is necessary to discuss the optimization direction and application preconditions of the entropy generation minimization. In this paper, we study this topic both theoretically and numerically. Our analyses show that the concept of entropy generation directly measures the exergy loss or the ability loss of doing work, so the optimization objective of the entropy generation minimization is to minimize the exergy loss and maximize the ability to do work for the optimized system. However, we have different design objectives in engineering, such as the maximum heat transfer rate, the maximum heat exchanger effectiveness, the minimum average temperature of the heated domain, the maximum output power, the maximum coefficient of performance of heat pump systems, the homogenization of temperature field, etc. Not all of these objectives are consistent with the optimization direction of the entropy generation minimization. Therefore, it is reasonable that the entropy generation minimization is not always applicable. Furthermore, when the relationship between entropy generation and design objective can be set up, the application preconditions of the entropy generation minimization are also discussed. When the preconditions are not satisfied, the entropy generation minimization does not always lead to the best system performance, either. Some examples are also presented to verify the theoretical analyses above. For heat transfer, a one-dimensional heat transfer problem and the entropy generation paradox in heat exchanger are analyzed. For the one-dimensional heat transfer problem, the entropy generation minimization leads to the minimum heat transfer rate when the temperature difference between the boundaries is fixed. Therefore, if our design objective is the maximum heat transfer rate, the entropy generation minimization is not applicable. When the heat transfer rate is fixed, smaller entropy generation rate leads to higher boundary temperature. Therefore, if our design objective is to reduce the boundary temperature, the entropy generation minimization is not applicable, either. For the entropy generation paradox, it is shown that the concept of entropy generation cannot describe the heat transfer performance of heat exchangers. Therefore, the paradox still exists and has not been removed to date. This is verified by the theoretical analyses and the numerical simulation for a parallel flow heat exchanger in which the irreversibility from the pressure drop can be ignored. For heat-work conversion, the energy flow and the exergy flow are analyzed. According to the analyses, we discuss the applicability of the entropy generation minimization to the heat-work conversion system in which the output power, the heat-work conversion efficiency and the thermo-economic performance are taken as the optimization objectives. It is also shown that the application of the entropy generation minimization is conditional. In a word, the discussion on the examples verifies the theoretical analyses.

Keywords:

Authors and contacts

1.
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

Corresponding author: Cheng Xue-Tao, chengxt02@gmail.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51376101).

References

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[2]	Shah R K, Skiepko T 2004 J. Heat Transfer 126 994
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[30]	Ogiso K 2003 J. Heat Transfer 125 530
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[38]	Cheng X T, Liang X G 2015 Chin. Phys. B 24 060510
[39]	Salamon P, Nitzan A 1981 J. Chem. Phys. 74 3546
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[41]	Zhao K H, Luo W Y 2002 Thermotics (Beijing: Higher Education Press) pp1-220 (in Chinese) [赵凯华, 罗蔚茵 2002 热学 (北京: 高等教育出版社) 第1-220]
[42]	Cheng X T, Liang X G 2013 Int. J. Heat Mass Transfer 64 903
[43]	Onsager L 1931 Phys. Rev. 37 405
[44]	Sauar E, Kjelstrup R S, Lien K M 1996 Ind. Eng. Chem. Res. 35 4147
[45]	Nummedal L, Kjelstrup S 2001 Int. J. Heat Mass Transfer 44 2827
[46]	Cheng X T, Liang X G 2014 Chin. Sci. Bull. 59 5309
[47]	Cheng X G 2004 Ph. D. Dissertation (Beijing: Tsinghua University) [程新广 2004 博士学位论文 (北京: 清华大学)]
[48]	Bejan A 2016 Renewable Sustainable Energy Rev. 53 1636
[49]	Kays W M, London A L 1984 Compact Heat Exchangers (New York: McGraw-Hill) pp5-98
[50]	Liu X B, Guo Z Y 2009 Acta Phys. Sin. 58 4766 (in Chinese) [柳雄斌, 过增元 2009 58 4766]
[51]	Xia S J, Chen L G, Sun F R 2009 Chin. Sci. Bull. 54 3587
[52]	Chen L G 2012 Chin. Sci. Bull. 57 4404
[53]	Wu Y Q 2015 Chin. Phys. B 24 070506
[54]	Wu Y Q, Cai L, Wu H J 2016 Chin. Phys. B 25 060506
[55]	Cheng X T, Liang X G 2013 Energy Build. 67 387
[56]	Cheng X T, Liang X G 2013 Chin. Sci. Bull. 58 4696
[57]	Cheng X T, Liang X G 2014 Energy Convers. Manag. 80 238

