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Licensed Unlicensed Requires Authentication Published by De Gruyter September 16, 2022

Heat Engine Cycle Configurations for Maximum Work Output with Generalized Models of Reservoir Thermal Capacity and Heat Resistance

  • Lingen Chen EMAIL logo and Shaojun Xia

Abstract

A class of two finite-heat-reservoir endoreversible heat engine with the generalized models of both the reservoir thermal capacities and heat resistances is investigated. The optimality condition for cycle maximum work output is derived by applying optimal control theory, and impacts of both thermal capacity characteristics of heat reservoirs and heat transfer laws on the optimal configurations are discussed. The results obtained in some previous researches are special cases of those obtained herein, which can provide some guidelines for optimal design of actual heat engines.

Award Identifier / Grant number: 52171317

Funding statement: This paper is supported by the National Natural Science Foundation of China (Project No. 52171317).

Acknowledgment

The authors wish to thank the reviewer for the careful, unbiased, and constructive suggestions, which led to this revised manuscript.

References

[1] B. Andresen, Finite-Time Thermodynamics, University of Copenhagen, 1983.Search in Google Scholar

[2] K. H. Hoffmann, J. M. Burzler and S. Schubert, Endoreversible thermodynamics, J. Non-Equilib. Thermodyn. 22 (1997), no. 4, 311–355.Search in Google Scholar

[3] L. G. Chen, C. Wu and F. R. Sun, Finite time thermodynamic optimization or entropy generation minimization of energy systems, J. Non-Equilib. Thermodyn. 22 (1999), no. 4, 327–359.10.1515/JNETDY.1999.020Search in Google Scholar

[4] K. H. Hoffman, J. Burzler, A. Fischer, M. Schaller and S. Schubert, Optimal process paths for endoreversible systems, J. Non-Equilib. Thermodyn. 28 (2003), no. 3, 233–268.10.1515/JNETDY.2003.015Search in Google Scholar

[5] B. Andresen, Current trends in finite-time thermodynamics, Angew. Chem. Int. Ed. 50 (2011), no. 12, 2690–2704.10.1002/anie.201001411Search in Google Scholar PubMed

[6] R. S. Berry, P. Salamon and B. Andresen, How it all began, Entropy 22 (2020), no. 8, 908.10.3390/e22080908Search in Google Scholar PubMed PubMed Central

[7] S. Levario-Medina, G. Valencia-Ortega and M. A. Barranco-Jimenez, Energetic optimization considering a generalization of the ecological criterion in traditional simple-cycle and combined cycle power plants, J. Non-Equilib. Thermodyn. 45 (2020), no. 3, 269–290.10.1515/jnet-2019-0088Search in Google Scholar

[8] Z. Smith, P. S. Pal and S. Deffner, Endoreversible Otto engines at maximal power, J. Non-Equilib. Thermodyn. 45 (2020), no. 3, 305–310.10.1515/jnet-2020-0039Search in Google Scholar

[9] Z. M. Ding, Y. L. Ge, L. G. Chen, H. J. Feng and S. J. Xia, Optimal performance regions of Feynman’s ratchet engine with different optimization criteria, J. Non-Equilib. Thermodyn. 45 (2020), no. 2, 191–207.10.1515/jnet-2019-0102Search in Google Scholar

[10] S. Y. Boikov, B. Andresen, A. A. Akhremenkov and A. M. Tsirlin, Evaluation of irreversibility and optimal organization of an integrated multi-stream heat exchange system, J. Non-Equilib. Thermodyn. 45 (2020), no. 2, 155–171.10.1515/jnet-2019-0078Search in Google Scholar

[11] L. G. Chen, F. K. Meng, Y. L. Ge and H. J. Feng, Performance optimization for a multielement thermoelectric refrigerator with another linear heat transfer law, J. Non-Equilib. Thermodyn. 46 (2021), no. 2, 149–162.10.1515/jnet-2020-0050Search in Google Scholar

[12] C. Z. Qi, Z. M. Ding, L. G. Chen, Y. L. Ge and H. J. Feng, Modelling of irreversible two-stage combined thermal Brownian refrigerators and their optimal performance, J. Non-Equilib. Thermodyn. 46 (2021), no. 2, 175–189.10.1515/jnet-2020-0084Search in Google Scholar

[13] Z. M. Ding, S. S. Qiu, L. G. Chen and W. H. Wang, Modeling and performance optimization of double-resonance electronic cooling device with three electron reservoirs, J. Non-Equilib. Thermodyn. 46 (2021), no. 3, 273–289.10.1515/jnet-2020-0105Search in Google Scholar

