{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T03:14:45Z","timestamp":1781752485026,"version":"3.54.5"},"reference-count":90,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,19]],"date-time":"2022-10-19T00:00:00Z","timestamp":1666137600000},"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":["52171317"],"award-info":[{"award-number":["52171317"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"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>This paper combines the mechanical efficiency theory and finite time thermodynamic theory to perform optimization on an irreversible Stirling heat-engine cycle, in which heat transfer between working fluid and heat reservoir obeys linear phenomenological heat-transfer law. There are mechanical losses, as well as heat leakage, thermal resistance, and regeneration loss. We treated temperature ratio x of working fluid and volume compression ratio \u03bb as optimization variables, and used the NSGA-II algorithm to carry out multi-objective optimization on four optimization objectives, namely, dimensionless shaft power output P\u00afs, braking thermal efficiency \u03b7s, dimensionless efficient power E\u00afp and dimensionless power density P\u00afd. The optimal solutions of four-, three-, two-, and single-objective optimizations are reached by selecting the minimum deviation indexes D with the three decision-making strategies, namely, TOPSIS, LINMAP, and Shannon Entropy. The optimization results show that the D reached by TOPSIS and LINMAP strategies are both 0.1683 and better than the Shannon Entropy strategy for four-objective optimization, while the Ds reached for single-objective optimizations at maximum P\u00afs, \u03b7s, E\u00afp, and P\u00afd conditions are 0.1978, 0.8624, 0.3319, and 0.3032, which are all bigger than 0.1683. This indicates that multi-objective optimization results are better when choosing appropriate decision-making strategies.<\/jats:p>","DOI":"10.3390\/e24101491","type":"journal-article","created":{"date-parts":[[2022,10,19]],"date-time":"2022-10-19T20:32:23Z","timestamp":1666211543000},"page":"1491","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5529-6652","authenticated-orcid":false,"given":"Haoran","family":"Xu","sequence":"first","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China"},{"name":"School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":"Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China"},{"name":"School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanlin","family":"Ge","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China"},{"name":"School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huijun","family":"Feng","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China"},{"name":"School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,19]]},"reference":[{"key":"ref_1","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_2","unstructured":"Andresen, B. (1983). Finite-Time Thermodynamics, University of Copenhagen."},{"key":"ref_3","first-page":"311","article-title":"Endoreversible thermodynamics","volume":"22","author":"Hoffmann","year":"1997","journal-title":"J. Non Equilib. Thermodyn."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1140\/epjb\/e2006-00399-x","article-title":"Performance characteristics of an irreversible thermally driven Brownian microscopic heat engine","volume":"53","author":"Zhang","year":"2006","journal-title":"Eur. Phys. J. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.enconman.2014.02.011","article-title":"Advanced exergoenvironmental assessment of a natural gas-fired electricity generating facility","volume":"81","author":"Aras","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.ijepes.2015.01.003","article-title":"Methods used for evaluation actual power generating thermal cycles and comparing them","volume":"69","year":"2015","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.rser.2016.09.033","article-title":"Thermal models for analysis of performance of Stirling engine: A review","volume":"68","author":"Ahmadi","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","unstructured":"Kaushik, S.C., Tyagi, S.K., and Kumar, P. (2018). Finite Time Thermodynamics of Power and Refrigeration Cycles, Springer.","DOI":"10.1007\/978-3-319-62812-7"},{"key":"ref_11","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_12","doi-asserted-by":"crossref","unstructured":"Feidt, M., and Costea, M. (2019). Progress in Carnot and Chambadal modeling of thermomechnical engine by considering entropy and heat transfer entropy. Entropy, 21.","DOI":"10.3390\/e21121232"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Patel, V.K., Savsani, V.J., and Tawhid, M.A. (2019). Thermal System