{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:34:37Z","timestamp":1760243677034,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2012,7,12]],"date-time":"2012-07-12T00:00:00Z","timestamp":1342051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In recent decades, the approach known as Finite-Dimension Thermodynamics has provided a fruitful theoretical framework for the optimization of heat engines operating between a heat source (at temperature Ths) and a heat sink (at temperature Tcs). We will show in this paper that the approach detailed in a previous paper [1] can be used to analytically model irreversible heat engines (with an additional assumption on the linearity of the heat transfer laws). By defining two dimensionless parameters, the intensity of internal dissipation and heat leakage within a heat engine were quantified. We then established the analogy between an endoreversible heat engine and an irreversible heat engine by using the apparent temperatures (Tcs \u2192 T\u03bb,\u03c6 cs, Ths \u2192 T\u03bb,\u03c6 hs) and apparent conductances (Kh \u2192 K\u03bb h, Kc \u2192 K\u03bb c). We thus found the analytical expression of the maximum power of an irreversible heat engine. However, these apparent temperatures should not be used to calculate the conversion efficiency at the optimal operating point by analogy with the case of an endoreversible heat engine.<\/jats:p>","DOI":"10.3390\/e14071234","type":"journal-article","created":{"date-parts":[[2012,7,13]],"date-time":"2012-07-13T05:28:49Z","timestamp":1342157329000},"page":"1234-1258","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Association of Finite-Dimension Thermodynamics and a Bond-Graph Approach for Modeling an Irreversible Heat Engine"],"prefix":"10.3390","volume":"14","author":[{"given":"Yuxiang","family":"Dong","sequence":"first","affiliation":[{"name":"Renault, Advanced Electronics and Technologies Division, Technocentre Renault, 1 avenue de Golf Guyancourt 78288, France"},{"name":"Laboratoire du G\u00e9nie des Proc\u00e9d\u00e9s pour l\u2019Environnement, l\u2019\u00c9nergie et la Sant\u00e9 (LGP2ES-EA21), Cnam-Cemagref, case 2D3R20, 292 rue saint Martin Paris 75003, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amin","family":"El-Bakkali","sequence":"additional","affiliation":[{"name":"Renault, Advanced Electronics and Technologies Division, Technocentre Renault, 1 avenue de Golf Guyancourt 78288, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Feidt","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Energ\u00e9tique et de M\u00e9canique Th\u00e9orique et Appliqu\u00e9e, ENSEM, 2, avenue de la For\u00eat de Haye Vandoeuvre 54516, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Georges","family":"Descombes","sequence":"additional","affiliation":[{"name":"Laboratoire du G\u00e9nie des Proc\u00e9d\u00e9s pour l\u2019Environnement, l\u2019\u00c9nergie et la Sant\u00e9 (LGP2ES-EA21), Cnam-Cemagref, case 2D3R20, 292 rue saint Martin Paris 75003, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christelle","family":"P\u00e9rilhon","sequence":"additional","affiliation":[{"name":"Laboratoire du G\u00e9nie des Proc\u00e9d\u00e9s pour l\u2019Environnement, l\u2019\u00c9nergie et la Sant\u00e9 (LGP2ES-EA21), Cnam-Cemagref, case 2D3R20, 292 rue saint Martin Paris 75003, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"642","DOI":"10.3390\/e14040642","article-title":"Association of finite-time thermodynamics and a bond-graph approach for modeling an endoreversible heat engine","volume":"14","author":"Dong","year":"2012","journal-title":"Entropy"},{"key":"ref_2","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. 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