A theoretical model for irreversible double resonance ESE (energy selective electron) device with phonon induced bypass heat leakage which is operating as heat engine system is proposed. The thermodynamic performance is optimized and the impacts of heat leakage and structure parameters of the electron system on its performance are discussed in detail by using FTT (finite time thermodynamics). Moreover, performances of the ESE system with multiple optimization objective functions, including power output, thermal efficiency, ecological function and efficient power, are explored by numerical examples. New optimal performance regions and the selection plans of optimization objective functions of the ESE system are obtained. It reveals that the characteristic of power versus efficiency behave as loop-shaped curves in spite of the heat leakage which will always decrease the efficiency of the electron engine. By properly choosing the design parameters, the ESE engine can be designed to operate at optimal conditions according to different design purpose. The preferred design area should be located between the optimal effective power condition and the optimal ecological function condition.
the National Natural Science Foundation of China(Grant,Nos.,51576207,51306206)
and Hubei Provincial Natural Science Foundation of China(Grant,No.,2017CFB498)
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51576207, 51306206), and the Hubei Provincial Natural Science Foundation of China (Grant No. 2017CFB498).
[1] Clark A M, Williams A, Ruggiero S T, et al. Practical electron-tunneling refrigerator. Appl Phys Lett, 2004, 84: 625-627 CrossRef ADS Google Scholar
[2] Pekola J. Tunnelling into the chill. Nature, 2005, 435: 889-890 CrossRef PubMed ADS Google Scholar
[3] Giazotto F, Heikkil? T T, Luukanen A, et al. Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications. Rev Mod Phys, 2006, 78: 217-274 CrossRef ADS Google Scholar
[4] Pekola J P, Giazotto F, Saira O P. Radio-frequency single-electron refrigerator. Phys Rev Lett, 2007, 98: 037201 CrossRef PubMed ADS Google Scholar
[5] Sols F. Aspects of quantum cooling in electron and atom systems. Physica E-Low-dimensional Syst NanoStruct, 2010, 42: 466-471 CrossRef ADS arXiv Google Scholar
[6] Humphrey T E, Newbury R, Taylor R P, et al. Reversible quantum Brownian heat engines for electrons. Phys Rev Lett, 2002, 89: 116801 CrossRef PubMed ADS Google Scholar
[7] Humphrey T E. Mesoscopic Quantum Ratchets and the Thermodynamics of Energy Selective Electron Heat Engines. Dissertation for Dcotoral Degree. Sydney: University of New South Wales, 2003. Google Scholar
[8] Edwards H L, Niu Q, de Lozanne A L. A quantum-dot refrigerator. Appl Phys Lett, 1993, 63: 1815–1817. Google Scholar
[9] Vashaee D, Shakouri A. Improved thermoelectric power factor in metal-based superlattices. Phys Rev Lett, 2004, 92: 106103 CrossRef PubMed ADS Google Scholar
[10] O’Dwyer M F. Solid-State Refrigeration and Power Generation Using Semiconductor Nanostructures. Dissertation for Dcotoral Degree. Wollongong: University of Wollongong, 2007. Google Scholar
[11] Humphrey T E, O’Dwyer M F, Linke H. Power optimization in thermionic devices. J Phys D-Appl Phys, 2005, 38: 2051-2054 CrossRef ADS Google Scholar
[12] O'Dwyer M F, Humphrey T E, Lewis R A, et al. Efficiency in nanometre gap vacuum thermionic refrigerators. J Phys D-Appl Phys, 2009, 42: 035417 CrossRef ADS Google Scholar
[13] He J Z, Wang X M, Liang H N. Optimum performance analysis of an energy selective electron refrigerator affected by heat leaks. Phys Scr, 2009, 80: 035701 CrossRef ADS Google Scholar
[14] Ding Z M, Chen L G, Sun F R. Performance characteristic of energy selective electron (ESE) refrigerator with filter heat conduction. Rev Mex Fis, 2010, 56: 125–131. Google Scholar
[15] Ding Z M, Chen L G, Sun F R. Ecological optimization of energy selective electron (ESE) heat engine. Appl Math Model, 2011, 35: 276-284 CrossRef Google Scholar
[16] Ding Z M, Chen L G, Sun F R. Performance characteristic of energy selective electron (ESE) heat engine with filter heat conduction. Int J Energy Environ, 2011, 2: 627–640. Google Scholar