Cited By

[1]	Guo Z Y, Zhu H Y, Liang X G 2007 Int. J. Heat Mass Transfer 50 2545
[2]	Shah R K, Skiepko T 2004 J. Heat Transfer 126 994
[3]	Bejan A 1997 Int. J. Heat Mass Transfer 40 799
[4]	Bejan A 1997 Advanced Engineering Thermodynamics (NewYork: John Wiley Sons) pp604-606
[5]	Sun C, Cheng X T, Liang X G 2014 Chin. Phys. B 23 050513
[6]	Xu Y C, Chen Q 2012 Int. J. Heat Mass Transfer 55 5148
[7]	Onsager L 1931 Phys. Rev. 38 2265
[8]	Onsager L, Machlup S 1953 Phys. Rev. 91 1505
[9]	Prigogine I 1967 Introduction to Thermodynamics of Irreversible Processes (3rd Ed.) (New York: Interscience Publishers) pp76-77
[10]	Bejan A 1982 Entropy Generation Through Heat and Fluid Flow (New York: John Wiley Sons Inc.) pp119-134
[11]	Bejan A 1996 Entropy Generation Minimization (Florida: CRC Press) pp47-112
[12]	Erek A, Dincer I 2008 Int. J. Therm. Sci. 47 1077
[13]	Ibez G, Cuevas S 2010 Energy 35 4149
[14]	Guo J, Cheng L, Xu M 2009 Appl. Therm. Eng. 29 2954
[15]	Azoumah Y, Neveu P, Mazet N 2006 Int. J. Therm. Sci. 45 716
[16]	Narayan G P, John H L V, Zubair S M 2010 Int. J. Therm. Sci. 49 2057
[17]	Zhou S, Chen L, Sun F 2007 J. Phys. D: Appl. Phys. 40 3545
[18]	Chen L, Zheng J, Sun F, Wu C 2001 J. D: Appl. Phys. 34 422
[19]	Chen Q, Zhu H Y, Pan N, Guo Z Y 2011 Proc. R. Soc. A：Math. Phys. Eng. Sci. 467 1012
[20]	Guo Z Y, Liu X B, Tao W Q, Shah R K 2010 Int. J. Heat Mass Transfer 53 2877
[21]	Cheng X T, Liang X G 2014 Acta Phys. Sin. 63 190501 (in Chinese) [程雪涛, 梁新刚 2014 63 190501]
[22]	Zhou B, Cheng X T, Liang X G 2013 Chin. Phys. B 22 084401
[23]	Klein S A, Reindl D T 1998 J. Energy Res. 120 172
[24]	Cheng X T, Liang X G 2013 Chin. Phys. B 22 010508
[25]	Salamon P, Hoffmann K H, Schubert S, Berry R S, Andresen B 2001 J. Non-Equilib. Thermodyn. 26 73
[26]	Cheng X T, Liang X G 2013 Energy Convers. Manag. 73 121
[27]	Witte L C, Shamsundar N 1983 J. Eng. Power 105 199
[28]	Xu Z M, Yang S R 1996 J. Therm. Sci. 5 257
[29]	Hesselgreaves J E 2000 Int. J. Heat Mass Transfer 43 4189
[30]	Ogiso K 2003 J. Heat Transfer 125 530
[31]	Cheng X T, Liang X G 2012 Energy 46 386
[32]	Cheng X T, Liang X G 2014 Int. J. Heat Mass Transfer 76 263
[33]	Cheng X T, Zhang Q Z, Xu X H, Liang X G 2013 Chin. Phys. B 22 020503
[34]	Cheng X T, Xu X H, Liang X G 2016 J. Ordnance Equip. Eng. 5 1 (in Chinese) [程雪涛, 徐向华, 梁新刚 2016 兵器装备工程学报 5 1]
[35]	Cheng X T, Liang X G 2012 Energy 47 421
[36]	Wang W H, Cheng X T, Liang X G 2013 Chin. Phys. B 22 110506
[37]	Vos A D 1995 Energy Convers. Manag. 36 1
[38]	Cheng X T, Liang X G 2015 Chin. Phys. B 24 060510
[39]	Salamon P, Nitzan A 1981 J. Chem. Phys. 74 3546
[40]	Feit M 2013 12th Joint European Thermodynamics Conference Brescia, Italy, July 1-5, 2013 p16
[41]	Zhao K H, Luo W Y 2002 Thermotics (Beijing: Higher Education Press) pp1-220 (in Chinese) [赵凯华, 罗蔚茵 2002 热学 (北京: 高等教育出版社) 第1-220]
[42]	Cheng X T, Liang X G 2013 Int. J. Heat Mass Transfer 64 903
[43]	Onsager L 1931 Phys. Rev. 37 405
[44]	Sauar E, Kjelstrup R S, Lien K M 1996 Ind. Eng. Chem. Res. 35 4147
[45]	Nummedal L, Kjelstrup S 2001 Int. J. Heat Mass Transfer 44 2827
[46]	Cheng X T, Liang X G 2014 Chin. Sci. Bull. 59 5309
[47]	Cheng X G 2004 Ph. D. Dissertation (Beijing: Tsinghua University) [程新广 2004 博士学位论文 (北京: 清华大学)]
[48]	Bejan A 2016 Renewable Sustainable Energy Rev. 53 1636
[49]	Kays W M, London A L 1984 Compact Heat Exchangers (New York: McGraw-Hill) pp5-98
[50]	Liu X B, Guo Z Y 2009 Acta Phys. Sin. 58 4766 (in Chinese) [柳雄斌, 过增元 2009 58 4766]
[51]	Xia S J, Chen L G, Sun F R 2009 Chin. Sci. Bull. 54 3587
[52]	Chen L G 2012 Chin. Sci. Bull. 57 4404
[53]	Wu Y Q 2015 Chin. Phys. B 24 070506
[54]	Wu Y Q, Cai L, Wu H J 2016 Chin. Phys. B 25 060506
[55]	Cheng X T, Liang X G 2013 Energy Build. 67 387
[56]	Cheng X T, Liang X G 2013 Chin. Sci. Bull. 58 4696
[57]	Cheng X T, Liang X G 2014 Energy Convers. Manag. 80 238

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Vol. 65, Issue 18 - 2016-09-20

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