{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T23:51:55Z","timestamp":1778543515139,"version":"3.51.4"},"reference-count":99,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,5]],"date-time":"2018-03-05T00:00:00Z","timestamp":1520208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of P.R. China","award":["51576207"],"award-info":[{"award-number":["51576207"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Power output (   P   ), thermal efficiency (   \u03b7   ) and ecological function (   E   ) characteristics of an endoreversible Dual-Miller cycle (DMC) with finite speed of the piston and finite rate of heat transfer are investigated by applying finite time thermodynamic (FTT) theory. The parameter expressions of the non-dimensional power output (    P \u00af    ),    \u03b7    and non-dimensional ecological function (    E \u00af    ) are derived. The relationships between     P \u00af     and cut-off ratio (   \u03c1   ), between     P \u00af     and    \u03b7   , as well as between     E \u00af     and    \u03c1    are demonstrated. The influences of    \u03c1    and piston speeds in different processes on     P \u00af    ,    \u03b7    and     E \u00af     are investigated. The results show that     P \u00af     and     E \u00af     first increase and then start to decrease with increasing    \u03c1   . The optimal cut-off ratio      \u03c1  o p t       will increase if piston speeds increase in heat addition processes and heat rejection processes. As piston speeds in different processes increase, the maximum values of     P \u00af     and     E \u00af     increase. The results include the performance characteristics of various simplified cycles of DMC, such as Otto cycle, Diesel cycle, Dual cycle, Otto-Atkinson cycle, Diesel-Atkinson cycle, Dual-Atkinson cycle, Otto-Miller cycle and Diesel-Miller cycle. Comparing performance characteristics of the DMC with different optimization objectives, when choosing     E \u00af     as optimization objective,    \u03b7    improves 26.4% compared to choosing     P \u00af     as optimization objective, while     P \u00af     improves 74.3% compared to choosing    \u03b7    as optimization objective. Thus, optimizing    E    is the best compromise between optimizing    P    and optimizing    \u03b7   . The results obtained can provide theoretical guidance to design practical DMC engines.<\/jats:p>","DOI":"10.3390\/e20030165","type":"journal-article","created":{"date-parts":[[2018,3,6]],"date-time":"2018-03-06T07:37:25Z","timestamp":1520321845000},"page":"165","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Thermodynamic Optimization for an Endoreversible Dual-Miller Cycle (DMC) with Finite Speed of Piston"],"prefix":"10.3390","volume":"20","author":[{"given":"Zhixiang","family":"Wu","sequence":"first","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Naval University of Engineering, Wuhan 430033, China"},{"name":"Military Key Laboratory for Naval Ship Power Engineering, Naval University of Engineering, Wuhan 430033, China"},{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lingen","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Naval University of Engineering, Wuhan 430033, China"},{"name":"Military Key Laboratory for Naval Ship Power Engineering, Naval University of Engineering, Wuhan 430033, China"},{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huijun","family":"Feng","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Naval University of Engineering, Wuhan 430033, China"},{"name":"Military Key Laboratory for Naval Ship Power Engineering, Naval University of Engineering, Wuhan 430033, China"},{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,5]]},"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. 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