[17] Wang H, Wu G, Lu H. Performance of an energy selective electron refrigerator at maximum cooling rate. Phys Scr, 2011, 83: 055801 CrossRef ADS Google Scholar
[18] Ding Z M, Chen L G, Sun F R. Modeling and performance analysis of energy selective electron (ESE) engine with heat leakage and transmission probability. Sci China-Phys Mech Astron, 2011, 54: 1925-1936 CrossRef ADS Google Scholar
[19] Ding Z M, Chen L G, Wang W H, et al. Exploring the operation of a microscopic energy selective electron engine. Physica A-Statistical Mech its Appl, 2015, 431: 94-108 CrossRef ADS Google Scholar
[20] He J Z, He B X. Energy selective electron heat pump with transmission probability (in Chinese). Acta Phys Sin, 2010, 59: 2345–2349. Google Scholar
[21] Ding Z M, Chen L G, Sun F R. Performance analysis of irreversible energy selective electron (ESE) heat pump with heat leakage. J Energy Institute, 2012, 85: 227-235 CrossRef Google Scholar
[22] Chen L G, Ding Z M, Sun F R. Model of a total momentum filtered energy selective electron heat pump affected by heat leakage and its performance characteristics. Energy, 2011, 36: 4011-4018 CrossRef Google Scholar
[23] Su S H, Guo J C, Su G Z, et al. Performance optimum analysis and load matching of an energy selective electron heat engine. Energy, 2012, 44: 570-575 CrossRef Google Scholar
[24] Luo X G, Li C, Liu N, et al. The impact of energy spectrum width in the energy selective electron low-temperature thermionic heat engine at maximum power. Phys Lett A, 2013, 377: 1566-1570 CrossRef ADS Google Scholar
[25] Zhou J L, Chen L G, Ding Z M, et al. Exploring the optimal performances of irreversible single resonance energy selective electron refrigerators. Eur Phys J Plus, 2016, 131: 149 CrossRef ADS Google Scholar
[26] Zhou J L, Chen L G, Ding Z M, et al. Analysis and optimization with ecological objective function of irreversible single resonance energy selective electron heat engines. Energy, 2016, 111: 306-312 CrossRef Google Scholar
[27] Wang X M, He J Z, Tang W. Performance characteristics of an energy selective electron refrigerator with double resonances. Chin Phys B, 2009, 18: 984-991 CrossRef ADS Google Scholar
[28] Luo X G, He J Z. Performance optimization analysis of a thermoelectric refrigerator with two resonances. Chin Phys B, 2011, 20: 030509 CrossRef ADS Google Scholar
[29] Ding Z M, Chen L G, Sun F R. Performance optimization of a total momentum filtered energy selective electron (ESE) heat engine with double resonances. Math Comput Model, 2011, 54: 2064-2076 CrossRef Google Scholar
[30] Yu Y H, Ding Z M, Chen L G, et al. Power and efficiency optimization for an energy selective electron heat engine with double-resonance energy filter. Energy, 2016, 107: 287-294 CrossRef Google Scholar
[31] Curzon F L, Ahlborn B. Efficiency of a Carnot engine at maximum power output. Am J Phys, 1975, 43: 22-24 CrossRef ADS Google Scholar
[32] Andresen B, Salamon P, Berry R S. Thermodynamics in finite time. Phys Today, 1984, 37: 62-70 CrossRef ADS Google Scholar
[33] Hoffmann K H, Burzler J M, Schubert S. Endoreversible thermodynamics. J Non-Equilib Thermodyn, 1997, 22: 311–355. Google Scholar
[34] Chen L G, Wu C, Sun F R. Finite time thermodynamic optimization of entropy generation minimization of energy systems. J Non-Equilib Thermodyn, 1999, 24: 327–359. Google Scholar
[35] Sieniutycz S. Hamilton-Jacobi-Bellman framework for optimal control in multistage energy systems. Phys Rep, 2000, 326: 165-258 CrossRef ADS Google Scholar
[36] Chen L G, Sun F R. Advances in Finite Time Thermodynamics: Analysis and Optimization. New York: Nova Science Publishers, 2004. Google Scholar
[37] Van den Broeck C. Thermodynamic efficiency at maximum power. Phys Rev Lett, 2005, 95: 190602 CrossRef PubMed ADS Google Scholar
[38] Andresen B. Current trends in finite-time thermodynamics. Angew Chem Int Ed, 2011, 50: 2690-2704 CrossRef PubMed Google Scholar
[39] Ding Z M, Chen L G, Wang W H, Sun F R. Progress in study on finite time thermodynamic performance optimization for three kinds of microscopic energy conversion systems (in Chinese). Sci Sin Tech, 2015, 45: 889–918. Google Scholar
