Abstract
In this paper, the entransy functions for steady heat transfer are summarized and discussed based on the variational theory and the entransy theory. The entransy functions for steady convective heat transfer are derived for the first time. In steady heat transfer processes, it is shown that the steady distributions of heat flux and temperature (radiative thermal potential) should make the corresponding entransy functions reach their minimum values when the temperature (radiative thermal potential) or the heat flux of the boundary is given. The extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles are compared with the entransy functions It is shown that the entransy functions can describe a steady state, but cannot directly give a way to optimize heat transfer processes, while the extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles act in an opposite way.
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References
Bergles A E. Application of Heat Transfer Augmentation. Washington: Hemisphere, 1981
Gupta J P. Fundamentals of Heat Exchanger and Pressure Vessel Technology. Washington: Hemisphere, 1985
Webb R L. Principles of Enhanced Heat Transfer. Washington: Hemisphere, 1995
Guo Z Y, Zhou S Q, Li Z X, et al. Theoretical analysis and experimental confirmation of the uniformity principle of temperature difference field in heat exchanger. Int J Heat Mass Transfer, 2002, 45: 2119–2127
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
Cheng X T, Liang X G. Entransy analyses of the thermodynamic cycle in a turbojet engine. Sci China Tech Sci, 2017, 60: 1160–1167
Cheng X T, Liang X G. Analyses of entropy generation and heat entransy loss in heat transfer and heat-work conversion. Int J Heat Mass Transfer, 2013, 64: 903–909
Wu Y Q. Analyses of thermodynamic performance for the endoreversible Otto cycle with the concepts of entropy generation and entransy. Sci China Tech Sci, 2017, 60: 692–700
Wu Y Q, Cai L, Wu H J. Analyses of an air conditioning system with entropy generation minimization and entransy theory. Chin Phys B, 2016, 25: 060507
Chen Q, Liang X G, Guo Z Y. Entransy theory for the optimization of heat transfer—A review and update. Int J Heat Mass Transfer, 2013, 63: 65–81
Hua Y C, Zhao T, Guo Z Y. Irreversibility and action of the heat conduction process. Entropy, 2018, 20: 206
Poulikakos D, Bejan A. Fin geometry for minimum entropy generation in forced convection. J Heat Transfer, 1982, 104: 616–623
Erek A, Dincer I. An approach to entropy analysis of a latent heat storage module. Int J Thermal Sci, 2008, 47: 1077–1085
Cheng X T. A Critical Perspective of Entropy Generation Minimization in Thermal Analyses and Optimizations. Newcastle: Cambridge Scholars Publishing, 2019
Shah R K, Skiepko T. Entropy generation extrema and their relationship with heat exchanger effectiveness-number of transfer unit behavior for complex flow arrangements. J Heat Transfer, 2004, 126: 994–1002
Guo Z Y, Liu X B, Tao W Q, et al. Effectiveness-thermal resistance method for heat exchanger design and analysis. Int J Heat Mass Transfer, 2010, 53: 2877–2884
Cheng X, Liang X. Optimization principles for two-stream heat exchangers and two-stream heat exchanger networks. Energy, 2012, 46: 386–392
Cheng X, Zhang Q, Liang X. Analyses of entransy dissipation, entropy generation and entransy-dissipation-based thermal resistance on heat exchanger optimization. Appl Thermal Eng, 2012, 38: 31–39
Xu Z M, Yang S R, Chen Z Q. A modified entropy generation number for heat exchangers. J Thermal Sci, 1996, 5: 257–263
Haseli Y. Performance of irreversible heat engines at minimum entropy generation. Appl Math Model, 2013, 37: 9810–9817
You J, Chen L G, Wu Z X, et al. Thermodynamic performance of Dual-Miller cycle (DMC) with polytropic processes based on power output, thermal efficiency and ecological function. Sci China Tech Sci, 2018, 61: 453–463
Klein S A, Reindl D T. The relationship of optimum heat exchanger allocation and minimum entropy generation rate for refrigeration cycles. J Energ Res, 1998, 120: 172–178
