{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:42:57Z","timestamp":1777646577322,"version":"3.51.4"},"reference-count":146,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T00:00:00Z","timestamp":1614297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51779262"],"award-info":[{"award-number":["51779262"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An improved irreversible closed modified simple Brayton cycle model with one isothermal heating process is established in this paper by using finite time thermodynamics. The heat reservoirs are variable-temperature ones. The irreversible losses in the compressor, turbine, and heat exchangers are considered. Firstly, the cycle performance is optimized by taking four performance indicators, including the dimensionless power output, thermal efficiency, dimensionless power density, and dimensionless ecological function, as the optimization objectives. The impacts of the irreversible losses on the optimization results are analyzed. The results indicate that four objective functions increase as the compressor and turbine efficiencies increase. The influences of the latter efficiency on the cycle performances are more significant than those of the former efficiency. Then, the NSGA-II algorithm is applied for multi-objective optimization, and three different decision methods are used to select the optimal solution from the Pareto frontier. The results show that the dimensionless power density and dimensionless ecological function compromise dimensionless power output and thermal efficiency. The corresponding deviation index of the Shannon Entropy method is equal to the corresponding deviation index of the maximum ecological function.<\/jats:p>","DOI":"10.3390\/e23030282","type":"journal-article","created":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T04:36:24Z","timestamp":1614314184000},"page":"282","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":63,"title":["Four-Objective Optimizations for an Improved Irreversible Closed Modified Simple Brayton Cycle"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6054-5606","authenticated-orcid":false,"given":"Chenqi","family":"Tang","sequence":"first","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9012-6736","authenticated-orcid":false,"given":"Lingen","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}]},{"given":"Huijun","family":"Feng","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}]},{"given":"Yanlin","family":"Ge","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1243\/PIME_PROC_1991_205_039_02","article-title":"On the role of the harmonic mean isentropic exponent in the analysis of the closed-cycle gas turbine","volume":"205","author":"Wood","year":"1991","journal-title":"Proc. Inst. Mech. Eng. Part. A J. Power Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1016\/j.energy.2019.06.010","article-title":"Power optimization and comparison between simple recuperated and recompressing supercritical carbon dioxide Closed-Brayton-Cycle with finite cold source on hypersonic vehicles","volume":"181","author":"Cheng","year":"2019","journal-title":"Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"113110","DOI":"10.1016\/j.enconman.2020.113110","article-title":"Thermodynamic and exergy analysis of a S-CO2 Brayton cycle with various of cooling modes","volume":"220","author":"Hu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"115611","DOI":"10.1016\/j.applthermaleng.2020.115611","article-title":"Optimization of a closed Brayton cycle for space power systems","volume":"179","author":"Liu","year":"2020","journal-title":"Appl. Therm. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1002\/(SICI)1099-114X(199702)21:2<113::AID-ER219>3.0.CO;2-5","article-title":"Analysis of a concept for increasing the efficiency of a Brayton cycle via isothermal heat addition","volume":"21","author":"Vecchiarelli","year":"1997","journal-title":"Int. J. Energy Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1016\/S0196-8904(99)00014-X","article-title":"Thermal efficiency of a regenerative Brayton cycle with isothermal heat addition","volume":"40","author":"Yavuz","year":"1999","journal-title":"Energy Convers. Manag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0306-2619(00)00055-6","article-title":"Optimal design of the regenerative gas turbine engine with isothermal heat addition","volume":"68","author":"Erbay","year":"2001","journal-title":"Appl. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"172","DOI":"10.3390\/e7030172","article-title":"Exergy analysis and second law efficiency of a regenerative Brayton cycle with isothermal heat addition","volume":"7","author":"Jubeh","year":"2005","journal-title":"Entropy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.enconman.2013.05.002","article-title":"Binary Brayton cycle with two isothermal processes","volume":"73","year":"2013","journal-title":"Energy Convers. Manag."