[14] V. Badescu, Self-driven reverse thermal engines under monotonous and oscillatory optimal operation, J. Non-Equilib. Thermodyn. 46 (2021), no. 3, 291–319.10.1515/jnet-2020-0103Search in Google Scholar

[15] C. Z. Qi, Z. M. Ding, L. G. Chen, Y. L. Ge and H. J. Feng, Modelling of irreversible two-stage combined thermal Brownian refrigerators and their optimal performance, J. Non-Equilib. Thermodyn. 46 (2021), no. 2, 175–189.10.1515/jnet-2020-0084Search in Google Scholar

[16] G. Valencia-Ortega, S. Levario-Medina and M. A. Barranco-Jiménez, The role of internal irreversibilities in the performance and stability of power plant models working at maximum ϵ-ecological function, J. Non-Equilib. Thermodyn. 46 (2021), no. 4, 413–429.10.1515/jnet-2021-0030Search in Google Scholar

[17] S. S. Qiu, Z. M. Ding, L. G. Chen and Y. L. Ge, Performance optimization of three-terminal energy selective electron generators, Sci. China, Technol. Sci. 64 (2021), no. 8, 1641–1652.10.1007/s11431-020-1828-5Search in Google Scholar

[18] V. Badescu, Maximum work rate extractable from energy fluxes, J. Non-Equilib. Thermodyn. 47 (2022), no. 1, 77–93.10.1515/jnet-2021-0039Search in Google Scholar

[19] R. Paul and K. H. Hoffmann, Optimizing the piston paths of Stirling cycle cryocoolers, J. Non-Equilib. Thermodyn. 47 (2022), no. 2, 195–203.10.1515/jnet-2021-0073Search in Google Scholar

[20] Y. L. Ge, S. S. Shi, L. G. Chen, D. F. Zhang and H. J. Feng, Power density analysis and multi-objective optimization for an irreversible Dual cycle, J. Non-Equilib. Thermodyn. 47 (2022), no. 3, 289–309.10.1515/jnet-2021-0083Search in Google Scholar

[21] P. L. Li, L. G. Chen, S. J. Xia, R. Kong and Y. L. Ge, Total entropy generation rate minimization configuration of a membrane reactor of methanol synthesis via carbon dioxide hydrogenation, Sci. China, Technol. Sci. 65 (2022), no. 3, 657–678.10.1007/s11431-021-1935-4Search in Google Scholar

[22] L. G. Chen, P. L. Li, S. J. Xia, R. Kong and Y. L. Ge, Multi-objective optimization of membrane reactor for steam methane reforming heated by molten salt, Sci. China, Technol. Sci. 65 (2022), no. 6, 1396–1414.10.1007/s11431-021-2003-0Search in Google Scholar

[23] F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys. 43 (1975), no. 1, 22–24.10.1119/1.10023Search in Google Scholar

[24] D. Gutowicz-Krusin, J. Procaccia and J. Ross, On the efficiency of rate processes: Power and efficiency of heat engines, J. Chem. Phys. 69 (1978), no. 9, 3898–3906.10.1063/1.437127Search in Google Scholar

[25] A. de Vos, Efficiency of some heat engines at maximum power conditions, Am. J. Phys. 53 (1985), no. 6, 570–573.10.1119/1.14240Search in Google Scholar

[26] L. X. Chen and Z. J. Yan, The effect of heat transfer law on the performance of a two-heat-source endoreversible cycle, J. Chem. Phys. 90 (1989), no. 7, 3740–3743.10.1063/1.455832Search in Google Scholar

[27] A. Bejan, Theory of heat transfer-irreversible power plant, Int. J. Heat Mass Transf. 31 (1988), no. 6, 1211–1219.10.1016/0017-9310(88)90064-6Search in Google Scholar

[28] L. G. Chen, C. Wu and F. R. Sun, A generalized model of real heat engines and its performance, J. Energy Inst. 69 (1996), no. 481, 214–222.Search in Google Scholar

[29] L. G. Chen, F. R. Sun and C. Wu, Effect of heat transfer law on the performance of a generalized irreversible Carnot engine, J. Phys. D, Appl. Phys. 32 (1999), no. 2, 99–105.10.1088/0022-3727/32/2/006Search in Google Scholar