Cheng X T, Liang X G. Discussion on the applicability of entropy generation minimization and entransy theory to the evaluation of thermodynamic performance for heat pump systems. Energy Convers Manage, 2014, 80: 238–242
Cheng X T, Liang X G. Analyses and optimizations of thermodynamic performance of an air conditioning system for room heating. Energy Buildings, 2013, 67: 387–391
Cheng X T, Liang X G. Role of entropy generation minimization in thermal optimization. Chin Phys B, 2017, 26: 120505
Cheng X T, Liang X G. Optimization of combined endoreversible Carnot heat engines with different objectives. Chin Phys B, 2015, 24: 060510
Cheng X T, Liang X G. Applicability of the minimum entropy generation method for optimizing thermodynamic cycles. Chin Phys B, 2013, 22: 010508
Wu Y Q. Output power analyses of an endoreversible Carnot heat engine with irreversible heat transfer processes based on generalized heat transfer law. Chin Phys B, 2015, 24: 070506
Cheng X T, Liang X G, Guo Z Y. Entransy decrease principle of heat transfer in an isolated system. Chin Sci Bull, 2011, 56: 847–854
Feng H J, Chen L G, Sun F R. “Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale. Sci China Tech Sci, 2012, 55: 779–794
Chen L, Feng H, Xie Z, et al. Constructal optimization for “disc-point” heat conduction at micro and nanoscales. Int J Heat Mass Transfer, 2013, 67: 704–711
Xiao Q H, Chen L G, Sun F R. Constructal entransy dissipation rate minimization for “disc-to-point” heat conduction. Chin Sci Bull, 2011, 56: 102–112
Xiao Q H, Chen L G, Sun F R. Constructal entransy dissipation rate minimization for heat conduction based on a tapered element. Chin Sci Bull, 2011, 56: 2400–2410
Wei S, Chen L, Sun F. Constructal entransy dissipation minimisation for “volume-point” heat conduction without the premise of optimised last-order construct. Int J Exergy, 2010, 7: 627–639
Feng H J, Chen L G, Xie Z H, et al. Constructal entransy dissipation rate minimization for “volume-point” heat conduction at micro and nanoscales. J Energy Institute, 2015, 88: 188–197
Jia H, Liu Z C, Liu W, et al. Convective heat transfer optimization based on minimum entransy dissipation in the circular tube. Int J Heat Mass Transfer, 2014, 73: 124–129
Cheng X T, Zhang Q Z, Xu X H, et al. Optimization of fin geometry in heat convection with entransy theory. Chin Phys B, 2013, 22: 020503
Chen Q, Wang M, Pan N, et al. Optimization principles for convective heat transfer. Energy, 2009, 34: 1199–1206
Cheng X, Liang X. Entransy flux of thermal radiation and its application to enclosures with opaque surfaces. Int J Heat Mass Transfer, 2011, 54: 269–278
Cheng X T, Xu X H, Liang X G. Radiative entransy flux in enclosures with non-isothermal or non-grey, opaque, diffuse surfaces and its application. Sci China Tech Sci, 2011, 54: 2446–2456
Wu J, Cheng X. Generalized thermal resistance and its application to thermal radiation based on entransy theory. Int J Heat Mass Transfer, 2013, 58: 374–381
Zhou B, Cheng X T, Liang X G. A comparison of different entransy flow definitions and entropy generation in thermal radiation optimization. Chin Phys B, 2013, 22: 084401
Xia S J, Chen L G, Sun F R. Optimization for entransy dissipation minimization in heat exchanger. Chin Sci Bull, 2009, 54: 3587–3595
Guo J F, Cheng L, Xu M T. Entransy dissipation number and its application to heat exchanger performance evaluation. Chin Sci Bull, 2009, 54: 2708–2713
Cheng X, Liang X. Application of entransy optimization to one-stream series-wound and parallel heat exchanger networks. Heat Transfer Eng, 2014, 35: 985–995
Xu Y C, Chen Q. Minimization of mass for heat exchanger networks in spacecrafts based on the entransy dissipation theory. Int J Heat Mass Transfer, 2012, 55: 5148–5156
Xu Y C, Chen Q, Guo Z Y. Optimization of heat exchanger networks based on Lagrange multiplier method with the entransy balance equation as constraint. Int J Heat Mass Transfer, 2016, 95: 109–115
Xu Y C, Chen Q, Guo Z Y. Entransy dissipation-based constraint for optimization of heat exchanger networks in thermal systems. Energy, 2015, 86: 696–708