},{"key":"ref_10","unstructured":"Moutier, J. (1872). \u00c9l\u00e9ments de Thermodynamique, Gautier-Villars."},{"key":"ref_11","first-page":"125","article-title":"The efficiency of atomic power stations (A review)","volume":"7","author":"Novikov","year":"1957","journal-title":"J. Nucl. Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1119\/1.10023","article-title":"Efficiency of a Carnot engine at maximum power output","volume":"43","author":"Curzon","year":"1975","journal-title":"Am. J. Phys."},{"key":"ref_13","unstructured":"Andresen, B. (1983). Finite-Time Thermodynamics, University of Copenhagen. Physics Laboratory II."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1016\/0360-5442(91)90024-G","article-title":"Work from irreversible heat engines","volume":"16","author":"Grazzini","year":"1991","journal-title":"Energy"},{"key":"ref_15","unstructured":"Bejan, A. (1996). Entropy Generation Minimization, CRC Press."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1515\/JNETDY.1999.020","article-title":"Finite time thermodynamic optimization or entropy generation minimization of energy systems","volume":"24","author":"Chen","year":"1999","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1002\/anie.201001411","article-title":"Current trends in finite-time thermodynamics","volume":"50","author":"Andresen","year":"2011","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"115075","DOI":"10.1016\/j.apenergy.2020.115075","article-title":"Review of thermoelectric geometry and structure optimization for performance enhancement","volume":"268","author":"Shittu","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Berry, R.S., Salamon, P., and Andresen, B. (2020). How it all began. Entropy, 22.","DOI":"10.3390\/e22080908"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1515\/JNETDY.2003.015","article-title":"Optimal process paths for endoreversible systems","volume":"28","author":"Hoffman","year":"2003","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1515\/jnet-2018-0007","article-title":"Finite time thermodynamics: Realizability domain of heat to work converters","volume":"44","author":"Zaeva","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Masser, R., and Hoffmann, K.H. (2020). Endoreversible modeling of a hydraulic recuperation system. Entropy, 22.","DOI":"10.3390\/e22040383"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kushner, A., Lychagin, V., and Roop, M. (2020). Optimal thermodynamic processes for gases. Entropy, 22.","DOI":"10.3390\/e22040448"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"De Vos, A. (2020). Endoreversible models for the thermodynamics of computing. Entropy, 22.","DOI":"10.3390\/e22060660"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Masser, R., Khodja, A., Scheunert, M., Schwalbe, K., Fischer, A., Paul, R., and Hoffmann, K.H. (2020). Optimized piston motion for an alpha-type Stirling engine. Entropy, 22.","DOI":"10.3390\/e22060700"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Ma, K., Ge, Y.L., and Feng, H.J. (2020). Re-optimization of expansion work of a heated working fluid with generalized radiative heat transfer law. Entropy, 22.","DOI":"10.3390\/e22070720"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Tsirlin, A., and Gagarina, L. (2020). Finite-time thermodynamics in economics. Entropy, 22.","DOI":"10.3390\/e22080891"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Tsirlin, A., and Sukin, I. (2020). Averaged optimization and finite-time thermodynamics. Entropy, 22.","DOI":"10.3390\/e22090912"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Muschik, W., and Hoffmann, K.H. (2020). Modeling, simulation, and reconstruction of 2-reservoir heat-to-power processes in finite-time thermodynamics. Entropy, 22.","DOI":"10.3390\/e22090997"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Insinga, A.R. (2020). The quantum friction and optimal finite-time performance of the quantum Otto cycle. Entropy, 22.","DOI":"10.3390\/e22091060"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Sch\u00f6n, J.C. (2020). Optimal control of hydrogen atom-like systems as thermodynamic engines in finite time. Entropy, 22.","DOI":"10.3390\/e22101066"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Andresen, B., and Essex, C. (2020). Thermodynamics at very long time and space scales. Entropy, 22.","DOI":"10.3390\/e22101090"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Ma, K., Feng, H.J., and Ge, Y.L. (2020). Optimal configuration of a gas expansion process in a piston-type cylinder with generalized convective heat transfer law. Energies, 13.","DOI":"10.3390\/en13123229"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Scheunert, M., Masser, R., Khodja, A., Paul, R., Schwalbe, K., Fischer, A., and Hoffmann, K.H. (2020). Power-optimized sinusoidal piston motion and its performance gain for an Alpha-type Stirling engine with limited regeneration. Energies, 