{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:36Z","timestamp":1760242776273,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2016,6,28]],"date-time":"2016-06-28T00:00:00Z","timestamp":1467072000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As part of the efforts to unify the various branches of Irreversible Thermodynamics, the proposed work reconsiders the approach of the Carnot engine taking into account the finite physical dimensions (heat transfer conductances) and the finite speed of the piston. The models introduce the irreversibility of the engine by two methods involving different constraints. The first method introduces the irreversibility by a so-called irreversibility ratio in the entropy balance applied to the cycle, while in the second method it is emphasized by the entropy generation rate. Various forms of heat transfer laws are analyzed, but most of the results are given for the case of the linear law. Also, individual cases are studied and reported in order to provide a simple analytical form of the results. The engine model developed allowed a formal optimization using the calculus of variations.<\/jats:p>","DOI":"10.3390\/e18070243","type":"journal-article","created":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T06:20:33Z","timestamp":1467181233000},"page":"243","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Nonlinear Thermodynamic Analysis and Optimization of a Carnot Engine Cycle"],"prefix":"10.3390","volume":"18","author":[{"given":"Michel","family":"Feidt","sequence":"first","affiliation":[{"name":"Laboratoire d'\u00c9nerg\u00e9tique et de M\u00e9canique Th\u00e9orique et Appliqu\u00e9e, UMR 7563, Universit\u00e9 de Lorraine, 2, avenue de la For\u00eat de Haye, Vandoeuvre-l\u00e8s-Nancy 54518, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Monica","family":"Costea","sequence":"additional","affiliation":[{"name":"Department of Engineering Thermodynamics, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stoian","family":"Petrescu","sequence":"additional","affiliation":[{"name":"Department of Engineering Thermodynamics, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Camelia","family":"Stanciu","sequence":"additional","affiliation":[{"name":"Department of Engineering Thermodynamics, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,6,28]]},"reference":[{"key":"ref_1","unstructured":"Carnot, S. 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