Optimization, Springer.","DOI":"10.1007\/978-3-030-10477-1"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1504\/IJEX.2019.104099","article-title":"Performance simulation of a double-reheat Rankine cycle mercury turbine system based on exergy","volume":"30","author":"Gonca","year":"2019","journal-title":"Int. J. Exergy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5897","DOI":"10.1002\/er.4696","article-title":"Performance analysis of a novel eco-friendly internal combustion engine cycle","volume":"43","author":"Gonca","year":"2019","journal-title":"Int. J. Energy Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5811","DOI":"10.1007\/s13369-019-03747-4","article-title":"Performance Analysis and Simulation of a Diesel-Miller Cycle (DiMC) Engine","volume":"44","author":"Gonca","year":"2019","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.enconman.2019.02.081","article-title":"Thermoecology-based performance simulation of a Gas-Mercury-Steam power generation system (GMSPGS)","volume":"189","author":"Gonca","year":"2019","journal-title":"Energy Convers. Manag."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Feidt, M. (2020). Carnot cycle and heat engine: Fundamentals and applications. Entropy, 22.","DOI":"10.3390\/e22030348"},{"key":"ref_19","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_20","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_21","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_22","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_23","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1515\/jnet-2019-0102","article-title":"Optimal performance regions of Feynman\u2019s ratchet engine with different optimization criteria","volume":"45","author":"Ding","year":"2020","journal-title":"J. Non Equilib. Thermodyn."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Paul, R., and Hoffmann, K.H. (2021). A class of reduced-order regenerator models. Energies, 14.","DOI":"10.3390\/en14217295"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3675","DOI":"10.2298\/TSCI190710180G","article-title":"Exergy-based performance analysis and evaluation of a dual-diesel cycle engine","volume":"25","author":"Gonca","year":"2021","journal-title":"Therm. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1515\/jnet-2020-0084","article-title":"Modelling of irreversible two-stage combined thermal Brownian refrigerators and their optimal performance","volume":"46","author":"Qi","year":"2021","journal-title":"J. Non Equilib. Thermodyn."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Andresen, B., and Salamon, P. (2022). Future perspectives of finite-time thermodynamics. Entropy, 24.","DOI":"10.3390\/e24050690"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1504\/IJEX.2022.120893","article-title":"Investigation of maximum performance characteristics of seven-process cycle engine","volume":"37","author":"Gonca","year":"2022","journal-title":"Int. J. Exergy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2454","DOI":"10.1002\/er.7320","article-title":"Performance investigation and evaluation of an engine operating on a modified dual cycle","volume":"46","author":"Gonca","year":"2022","journal-title":"Int. J. Energy Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1515\/jnet-2021-0073","article-title":"Optimizing the piston paths of Stirling cycle cryocoolers","volume":"47","author":"Paul","year":"2022","journal-title":"J. Non Equilib. Thermodyn."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0360-5442(94)90111-2","article-title":"Power optimization of an endoreversible Stirling cycle with regeneration","volume":"19","author":"Blank","year":"1994","journal-title":"Energy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/01430750.1997.9675265","article-title":"The effect of regenerative losses on the efficiency of a Stirling heat engine at maximum power output","volume":"18","author":"Chen","year":"1997","journal-title":"Int. J. Ambient Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1002\/(SICI)1099-114X(199807)22:9<805::AID-ER404>3.0.CO;2-K","article-title":"Efficiency bound of a solar-driven Stirling heat engine system","volume":"22","author":"Chen","year":"1998","journal-title":"Int. J. Energy Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1016\/S0196-8904(97)10036-X","article-title":"Sun, F.R. Optimum performance of irreversible Stirling engine with imperfect regeneration","volume":"39","author":"Wu","year":"1998","journal-title":"Energy Convers. Manag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1243\/14680874JER01707","article-title":"Thermodynamic analysis of the Stirling heat engine with regenerative losses and internal irreversibilities","volume":"9","author":"Tlili","year":"2008","journal-title":"Int. J. Engine Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2234","DOI":"10.1016\/j.rser.2012.01.022","article-title":"Finite