13.","DOI":"10.3390\/en13174564"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1515\/jnet-2019-0078","article-title":"Evaluation of irreversibility and optimal organization of an integrated multi-stream heat exchange system","volume":"45","author":"Boikov","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"113261","DOI":"10.1016\/j.enconman.2020.113261","article-title":"Maximum energy output chemical pump configuration with an infinite-low- and a finite-high-chemical potential mass reservoirs","volume":"223","author":"Chen","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_37","first-page":"311","article-title":"Endoreversible thermodynamics","volume":"22","author":"Hoffmann","year":"1997","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1515\/jnet-2015-0061","article-title":"Endoreversible modeling of a PEM fuel cell","volume":"40","author":"Wagner","year":"2015","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/jnet-2018-0087","article-title":"Concepts of phenominological irreversible quantum thermodynamics I: Closed undecomposed Schottky systems in semi-classical description","volume":"44","author":"Muschik","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1515\/jnet-2018-0009","article-title":"Attainability of maximum work and the reversible efficiency of minimally nonlinear irreversible heat engines","volume":"44","author":"Ponmurugan","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1515\/jnet-2019-0020","article-title":"Performance analysis of Diesel cycle under efficient power density condition with variable specific heat of working fluid","volume":"44","author":"Raman","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1515\/jnet-2019-0063","article-title":"Stochastic Novikov engine with Fourier heat transport","volume":"44","author":"Schwalbe","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.applthermaleng.2014.04.004","article-title":"Maximum power of a multistage Rankine cycle in low-grade thermal energy conversion","volume":"69","author":"Morisaki","year":"2014","journal-title":"Appl. Thermal Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1016\/j.egypro.2017.09.224","article-title":"Application of finite time thermodynamics for evaluation method of heat engines","volume":"129","author":"Yasunaga","year":"2017","journal-title":"Energy Proc."},{"key":"ref_45","first-page":"65","article-title":"Performance evaluation of heat exchangers for application to ocean thermal energy conversion system","volume":"22","author":"Yasunaga","year":"2017","journal-title":"Ocean Thermal Energy Convers."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Yasunaga, T., Koyama, N., Noguchi, T., Morisaki, T., and Ikegami, Y. (2018, January 17\u201322). Thermodynamical optimum heat source mean velocity in heat exchangers on OTEC. Proceedings of the Grand Renewable Energy 2018, Yokohama, Japan.","DOI":"10.1299\/jsmepes.2018.23.E121"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Yasunaga, T., Noguchi, T., Morisaki, T., and Ikegami, Y. (2018). Basic heat exchanger performance evaluation method on OTEC. J. Mar. Sci. Eng., 6.","DOI":"10.3390\/jmse6020032"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Fontaine, K., Yasunaga, T., and Ikegami, Y. (2019). OTEC maximum net power output using Carnot cycle and application to simplify heat exchanger selection. Entropy, 21.","DOI":"10.3390\/e21121143"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Yasunaga, T., and Ikegami, Y. (2020). Finite-time thermodynamic model for evaluating heat engines in ocean thermal energy conversion. Entropy, 22.","DOI":"10.3390\/e22020211"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"112422","DOI":"10.1016\/j.enconman.2019.112422","article-title":"Comprehensive study and optimization of concentrated photovoltaic-thermoelectric considering all contact resistances","volume":"205","author":"Shittu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Feidt, M. (2020). Carnot cycle and heat engine: Fundamentals and applications. Entropy, 22.","DOI":"10.3390\/e22030348"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Feidt, M., and Costea, M. (2020). Effect of machine entropy production on the optimal performance of a refrigerator. Entropy, 22.","DOI":"10.3390\/e22090913"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Ma, Y.H. (2020). Effect of finite-size heat source\u2019s heat capacity on the efficiency of heat engine. Entropy, 22.","DOI":"10.3390\/e22091002"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Rogolino, P., and Cimmelli, V.A. (2020). Thermoelectric efficiency of Silicon\u2013Germanium alloys in finite-time thermodynamics. Entropy, 22.","DOI":"10.3390\/e22101116"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Dann, R., Kosloff, R., and Salamon, P. (2020). Quantum finite time thermodynamics: Insight from a single qubit engine. Entropy, 22.","DOI":"10.3390\/e22111255"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1515\/jnet-2020-0028","article-title":"Exergy-based