[30] L. G. Chen, J. Li and R. F. Sun, Generalized irreversible heat engine experiencing a complex heat transfer law, Appl. Energy 85 (2008), no. 1, 52–60.10.1016/j.apenergy.2007.06.001Search in Google Scholar

[31] A. Khanna and R. S. Johal, Maximum power point characteristics of generalized heat engines with finite time and finite heat capacities, J. Thermodyn. (2012), Article ID 246914.10.1155/2012/246914Search in Google Scholar

[32] R. Odes and M. Kribus, Performance of heat engines with non-zero heat capacity, Energy Convers. Manag. 65 (2013), 108–119.10.1016/j.enconman.2012.08.010Search in Google Scholar

[33] H. Park and M. S. Kim, Thermodynamic performance analysis of sequential Carnot cycles using heat sources with finite heat capacity, Energy 68 (2014), 592–598.10.1016/j.energy.2014.02.073Search in Google Scholar

[34] Y. H. Ma, Effect of finite-size heat source’s heat capacity on the efficiency of heat engine, Entropy 22 (2020), no. 9, 1002.10.3390/e22091002Search in Google Scholar PubMed PubMed Central

[35] O. M. Ibrahim and R. I. Bourisli, The maximum power cycle operating between a heat source and heat sink with finite heat capacities, J. Non-Equilib. Thermodyn. 46 (2021), no. 4, 383–402.10.1515/jnet-2020-0086Search in Google Scholar

[36] M. J. Ondrechen, M. H. Rubin and Y. B. Band, The generalized Carnot cycles: a working fluid operating in finite time between heat sources and sinks, J. Chem. Phys. 78 (1983), no. 7, 4721–4727.10.1063/1.445318Search in Google Scholar

[37] Z. J. Yan and L. X. Chen, Optimal performance of a generalized Carnot cycles for another linear heat transfer law, J. Chem. Phys. 92 (1990), no. 3, 1994–1998.10.1063/1.458031Search in Google Scholar

[38] G. H. Xiong, J. C. Chen and Z. J. Yan, The effect of heat transfer law on the performance of a generalized Carnot cycle, J. Xiamen Univ. Natur. Sci. 28 (1989), no. 5, 489–494 (in Chinese).Search in Google Scholar

[39] L. G. Chen, X. Q. Zhu, F. R. Sun and C. Wu, Optimal configurations and performance for a generalized Carnot cycle assuming the generalized convective heat transfer law, Appl. Energy 78 (2004), no. 3, 305–313.10.1016/j.apenergy.2003.08.006Search in Google Scholar

[40] L. G. Chen, X. Q. Zhu, F. R. Sun and C. Wu, Effect of mixed heat resistance on the optimal configuration and performance of a heat-engine cycle, Appl. Energy 83 (2006), no. 6, 537–544.10.1016/j.apenergy.2005.05.005Search in Google Scholar

[41] J. Li, L. G. Chen and F. R. Sun, Optimal configuration for a finite high-temperature source heat engine cycle with complex heat transfer law, Sci. China, Ser. G, Phys. Mech. Astron. 52 (2009), no. 4, 587–592.10.1007/s11433-009-0074-5Search in Google Scholar

[42] J. Li and L. G. Chen, Optimal configuration of finite source heat engine cycle for maximum output work with complex heat transfer law, J. Non-Equilib. Thermodyn. (2022), DOI: 10.1515/jnet-2022-0024.Search in Google Scholar

[43] L. G. Chen, S. B. Zhou, F. R. Sun and C. Wu, Optimal configuration and performance of heat engines with heat leak and finite heat capacity, Open Syst. Inf. Dyn. 9 (2002), no. 1, 85–96.10.1023/A:1014235029474Search in Google Scholar

[44] L. G. Chen, F. R. Sun and C. Wu, Optimal configuration of a two-heat-reservoir heat-engine with heat leak and finite thermal capacity, Appl. Energy 83 (2006), no. 2, 71–81.10.1016/j.apenergy.2004.09.004Search in Google Scholar

[45] J. Li, L. G. Chen, F. R. Sun and C. Wu, Power vs efficiency characteristic of an endoreversible Carnot heat engine with heat transfer law q ( Δ T n ) m , Int. J. Ambient Energy 29 (2008), no. 3, 149–152.10.1080/01430750.2008.9675070Search in Google Scholar

Received: 2022-04-20
Revised: 2022-07-19
Accepted: 2022-08-17
Published Online: 2022-09-16
Published in Print: 2022-10-31

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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