[40] Ge Y L, Chen L G, Sun F R. Progress in finite time thermodynamic studies for internal combustion engine cycles. Entropy, 2016, 18: 139 CrossRef ADS Google Scholar
[41] Chen L G, Meng F K, Sun F R. Thermodynamic analyses and optimization for thermoelectric devices: The state of the arts. Sci China Technol Sci, 2016, 59: 442-455 CrossRef Google Scholar
[42] Sieniutycz S. Thermodynamic Approaches in Engineering Systems. Oxford: Elsevier, 2016. Google Scholar
[43] Bi Y H, Chen L G. Finite Time Thermodynamic Optimization for Air Heat Pumps (in Chinese). Beijing: Science Press, 2017. Google Scholar
[44] Chen L G, Xia S J. Generalized Thermodynamic Dynamic-Optimization for Irreversible Processes (in Chinese). Beijing: Science Press, 2017. Google Scholar
[45] Chen L G, Xia S J. Generalized Thermodynamic Dynamic-Optimization for Irreversible Cycles—Thermodynamic and Chemical Theoretical Cycles (in Chinese). Beijing: Science Press, 2017. Google Scholar
[46] Chen L G, Xia S J. Generalized Thermodynamic Dynamic-Optimization for Irreversible Cycles—Engineering Thermodynamic Plants and Generalized Engine Cycles (in Chinese). Beijing: Science Press, 2017. Google Scholar
[47] Badescu V. Optimal Control in Thermal Engineering. New York: Springer, 2017. Google Scholar
[48] Ding Z M, Chen L G, Liu X W. Thermodynamic optimization for irreversible thermal Brownian motors, energy selective electron engines and thermionic devices. Int J Ambient Energy, 2018, 12: 1-5 CrossRef Google Scholar
[49] Bejan A. Theory of heat transfer-irreversible power plants. Int J Heat Mass Transfer, 1988, 31: 1211-1219 CrossRef Google Scholar
[50] Bejan A. Theory of heat transfer-irreversible refrigeration plants. Int J Heat Mass Transfer, 1989, 32: 1631-1639 CrossRef Google Scholar
[51] Sears F W, Salinger G L. Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. London: Addison-Wesley, 1980. Google Scholar
[52] Angulo-Brown F. An ecological optimization criterion for finite-time heat engines. J Appl Phys, 1991, 69: 7465-7469 CrossRef ADS Google Scholar
[53] Yan Z. Comment on “Ecological optimization criterion for finite-time heat-engines”. J Appl Phys, 1993, 73: 3583. Google Scholar
[54] Chen L G, Sun F R, Chen W Z. On the ecological figures-of-merit for thermodynamic cycles (in Chinese). J Eng Therm Energy Power, 1996, 9: 374–376. Google Scholar
[55] Yan Z. η and P of a Carnot engine at maximum ηP (in Chinese). J Xiamen Univ, 1986, 25: 279–286. Google Scholar
[56] Yilmaz T, Durmu?o?lu Y. Efficient power analysis for an irreversible Carnot heat engine. Int J Energy Res, 2008, 32: 623-628 CrossRef Google Scholar
[57] Chen L G, Ding Z M, Zhou J L, et al. Thermodynamic performance optimization for an irreversible vacuum thermionic generator. Eur Phys J Plus, 2017, 132: 293 CrossRef ADS Google Scholar
Figure 1
Model of an irreversible double resonance ESE heat engine.
Figure 2
Power output
Figure 3
Influence heat leakage on efficiency
Figure 4
Influence heat leakage on power output
Figure 5
Three dimensional diagram of power output
Figure 6
Three dimensional diagram of efficiency
Figure 7
Three dimensional diagram of ecological function
Figure 8
Three dimensional diagram of efficient power
Figure 9
(Color Online) Power output characteristics of the ESE heat engine (
Figure 10
(Color Online) Efficiency characteristics of the ESE heat engine (
Figure 11
(Color Online) Entropy generation rate characteristics of the ESE heat engine (
Design condition of the ESE system | Power output (×10–14 W) | Efficiency | Ecological function (×10–14 W) | Entropy generation rate (W/K) | |||||||
Maximum power output design | 6.8199 | 0.2997 | 1.3502 | 4.5581 | |||||||
Maximum ecological function design | 5.6066 | 0.3612 | 3.0203 | 2.1552 | |||||||
Maximum efficiency design | 2.4184 | 0.4029 | 1.7193 | 0.5826 | |||||||
Maximum efficient power design | 6.3333 | 0.3397 | 2.7454 | 2.9899 | |||||||
Copyright 2019 Science China Press Co., Ltd. 科学大众杂志社有限责任公司 版权所有
京ICP备18024590号-1
Download PDF