ecological optimization of an irreversible quantum Carnot heat pump with spin-1\/2 systems","volume":"46","author":"Liu","year":"2021","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"110656","DOI":"10.1016\/j.rser.2020.110656","article-title":"Finite-time thermodynamics modeling and analysis on compressed air energy storage systems with thermal storage","volume":"138","author":"Guo","year":"2021","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1515\/jnet-2020-0039","article-title":"Endoreversible Otto engines at maximal power","volume":"45","author":"Smith","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"113001","DOI":"10.1016\/j.enconman.2020.113001","article-title":"Power and efficiency optimization of open Maisotsenko-Brayton cycle and performance comparison with traditional open regenerated Brayton cycle","volume":"217","author":"Chen","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"113069","DOI":"10.1016\/j.enconman.2020.113069","article-title":"Analysis of integration method in multi-heat-source power generation systems based on finite-time thermodynamics","volume":"220","author":"Liu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"112424","DOI":"10.1016\/j.enconman.2019.112424","article-title":"Power output, thermal efficiency and exergy-based ecological performance optimizations of an irreversible KCS-34 coupled to variable temperature heat reservoirs","volume":"205","author":"Feng","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1007\/s42243-019-00355-2","article-title":"Thermal performance evaluation of subcritical organic Rankine cycle for waste heat recovery from sinter annular cooler","volume":"27","author":"Feng","year":"2020","journal-title":"J. Iron. Steel Res. Int."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"112727","DOI":"10.1016\/j.enconman.2020.112727","article-title":"Constructal thermodynamic optimization for ocean thermal energy conversion system with dual-pressure organic Rankine cycle","volume":"210","author":"Wu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"113360","DOI":"10.1016\/j.enconman.2020.113360","article-title":"Performance evaluation and parametric optimum design of irreversible thermionic generators based on van der Waals heterostructures","volume":"225","author":"Qiu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"260602","DOI":"10.1103\/PhysRevLett.125.260602","article-title":"Geometry of work fluctuations versus efficiency in microscopic thermal machines","volume":"125","author":"Miller","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Gonzalez-Ayala, J., Roco, J.M.M., Medina, A., and Calvo Hern\u00e1ndez, A. (2020). Optimization, stability, and entropy in endoreversible heat engines. Entropy, 22.","DOI":"10.3390\/e22111323"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Kong, R., Chen, L.G., Xia, S.J., Li, P.L., and Ge, Y.L. (2021). Minimizing entropy generation rate in hydrogen iodide decomposition reactor heated by high-temperature helium. Entropy, 23.","DOI":"10.3390\/e23010082"},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Albatati, F., and Attar, A. (2021). Analytical and experimental study of thermoelectric generator (TEG) system for automotive exhaust waste heat recovery. Energies, 14.","DOI":"10.3390\/en14010204"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"113585","DOI":"10.1016\/j.enconman.2020.113585","article-title":"Constructal thermodynamic optimization for dual-pressure organic Rankine cycle in waste heat utilization system","volume":"227","author":"Feng","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"113658","DOI":"10.1016\/j.enconman.2020.113658","article-title":"Single and multi-objective optimization of a TEG system for optimum power, cost and second law efficiency using genetic algorithm","volume":"228","author":"Garmejani","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1140\/epjp\/s13360-021-01162-z","article-title":"Ecological optimization of an irreversible Diesel cycle","volume":"136","author":"Ge","year":"2021","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"2640","DOI":"10.1007\/s11431-019-1518-x","article-title":"Performance optimization of a class of combined thermoelectric heating devices","volume":"63","author":"Chen","year":"2020","journal-title":"Sci. China Technol. Sci."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1088\/0022-3727\/28\/7\/005","article-title":"Efficiency of a Joule-Brayton engine at maximum power density","volume":"28","author":"Sahin","year":"1995","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1016\/0360-5442(96)00068-0","article-title":"Maximum power density analysis of an endoreversible Carnot heat engine","volume":"21","author":"Sahin","year":"1996","journal-title":"Energy"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1088\/0022-3727\/34\/3\/329","article-title":"Optimum distribution of heat exchanger inventory for power density optimization of an endoreversible closed Brayton cycle","volume":"34","author":"Chen","year":"2001","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1023\/A:1014073105663","article-title":"Power density optimization for an irreversible closed Brayton cycle","volume":"8","author":"Chen","year":"2001","journal-title":"Open Syst. Inf. Dyn."