{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T13:05:41Z","timestamp":1773320741582,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2012,3,28]],"date-time":"2012-03-28T00:00:00Z","timestamp":1332892800000},"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-Time Thermodynamics has provided a fruitful theoretical framework for the optimization of heat engines operating between a heat source (at temperature ) and a heat sink (at temperature ). The aim of this paper is to propose a more complete approach based on the association of Finite-Time Thermodynamics and the Bond-Graph approach for modeling endoreversible heat engines. This approach makes it possible for example to find in a simple way the characteristics of the optimal operating point at which the maximum mechanical power of the endoreversible heat engine is obtained with entropy flow rate as control variable. Furthermore it provides the analytical expressions of the optimal operating point of an irreversible heat engine where the energy conversion is accompanied by irreversibilities related to internal heat transfer and heat dissipation phenomena. This original approach, applied to an analysis of the performance of a thermoelectric generator, will be the object of a future publication.<\/jats:p>","DOI":"10.3390\/e14040642","type":"journal-article","created":{"date-parts":[[2012,3,28]],"date-time":"2012-03-28T11:20:43Z","timestamp":1332933643000},"page":"642-653","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Association of Finite-Time Thermodynamics and a Bond-Graph Approach for Modeling an Endoreversible 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 78288 Guyancourt, France"},{"name":"Laboratoire du g\u00e9nie des proc\u00e9d\u00e9s pour l\u2019environnement, l\u2019\u00e9nergie et la sant\u00e9 (LGP2ES-EA21), Cnam-Cemagref, case 2D3R20, 292 rue saint Martin 75003 Paris, 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 78288 Guyancourt, 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\u00e9nergie et la sant\u00e9 (LGP2ES-EA21), Cnam-Cemagref, case 2D3R20, 292 rue saint Martin 75003 Paris, 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 54516 Vandoeuvre, 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\u00e9nergie et la sant\u00e9 (LGP2ES-EA21), Cnam-Cemagref, case 2D3R20, 292 rue saint Martin 75003 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,3,28]]},"reference":[{"key":"ref_1","unstructured":"Chambadal, P. (1957). Les Centrales Nucl\u00e9aires, Armand Colin."},{"key":"ref_2","first-page":"125","article-title":"The efficiency of atomic power station","volume":"7","author":"Novikov","year":"1958","journal-title":"J. Nucl. Energy"},{"key":"ref_3","unstructured":"Feidt, M. (1987). Thermodynamique et Optimisation Energ\u00e9tique des Syst\u00e8mes et Proc\u00e9d\u00e9s, Lavoisier."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Jou, D., Casas-Vasquez, J., and Lebon, G. (2000). Extended Irreversible Thermodynamics, Springer Verlag.","DOI":"10.1007\/978-3-642-56565-6"},{"key":"ref_5","unstructured":"Andresen, B. (1983). Finite Time Thermodynamics, Physics Laboratory, University of Copenhagen."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1063\/1.362674","article-title":"Entropy generation minimization: The new thermodynamics of finite size, and finite time processes","volume":"79","author":"Bejan","year":"1997","journal-title":"J. Appl. Phys."},{"key":"ref_7","unstructured":"Bejan, A., Tsatsaronis, G., and Moran, M. (1996). Thermal Design and Optimization, John Wiley & Sons."},{"key":"ref_8","first-page":"113","article-title":"Recherche sur les conditions optimales de fonctionnement des pompes \u00e0 chaleur ou machines \u00e0 froid associ\u00e9es \u00e0 un cycle de Carnot endoreversible","volume":"303","author":"Goth","year":"1986","journal-title":"C. R. Acad. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/S0306-2619(03)00138-7","article-title":"Ecological optimization for generalized irreversible Carnot engines","volume":"77","author":"Chen","year":"2004","journal-title":"Appl. Energy"},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1016\/S0196-8904(96)00085-4","article-title":"Optimal performance of an endoreversible Carnot heat pump","volume":"38","author":"Chen","year":"1997","journal-title":"Energy Convers. Manag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/1359-4311(95)00030-5","article-title":"General performance characteristics of finite speed Carnot refrigerator","volume":"16","author":"Chen","year":"1996","journal-title":"Appl. Therm. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/0360-5442(92)90006-L","article-title":"Finite-time thermodynamic analysis of a Carnot engine with internal irreversibility","volume":"17","author":"Wu","year":"1992","journal-title":"Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"529","DOI":"10.3390\/e11040529","article-title":"Optimal thermodynamics\u2014New upperbounds","volume":"11","author":"Feidt","year":"2009","journal-title":"Entropy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/j.applthermaleng.2006.09.020","article-title":"Optimization of the direct Carnot cycle","volume":"27","author":"Feidt","year":"2007","journal-title":"Appl. Therm. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2470","DOI":"10.3390\/e12122470","article-title":"Reconsideration of criteria and modeling in order to optimize the efficiency of irreversible thermomechanical heat engines","volume":"12","author":"Feidt","year":"2010","journal-title":"Entropy"},{"key":"ref_17","first-page":"570","article-title":"Efficiency of a Carnot engine at maximum power conditions","volume":"53","author":"Curzon","year":"1975","journal-title":"Am. J. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.pecs.2003.10.003","article-title":"Optimization of thermal systems based on finite-time thermodynamics and thermoeconomics","volume":"30","author":"Durmayaza","year":"2004","journal-title":"Prog. Energy Combust. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/S0196-8904(99)00107-7","article-title":"A comparative performance analysis of irreversible Carnot heat engines under maximum power density and maximum power conditions","volume":"41","author":"Kodal","year":"2000","journal-title":"Energy Convers. Manag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0196-8904(94)00040-7","article-title":"Endoreversible thermoeconomics","volume":"36","year":"1995","journal-title":"Energy Convers. Manag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/S1290-0729(03)00101-7","article-title":"Thermoeconomic optimization and parametric study of an irreversible Stirling heat pump cycle","volume":"43","author":"Tyagi","year":"2004","journal-title":"Int. J. Therm. Sci."},{"key":"ref_22","first-page":"7465:1","article-title":"An ecological optimization criterion for finite-time heat engines","volume":"69","year":"1991","journal-title":"J. Appl. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/S0306-2619(03)00138-7","article-title":"Ecological optimization for generalized irreversible Carnot engines","volume":"77","author":"Chen","year":"2004","journal-title":"Appl. Energy"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.mechatronics.2008.11.016","article-title":"A bond graph model-based evaluation of a control scheme to improve the dynamic performance of a solid oxide fuel cell","volume":"19","author":"Vijay","year":"2009","journal-title":"Mechatronics"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1103\/PhysRev.37.405","article-title":"Reciprocal relations in irreversible processes. I","volume":"37","author":"Onsager","year":"1931","journal-title":"Phys. Rev."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2265","DOI":"10.1103\/PhysRev.38.2265","article-title":"Reciprocal relations in irreversible processes. II","volume":"38","author":"Onsager","year":"1931","journal-title":"Phys. Rev."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lenoir, B., Michenaud, J., and Dauscher, A. (2010). Thermo\u00e9lectricit\u00e9: Des Principes aux Applications. Technique de l\u2019ing\u00e9nieur, R\u00e9f\u00e9rence K730.","DOI":"10.51257\/a-v2-k730"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/4\/642\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:49:36Z","timestamp":1760219376000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/4\/642"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,28]]},"references-count":27,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,4]]}},"alternative-id":["e14040642"],"URL":"https:\/\/doi.org\/10.3390\/e14040642","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,28]]}}}