time thermodynamic evaluation of endoreversible Stirling heat engine at maximum power conditions","volume":"16","author":"Tlili","year":"2012","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.renene.2010.06.037","article-title":"Optimization of solar-powered Stirling heat engine with finite-time thermodynamics","volume":"36","author":"Li","year":"2011","journal-title":"Renew. Energy"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1093\/ijlct\/ctu030","article-title":"Investigation of the effect of design parameters on power output and thermal efficiency of a Stirling engine by thermodynamic analysis","volume":"11","author":"Ahmadi","year":"2016","journal-title":"Int. J. Low Carb. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.applthermaleng.2018.12.003","article-title":"Numerical modeling and optimization of beta-type Stirling engine","volume":"149","author":"Ahmed","year":"2019","journal-title":"Appl. Therm. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"051012","DOI":"10.1115\/1.4046629","article-title":"Thermodynamic analysis of solar low-temperature differential Stirling engine considering imperfect regeneration and thermal losses","volume":"142","author":"Ramachandran","year":"2020","journal-title":"J. Sol. Energy Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3688","DOI":"10.1016\/j.egyr.2021.06.063","article-title":"Study of coating effects on the performance of Stirling engine by non-ideal adiabatic thermodynamics modeling","volume":"7","author":"Ahadi","year":"2021","journal-title":"Energy Rep."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"101320","DOI":"10.1016\/j.tsep.2022.101320","article-title":"Thermodynamic-dynamic coupling of a Stirling engine for space exploration","volume":"32","author":"Henriques","year":"2022","journal-title":"Therm. Sci. Eng. Prog."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"128180","DOI":"10.1016\/j.physleta.2022.128180","article-title":"Performance of Heisenberg-coupled spins as quantum Stirling heat machine near quantum critical point","volume":"442","author":"Purkait","year":"2022","journal-title":"Phys. Lett. A"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"012006","DOI":"10.1088\/1742-6596\/2207\/1\/012006","article-title":"Molecular dynamics study of a nano-scale \u03b2-type Stirling engine","volume":"2207","author":"Kitaya","year":"2022","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_45","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_46","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_47","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1007\/s10765-009-0573-7","article-title":"A comparative performance analysis and optimization of irreversible Atkinson cycle under maximum power density and maximum power conditions","volume":"30","author":"Ust","year":"2009","journal-title":"Int. J. Thermophys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"6725","DOI":"10.1016\/j.apm.2016.02.010","article-title":"Performance analysis and optimization of irreversible Dual-Atkinson Cycle Engine (DACE) with heat transfer effects under maximum power and maximum power density conditions","volume":"40","author":"Gonca","year":"2016","journal-title":"Appl. Math. Model."},{"key":"ref_49","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_50","first-page":"475","article-title":"\u03b7 and P of a Carnot engine at maximum \u03b7P","volume":"7","author":"Yan","year":"1984","journal-title":"Chin. J. Nat."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1179\/174602206X90931","article-title":"A new performance criterion for heat engines: Efficient power","volume":"79","author":"Yilmaz","year":"2006","journal-title":"J. Energy Inst."},{"key":"ref_52","first-page":"643","article-title":"Efficient power of Brayton heat engine with friction","volume":"6","author":"Kumar","year":"2013","journal-title":"Int. J. Eng. Res. Technol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1093\/ijlct\/cts055","article-title":"Performance analysis of an Atkinson cycle with variable specific-heats of the working fluid under maximum efficient power conditions","volume":"8","author":"Patodi","year":"2013","journal-title":"Int. J. Low Carbon Technol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"043208","DOI":"10.1088\/1742-5468\/abf1f1","article-title":"Optimized efficiency at maximum figure of merit and efficient power of power law dissipative Carnot like heat engines","volume":"2021","author":"Nilavarasi","year":"2021","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"10492","DOI":"10.1016\/j.egyr.2022.08.188","article-title":"Optimal distribution of heat exchanger area for maximum efficient power of thermoelectric generators","volume":"8","author":"Tian","year":"2022","journal-title":"Energy Rep."