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0196-8904(01)00003-6","article-title":"Performance comparison of an endoreversible closed variable-temperature heat reservoir Brayton cycle under maximum power density and maximum power conditions","volume":"43","author":"Chen","year":"2002","journal-title":"Energy Convers. Manag."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1243\/095765005X31234","article-title":"Performance comparison of an irreversible closed variable-temperature heat reservoir Brayton cycle under maximum power density and maximum power conditions","volume":"219","author":"Chen","year":"2005","journal-title":"Proc. Inst. Mech. Eng. Part. A J. Power Energy"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.enconman.2015.12.059","article-title":"Thermodynamic analysis and performance maps for the irreversible Dual-Atkinson cycle engine (DACE) with considerations of temperature-dependent specific heats, heat transfer and friction losses","volume":"111","author":"Gonca","year":"2016","journal-title":"Energy Convers. Manag."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1504\/IJEX.2020.109985","article-title":"Performance assessment of a modified power generating cycle based on effective ecological power density and performance coefficient","volume":"33","author":"Gonca","year":"2020","journal-title":"Int. J. Exergy"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"50","DOI":"10.18186\/thermal.671148","article-title":"Comparative maximum power density analysis of a supercritical CO2 Brayton power cycle","volume":"6","author":"Karakurt","year":"2020","journal-title":"J. Therm. Eng."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"7465","DOI":"10.1063\/1.347562","article-title":"An ecological optimization criterion for finite-time heat engines","volume":"69","year":"1991","journal-title":"J. Appl. Phys."},{"key":"ref_83","first-page":"3583","article-title":"Comment on \u201cecological optimization criterion for finite-time heat engines\u201d","volume":"73","author":"Yan","year":"1993","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0196-8904(96)00180-X","article-title":"Ecological optimization of an endoreversible Brayton cycle","volume":"39","author":"Cheng","year":"1998","journal-title":"Energy Convers. Manag."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"015320","DOI":"10.1063\/1.5062615","article-title":"Ecological optimization for a combined diesel-organic Rankine cycle","volume":"9","author":"Ma","year":"2019","journal-title":"AIP Adv."},{"key":"ref_86","first-page":"267","article-title":"Thermodynamic assessment and optimization of performance of irreversible Atkinson cycle","volume":"39","author":"Ahmadi","year":"2020","journal-title":"Iran. J. Chem. Chem. Eng."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1515\/jnet-2019-0088","article-title":"Energetic optimization considering a generalization of the ecological criterion in traditional simple-cycle and combined cycle power plants","volume":"45","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"119235","DOI":"10.1016\/j.energy.2020.119235","article-title":"Power, efficiency, ecological function and ecological coefficient of performance optimizations of an irreversible Diesel cycle based on finite piston speed","volume":"216","author":"Wu","year":"2021","journal-title":"Energy"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1016\/S0196-8904(02)00221-2","article-title":"Parametric study of an irreversible regenerative Brayton cycle with isothermal heat addition","volume":"44","author":"Kaushik","year":"2003","journal-title":"Energy Convers. Manag."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"377","DOI":"10.3390\/e5050377","article-title":"Ecological optimization and parametric study of an irreversible regenerative modified Brayton cycle with isothermal heat addition","volume":"5","author":"Tyagi","year":"2003","journal-title":"Entropy"},{"key":"ref_91","first-page":"66","article-title":"Performance evaluation of an irreversible regenerative modified Brayton heat engine based on the thermoeconomic criterion","volume":"26","author":"Tyagi","year":"2006","journal-title":"Int. J. Power Energy Syst."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"279","DOI":"10.18186\/jte.44164","article-title":"Power optimization of an irreversible regenerative Brayton cycle with isothermal heat addition","volume":"1","author":"Kumar","year":"2015","journal-title":"J. Therm. Eng."