Wang W H, Cheng X T, Liang X G. Entransy definition and its balance equation for heat transfer with vaporization processes. Int J Heat Mass Transfer, 2015, 83: 536–544
Zhou B, Cheng X T, Wang W H, et al. Entransy analyses of thermal processes with variable thermophysical properties. Int J Heat Mass Transfer, 2015, 90: 1244–1254
Cheng X T, Chen Q, Hu G J, et al. Entransy balance for the closed system undergoing thermodynamic processes. Int J Heat Mass Transfer, 2013, 60: 180–187
Cheng X T, Liang X G. Discussion on the entransy expressions of the thermodynamic laws and their applications. Energy, 2013, 56: 46–51
Cheng X T, Liang X G. Entransy, entransy dissipation and entransy loss for analyses of heat transfer and heat-work conversion processes. J Thermal Sci Tech, 2013, 8: 337–352
Wang W H, Cheng X T, Liang X G. Analyses of the endoreversible Carnot cycle with entropy theory and entransy theory. Chin Phys B, 2013, 22: 110506
Cheng X, Liang X. Entransy loss in thermodynamic processes and its application. Energy, 2012, 44: 964–972
Cheng X T, Liang X G. Work entransy and its applications. Sci China Tech Sci, 2015, 58: 2097–2103
Han C H, Kim K H. Entransy and exergy analyses for optimizations of heat-work conversion with Carnot cycle. J Therm Sci, 2016, 25: 242–249
Yang A, Chen L, Xia S, et al. The optimal configuration of reciprocating engine based on maximum entransy loss. Chin Sci Bull, 2014, 59: 2031–2038
Zhu Y, Hu Z, Zhou Y, et al. Applicability of entropy, entransy and exergy analyses to the optimization of the Organic Rankine Cycle. Energy Convers Manage, 2014, 88: 267–276
Li T L, Yuan Z H, Xu P, et al. Entransy dissipation/loss-based optimization of two-stage organic Rankine cycle (TSORC) with R245fa for geothermal power generation. Sci China Tech Sci, 2016, 59: 1524–1536
Cheng X T, Zhao J M, Liang X G. Discussion on the extensions of the entransy theory. Sci China Tech Sci, 2017, 60: 363–373
Prigogine I. Introduction to Thermodynamics of Irreversible Processes. 3rd ed. New York: John Wiley & Sons, 1967
Cheng X G. Entransy and Its Application in Heat Transfer Optimization (in Chinese). Dissertation of Doctoral Degree. Beijing: Tsinghua University, 2004
Cheng X G, Li Z X, Guo Z Y. Variational principles in heat conduction (in Chinese). J Eng Thermophys, 2004, 25: 457–459
Cheng X T, Liang X G. Entransy: Its physical basis, applications and limitations. Chin Sci Bull, 2014, 59: 5309–5323
Lu M W, Luo X F. Basic Elastic Theory. Beijing: Tsinghua University Press, 2001
Cheng X T, Liang X G. Discussion on the analogy between heat and electric conductions. Int J Heat Mass Transfer, 2019, 131: 709–712
Kim K H, Kim K. Comparative analyses of energy-exergy-entransy for the optimization of heat-work conversion in power generation systems. Int J Heat Mass Transfer, 2015, 84: 80–90
Ahmadi M H, Ahmadi M A, Pourfayaz F, et al. Entransy analysis and optimization of performance of nano-scale irreversible Otto cycle operating with Maxwell-Boltzmann ideal gas. Chem Phys Lett, 2016, 658: 293–302
Cheng X T, Xu X H, Liang X G. Theoretical analyses of the performance of a concentrating photovoltaic/thermal solar system with a mathematical and physical model, entropy generation minimization and entransy theory. Sci China Tech Sci, 2018, 61: 843–852
Goudarzi N, Talebi S. Heat removal ability for different orientations of single-phase natural circulation loops using the entransy method. Ann Nucl Energy, 2018, 111: 509–522
Cheng X T, Liang X G. Analyses of coupled steady heat transfer processes with entropy generation minimization and entransy theory. Int J Heat Mass Transfer, 2018, 127: 1092–1098
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This work was supported by the Science Fund for Creative Research Groups of National Natural Science Foundation of China (Grant No. 51621062).
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Cheng, X., Liang, X. Entransy functions for steady heat transfer. Sci. China Technol. Sci. 62, 1726–1734 (2019). https://doi.org/10.1007/s11431-019-9502-4
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DOI: https://doi.org/10.1007/s11431-019-9502-4