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.renene.2013.05.005","article-title":"Application of the multi-objective optimization method for designing a powered Stirling heat engine: Design with maximized power, thermal efficiency and minimized pressure loss","volume":"60","author":"Ahmadi","year":"2013","journal-title":"Renew. Energy"},{"key":"ref_57","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_58","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1016\/j.rser.2016.05.034","article-title":"Designing a powered combined Otto and Stirling cycle power plant through multi-objective optimization approach","volume":"62","author":"Ahmadi","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.renene.2016.03.008","article-title":"Multi-objective optimization for GPU3 Stirling engine by combining multi-objective algorithms","volume":"94","author":"Luo","year":"2016","journal-title":"Renew. Energy"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.applthermaleng.2016.07.029","article-title":"Effective multi-objective optimization of Stirling engine systems","volume":"108","author":"Punnathanam","year":"2016","journal-title":"Appl. Therm. Eng."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1080\/01430750.2017.1303638","article-title":"Enhancing and multi-objective optimising of the performance of Stirling engine using third-order thermodynamic analysis","volume":"39","author":"Hooshang","year":"2018","journal-title":"Int. J. Ambient Energy"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/j.ijthermalsci.2017.10.030","article-title":"Performance analysis and multi-objective optimization of a Stirling engine based on MOPSOCD","volume":"124","author":"Dai","year":"2018","journal-title":"Int. J. Therm. Sci."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.enconman.2018.09.011","article-title":"Multi-objective thermodynamic optimization of a free piston Stirling engine using response surface methodology","volume":"176","author":"Ye","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1913","DOI":"10.1002\/htj.21463","article-title":"A multiobjective thermodynamic optimization of a nanoscale Stirling engine operated with Maxwell-Boltzmann gas","volume":"48","author":"Shah","year":"2019","journal-title":"Heat Transfer\u2014Asian Res."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1093\/ijlct\/ctaa073","article-title":"Thermodynamic assessment and performance optimization of solid oxide fuel cell-Stirling heat engine-reverse osmosis desalination","volume":"16","author":"Shakouri","year":"2021","journal-title":"Int. J. Low Carbon Technol."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"123468","DOI":"10.1016\/j.energy.2022.123468","article-title":"A potent numerical model coupled with multi-objective NSGA-II algorithm for the optimal design of Stirling engine","volume":"247","author":"Ahmed","year":"2022","journal-title":"Energy"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1002\/(SICI)1099-114X(199809)22:11<991::AID-ER427>3.0.CO;2-U","article-title":"Theoretical limits on the performance of Stirling engines","volume":"22","author":"Senft","year":"1998","journal-title":"Int. J. Energy Res."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Senft, J.R. (2007). Mechanical Efficiency of Heat Engines, Cambridge University Press.","DOI":"10.1017\/CBO9780511546105"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"124699","DOI":"10.1016\/j.energy.2022.124699","article-title":"Multi-objective optimization of Stirling heat engine with various heat transfer and mechanical losses","volume":"256","author":"Xu","year":"2022","journal-title":"Energy"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1080\/01430750.1989.9675133","article-title":"Power optimization of a finite-time solar radiant heat engine","volume":"10","author":"Wu","year":"1989","journal-title":"Int. J. Ambient Energy"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0196-8904(92)90119-H","article-title":"Optimal power from a radiating solar-powered thermionic engine","volume":"33","author":"Wu","year":"1992","journal-title":"Energy Convers. Manag."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/0360-5442(93)90043-D","article-title":"Design parameters of a radiative heat engine","volume":"18","author":"Goktun","year":"1993","journal-title":"Energy"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"2216","DOI":"10.1063\/1.354728","article-title":"Endoreversible thermal cycle with a nonlinear heat transfer law","volume":"74","year":"1993","journal-title":"J. Appl. Phys."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"014911","DOI":"10.1063\/1.2212271","article-title":"Convective heat transfer law for an endoreversible engine","volume":"100","author":"Huleihil","year":"2006","journal-title":"J. Appl. Phys."