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1504\/IJEX.2005.006435","article-title":"Optimum criteria based on the ecological function of an irreversible intercooled regenerative modified Brayton cycle","volume":"2","author":"Tyagi","year":"2005","journal-title":"Int. J. Exergy"},{"key":"ref_94","first-page":"592","article-title":"Irreversible modified complex Brayton cycle under maximum economic condition","volume":"44","author":"Tyagi","year":"2006","journal-title":"Indian J. Pure Appl. Phys."},{"key":"ref_95","first-page":"256","article-title":"Effects of intercooling on the performance of an irreversible regenerative modified Brayton cycle","volume":"27","author":"Tyagi","year":"2007","journal-title":"Int. J. Power Energy Syst."},{"key":"ref_96","first-page":"565","article-title":"Performance criteria on different pressure ratios of an irreversible modified complex Brayton cycle","volume":"46","author":"Tyagi","year":"2008","journal-title":"Indian J. Pure Appl. Phys."},{"key":"ref_97","first-page":"42","article-title":"Power and power density analyzes of an endoreversible modified variable-temperature reservoir Brayton cycle with isothermal heat addition","volume":"11","author":"Wang","year":"2016","journal-title":"Int. J. Low-Carbon Technol."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1080\/14786451.2013.772614","article-title":"Ecological performance analysis of an endoreversible modified Brayton cycle","volume":"33","author":"Wang","year":"2014","journal-title":"Int. J. Sustain. Energy"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.1016\/j.egyr.2020.06.012","article-title":"Power density analysis and multi-objective optimization for a modified endoreversible simple closed Brayton cycle with one isothermal heating process","volume":"6","author":"Tang","year":"2020","journal-title":"Energy Rep."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.asoc.2016.05.001","article-title":"Soft computing based multi-objective optimization of Brayton cycle power plant with isothermal heat addition using evolutionary algorithm and decision making","volume":"46","author":"Arora","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"28","DOI":"10.18186\/thermal.671079","article-title":"Thermodynamic optimization of an irreversible regenerated Brayton heat engine using modified ecological criteria","volume":"6","author":"Arora","year":"2020","journal-title":"J. Therm. Eng."},{"key":"ref_102","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Tang, C.Q., Feng, H.J., and Ge, Y.L. (2020). Power, efficiency, power density and ecological function optimizations for an irreversible modified closed variable-temperature reservoir regenerative Brayton cycle with one isothermal heating process. Energies, 13.","DOI":"10.3390\/en13195133"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.tsep.2018.06.003","article-title":"Power and efficiency performance analyses for a closed endoreversible binary Brayton cycle with two isothermal processes","volume":"7","author":"Qi","year":"2018","journal-title":"Therm. Sci. Eng. Prog."},{"key":"ref_104","doi-asserted-by":"crossref","unstructured":"Tang, C.Q., Chen, L.G., Feng, H.J., Wang, W.H., and Ge, Y.L. (2020). Power optimization of a closed binary Brayton cycle with isothermal heating processes and coupled to variable-temperature reservoirs. Energies, 13.","DOI":"10.3390\/en13123212"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/j.enconman.2013.07.078","article-title":"Optimal design of a solar driven heat engine based on thermal and thermo-economic criteria","volume":"75","author":"Ahmadi","year":"2013","journal-title":"Energy Convers. Manag."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.enconman.2013.06.030","article-title":"Multi-objective thermodynamic-based optimization of output power of Solar Dish-Stirling engine by implementing an evolutionary algorithm","volume":"75","author":"Ahmadi","year":"2013","journal-title":"Energy Convers. Manag."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.enconman.2014.03.033","article-title":"Multi-objective optimization of an irreversible Stirling cryogenic refrigerator cycle","volume":"82","author":"Ahmadi","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1016\/j.enconman.2014.09.041","article-title":"Thermodynamic and thermo-economic analysis and optimization of performance of irreversible four- temperature-level absorption refrigeration","volume":"88","author":"Ahmadi","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.enconman.2014.09.064","article-title":"Thermodynamic analysis and optimization of an irreversible Ericsson cryogenic refrigerator cycle","volume":"89","author":"Ahmadi","year":"2015","journal-title":"Energy Convers. Manag."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1016\/j.enconman.2017.10.027","article-title":"Thermodynamic evaluation and multi-objective optimization of molten carbonate fuel cell-supercritical CO2 Brayton cycle hybrid system","volume":"153","author":"Jokar","year":"2017","journal-title":"Energy Convers. Manag."},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.enconman.2018.04.022","article-title":"Multi-objective optimization and sensitivity analysis of an organic Rankine cycle coupled with a one-dimensional radial-inflow turbine efficiency prediction model","volume":"166","author":"Han","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1016\/j.enconman.2018.06.046","article-title":"Multi-objective optimization and decision making of endoreversible combined cycles with consideration of different heat exchangers by finite time thermodynamics","volume":"171","author":"Ghasemkhani","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1016\/j.energy.2017.12.028","article-title":"Multi-objective performance optimization of irreversible molten carbonate fuel cell\u2013Braysson heat engine and thermodynamic analysis with ecological objective approach","volume":"144","author":"Ahmadi","year":"2018","journal-title":"Energy"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1016\/j.applthermaleng.2018.09.075","article-title":"An innovative Organic Rankine Cycle (ORC) based Ocean Thermal Energy Conversion (OTEC) system with performance simulation and multi-objective optimization","volume":"145","author":"Wang","year":"2018","journal-title":"Appl. Therm. Eng."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.enconman.2018.12.109","article-title":"A comparative performance evaluation of the reversed Brayton cycle operated heat pump based on thermo-ecological criteria through many and multi-objective approaches","volume":"183","author":"Patela","year":"2019","journal-title":"Energy Convers. Manag."},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"117848","DOI":"10.1016\/j.energy.2020.117848","article-title":"Multi-objective optimization of organic Rankine cycle using hydrofluorolefins (HFOs) based on different target preferences","volume":"203","author":"Hu","year":"2020","journal-title":"Energy"},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"113331","DOI":"10.1016\/j.enconman.2020.113331","article-title":"How to design organic Rankine cycle system under fluctuating ambient temperature: A multi-objective approach","volume":"224","author":"Hu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_118","doi-asserted-by":"crossref","unstructured":"Sun, M., Xia, S.J., Chen, L.G., Wang, C., and Tang, C.Q. (2020). Minimum entropy generation rate and maximum yield optimization of sulfuric acid decomposition process using NSGA-II. Entropy, 22.","DOI":"10.3390\/e22101065"},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"113441","DOI":"10.1016\/j.enconman.2020.113441","article-title":"Exergoeconomic and multi-objective optimization of a solar thermochemical hydrogen production plant with heat recovery","volume":"225","author":"Sadeghi","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_120","doi-asserted-by":"crossref","unstructured":"Wu, Z.X., Feng, H.J., Chen, L.G., and Ge, Y.L. (2020). Performance optimization of a condenser in ocean thermal energy conversion (OTEC) system based on constructal theory and multi-objective genetic algorithm. Entropy, 22.","DOI":"10.3390\/e22060641"},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"104898","DOI":"10.1016\/j.icheatmasstransfer.2020.104898","article-title":"Entropy generation minimization of a pump running in reverse mode based on surrogate models and NSGA-II","volume":"118","author":"Ghorani","year":"2020","journal-title":"Int. Commun. Heat Mass Transfer"},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"117809","DOI":"10.1016\/j.energy.2020.117809","article-title":"Multi-objective optimization and off-design evaluation of organic Rankine cycle (ORC) for low-grade waste heat recovery","volume":"203","author":"Wang","year":"2020","journal-title":"Energy"},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"125679","DOI":"10.1016\/j.jclepro.2020.125679","article-title":"Exergo-environmental assessment and multi-objective optimization of waste heat recovery systems based on Organic Rankine cycle configurations","volume":"288","year":"2021","journal-title":"J. Clean. Prod."},{"key":"ref_124","doi-asserted-by":"crossref","unstructured":"Shi, S.S., Ge, Y.L., Chen, L.G., and Feng, F.J. (2020). Four objective optimization of irreversible Atkinson cycle based on NSGA-II. Entropy, 22.","DOI":"10.3390\/e22101150"},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"120013","DOI":"10.1016\/j.energy.2021.120013","article-title":"Constructal design for a boiler economizer","volume":"223","author":"Tang","year":"2021","journal-title":"Energy"},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1238\/Physica.Regular.064a00184","article-title":"Power density optimization for an irreversible regenerated closed Brayton cycle","volume":"64","author":"Chen","year":"2001","journal-title":"Phys. Scripta"},{"key":"ref_127","unstructured":"Bejan, A. (1982). Entropy Generation through Heat and Fluid Flow, Wiley."