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.apenergy.2007.06.001","article-title":"Generalized irreversible heat-engine experiencing a complex heat-transfer law","volume":"85","author":"Chen","year":"2008","journal-title":"Appl. Energy"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1515\/jnet-2022-0024","article-title":"Optimal configuration of finite source heat engine cycle for maximum output work with complex heat transfer law","volume":"47","author":"Li","year":"2022","journal-title":"J. Non Equilib. Thermodyn."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1515\/jnet-2022-0029","article-title":"Heat engine cycle configurations for maximum work output with generalized models of reservoir thermal capacity and heat resistance","volume":"47","author":"Chen","year":"2022","journal-title":"J. Non Equilib. Thermodyn."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.joei.2014.04.008","article-title":"Performance optimization of a linear phenomenological law system Stirling engine","volume":"88","author":"Ding","year":"2015","journal-title":"J. Energy Inst."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A fast and elitist multiobjective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"114065","DOI":"10.1016\/j.enconman.2021.114065","article-title":"Multi-objective optimization of concentrated photovoltaic-thermoelectric hybrid system via non-dominated sorting genetic algorithm (NSGA II)","volume":"236","author":"Yusuf","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"120953","DOI":"10.1016\/j.energy.2021.120953","article-title":"A multi-objective optimization strategy of steam power system to achieve standard emission and optimal economic by NSGA-\u2161","volume":"232","author":"Xiao","year":"2021","journal-title":"Energy"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"123315","DOI":"10.1016\/j.ijheatmasstransfer.2022.123315","article-title":"Multi-objective optimization of 3D micro-fins using NSGA-II","volume":"197","author":"Soleimani","year":"2022","journal-title":"Int. J. Heat Mass Transfer"},{"key":"ref_83","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_84","doi-asserted-by":"crossref","unstructured":"Hwang, C.L., and Yoon, K. (1981). Multiple Attribute Decision Making-Methods and Applications a State of the Art Survey, Springer.","DOI":"10.1007\/978-3-642-48318-9"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.applthermaleng.2013.05.041","article-title":"A hybrid method of modified NSGA-II and Topsis to optimize performance and emissions of a diesel engine using biodiesel","volume":"59","author":"Etghani","year":"2013","journal-title":"Appl. Therm. Eng."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"115060","DOI":"10.1016\/j.enconman.2021.115060","article-title":"Thermally regenerative electrochemical refrigerators decision-making process and multi-objective optimization","volume":"252","author":"Kamali","year":"2022","journal-title":"Energy Convers. Manag."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.energy.2011.11.048","article-title":"Efficiency enhancement of a gas turbine cycle using an optimized tubular recuperative heat exchanger","volume":"38","author":"Sayyaadi","year":"2012","journal-title":"Energy"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"117127","DOI":"10.1016\/j.applthermaleng.2021.117127","article-title":"Multi-generation energy system based on geothermal source to produce power, cooling, heating, and fresh water: Exergoeconomic analysis and optimum selection by LINMAP method","volume":"195","author":"Khanmohammadi","year":"2021","journal-title":"Appl. Therm. Eng."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1016\/j.mcm.2005.09.012","article-title":"Application of Shannon\u2019s entropy to classify emergent behaviors in a simulation of laser dynamics","volume":"42","author":"Guisado","year":"2005","journal-title":"Math. Comput. Modell."},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"Zang, P.C., Chen, L.G., Ge, Y.L., Shi, S.S., and Feng, H.J. (2022). Four-objective optimization for an irreversible Porous Medium cycle with linear variation in working fluid\u2019s specific heat. Entropy, 24.","DOI":"10.3390\/e24081074"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1491\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:57:07Z","timestamp":1760144227000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1491"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,19]]},"references-count":90,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["e24101491"],"URL":"https:\/\/doi.org\/10.3390\/e24101491","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,19]]}}}