},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1016\/0017-9310(88)90064-6","article-title":"Theory of heat transfer-irreversible power plant","volume":"31","author":"Bejan","year":"1988","journal-title":"Int. J. Heat Mass Transfer"},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1115\/1.2792711","article-title":"The equivalence of maximum power and minimum entropy generation rate in the optimization of power plants","volume":"118","author":"Bejan","year":"1996","journal-title":"J. Energy Res. Tech."},{"key":"ref_130","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1119\/1.18306","article-title":"Models of power plants that generate minimum entropy while operating at maximum power","volume":"64","author":"Bejan","year":"1996","journal-title":"Am. J. Phys."},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1515\/JNETDY.2001.006","article-title":"What conditions make minimum entropy production equivalent to maximum power production?","volume":"26","author":"Salamon","year":"2001","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"2086","DOI":"10.1103\/PhysRevA.15.2086","article-title":"Thermodynamics in finite time: The step-Carnot cycle","volume":"15","author":"Andresen","year":"1977","journal-title":"Phys. Rev. A"},{"key":"ref_133","first-page":"549","article-title":"Optimal control in problems of extremal of irreversible thermodynamic processes","volume":"46","author":"Orlov","year":"1985","journal-title":"Avtomatika Telemekhanika"},{"key":"ref_134","first-page":"51","article-title":"Thermodynamics with finite heat-transfer area or finite surface thermodynamics. Thermodynamics and the Design, Analysis, and Improvement of Energy Systems, ASME Adv","volume":"35","author":"Lu","year":"1995","journal-title":"Energy Sys. Div. Pub. AES"},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1063\/1.362674","article-title":"Entropy generation minimization: The new thermodynamics of finite size devices and finite time processes","volume":"79","author":"Bejan","year":"1996","journal-title":"J. Appl. Phys."},{"key":"ref_136","unstructured":"Feidt, M. (1996). Thermodynamique et Optimisation Energetique des Systems et Procedes, Technique et Documentation, Lavoisier. [2nd ed.]. (In French)."},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.3390\/e14071234","article-title":"Association of finite-dimension thermodynamics and a bond-graph approach for modeling an irreversible heat engine","volume":"14","author":"Dong","year":"2012","journal-title":"Entropy"},{"key":"ref_138","unstructured":"Feidt, M. (2013). Thermodynamique Optimale en Dimensions Physiques Finies, Herm\u00e8s."},{"key":"ref_139","unstructured":"Perescu, S., Costea, M., Feidt, M., Ganea, I., and Boriaru, N. (2015). Advanced Thermodynamics of Irreversible Processes with Finite Speed and Finite Dimensions, Editura AGIR."},{"key":"ref_140","doi-asserted-by":"crossref","unstructured":"Feidt, M. (2017). Finite Physical Dimensions Optimal Thermodynamics 1. Fundamental, ISTE Press and Elsevier.","DOI":"10.1016\/B978-1-78548-233-5.50001-8"},{"key":"ref_141","unstructured":"Feidt, M. (2018). Finite Physical Dimensions Optimal Thermodynamics 2. Complex. Systems, ISTE Press and Elsevier."},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/j.enconman.2018.02.056","article-title":"Influence of the working fluid properties on optimized power of an irreversible finite dimensions Carnot engine","volume":"163","author":"Blaise","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_143","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1515\/jnet-2017-0047","article-title":"From finite time to finite physical dimensions thermodynamics: The Carnot engine and Onsager\u2019s relations revisited","volume":"43","author":"Feidt","year":"2018","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_144","doi-asserted-by":"crossref","unstructured":"Dumitrascu, G., Feidt, M., Popescu, A., and Grigorean, S. (2019). Endoreversible trigeneration cycle design based on finite physical dimensions thermodynamics. Energies, 12.","DOI":"10.3390\/WEF-06905"},{"key":"ref_145","doi-asserted-by":"crossref","unstructured":"Feidt, M., and Costea, M. (2019). Progress in Carnot and Chambadal modeling of thermomechnical engine by considering entropt and heat transfer entropy. Entropy, 21.","DOI":"10.3390\/e21121232"},{"key":"ref_146","doi-asserted-by":"crossref","unstructured":"Feidt, M., Costea, M., Feidt, R., Danel, Q., and P\u00e9rilhon, C. (2020). New criteria to characterize the waste heat recovery. Energies, 13.","DOI":"10.3390\/en13040789"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/3\/282\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:29:05Z","timestamp":1760160545000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/3\/282"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,26]]},"references-count":146,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["e23030282"],"URL":"https:\/\/doi.org\/10.3390\/e23030282","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,26]]}}}