{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T13:53:37Z","timestamp":1762005217534,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,6,29]],"date-time":"2020-06-29T00:00:00Z","timestamp":1593388800000},"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":["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>Based on the theoretical model of a heated ideal working fluid in the cylinder, the optimal motion path of the piston in this system, for the maximum work output, is re-studied by establishing the changed Lagrangian function and applying the elimination method when the initial internal energy, initial volume, finial volume and the process time are given and generalized radiative heat transfer law between the working fluid and heat bath is considered. The analytical solutions of the intermediate Euler-Lagrange arc with square, cubic and radiative heat transfer laws are taken as examples and obtained. The optimal motion path of the piston with cubic heat transfer law, which is obtained by applying the elimination method, is compared with that obtained by applying the Taylor formula expansion method through numerical example. The comparing result shows that the accuracy of the result which is obtained by applying the elimination method is not affected by the length of time of the expansion process of the working fluid, so this result is more universal.<\/jats:p>","DOI":"10.3390\/e22070720","type":"journal-article","created":{"date-parts":[[2020,6,29]],"date-time":"2020-06-29T05:28:56Z","timestamp":1593408536000},"page":"720","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Re-Optimization of Expansion Work of a Heated Working Fluid with Generalized Radiative Heat Transfer Law"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9012-6736","authenticated-orcid":false,"given":"Lingen","family":"Chen","sequence":"first","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kang","family":"Ma","sequence":"additional","affiliation":[{"name":"Unit 92941 of PLA, Huludao 125001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanlin","family":"Ge","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huijun","family":"Feng","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1063\/1.2916405","article-title":"Thermodynamics in finite time","volume":"37","author":"Andresen","year":"1984","journal-title":"Phys. Today"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1063\/1.362674","article-title":"Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes","volume":"79","author":"Bejan","year":"1996","journal-title":"J. Appl. Phys."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1002\/anie.201001411","article-title":"Current trends in finite-time thermodynamics","volume":"50","author":"Andresen","year":"2011","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1007\/s11431-015-5970-5","article-title":"Thermodynamic analyses and optimizations for thermoelectric devices: The state of the arts","volume":"59","author":"Chen","year":"2016","journal-title":"Sci. China Technol. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ge, Y.L., Chen, L.G., and Sun, F.R. (2016). Progress in finite time thermodynamic studies for internal combustion engine cycles. Entropy, 18.","DOI":"10.3390\/e18040139"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Feidt, M. (2017). The history and perspectives of efficiency at maximum power of the Carnot engine. Entropy, 19.","DOI":"10.3390\/e19070369"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1360\/N092018-00220","article-title":"Progresses in generalized thermodynamic dynamic-optimization of irreversible processes","volume":"49","author":"Chen","year":"2019","journal-title":"Sci. Sin. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1360\/N092018-00220","article-title":"Progress in generalized thermodynamic dynamic-optimization of irreversible cycles","volume":"49","author":"Chen","year":"2019","journal-title":"Sci. Sin. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Badescu, V. (2017). Optimal Control in Thermal Engineering, Springer.","DOI":"10.1007\/978-3-319-52968-4"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0009-2614(80)80256-9","article-title":"Maximum work production from a heated gas in a cylinder with piston","volume":"72","author":"Band","year":"1980","journal-title":"Chem. Phys. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1063\/1.329960","article-title":"Finite time thermodynamics: Optimal expansion of a heated working fluid","volume":"53","author":"Band","year":"1982","journal-title":"J. Appl. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1063\/1.331584","article-title":"Maximum power from a cycling working fluid","volume":"53","author":"Salamon","year":"1982","journal-title":"J. Appl. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3742","DOI":"10.1063\/1.329835","article-title":"Power considerations in the operation of a piston fitted inside a cylinder containing a dynamically heated working fluid","volume":"52","author":"Aizenbud","year":"1981","journal-title":"J. Appl. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1277","DOI":"10.1063\/1.330633","article-title":"Optimization of a model internal combustion engine","volume":"53","author":"Aizenbud","year":"1982","journal-title":"J. Appl. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1063\/1.329931","article-title":"Optimization of a model external combustion engine","volume":"53","author":"Band","year":"1982","journal-title":"J. Appl. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0196-8904(96)00231-2","article-title":"Optimal expansion of a heated working fluid with phenomenological heat transfer","volume":"39","author":"Chen","year":"1998","journal-title":"Energy Convers. Manage."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1179\/014426009X12448168550226","article-title":"Optimization of a model external combustion engine with linear phenomenological heat transfer law","volume":"82","author":"Song","year":"2009","journal-title":"J. Energy Inst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/01430750.2010.9675804","article-title":"Optimization of a model internal combustion engine with linear phenomenological heat transfer law","volume":"31","author":"Chen","year":"2010","journal-title":"Int. J. Ambient Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"094901","DOI":"10.1063\/1.2802187","article-title":"Optimal expansion of a heated working fluid for maximum work output with generalized radiative heat transfer law","volume":"102","author":"Song","year":"2007","journal-title":"J. Appl. Phys."},{"key":"ref_21","first-page":"447","article-title":"Optimum expansion of a heated under Dulong-Petit heat transfer law","volume":"24","author":"Ma","year":"2009","journal-title":"J. Eng. Therm. Energy Power"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1080\/01430750.2010.9675105","article-title":"Optimal expansion of a heated working fluid with convective-radiative heat transfer law","volume":"31","author":"Chen","year":"2010","journal-title":"Int. J. Ambient Energy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1093\/ijlct\/cts051","article-title":"Optimal expansion of a heated ideal gas with time-dependent heat conductance","volume":"8","author":"Chen","year":"2013","journal-title":"Int. J. Low-Carbon Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1515\/jnetdy.2011.007","article-title":"Optimal expansion of a heated working fluid for maximum work output with time-dependent heat conductance and generalized radiative heat transfer law","volume":"36","author":"Chen","year":"2011","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Ma, K., Feng, H.J., and Ge, Y.L. (2020). Optimal configuration of a gas expansion process in a piston-type cylinder with generalized convective heat transfer law. Energies, 13.","DOI":"10.3390\/en13123229"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1515\/JNETDY.2003.015","article-title":"Optimal process paths for endoreversible systems","volume":"28","author":"Hoffmann","year":"2003","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1515\/jnet-2018-0003","article-title":"Novikov engine with fluctuating heat bath temperature","volume":"43","author":"Schwalbe","year":"2018","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1515\/jnet-2019-0063","article-title":"Stochastic Novikov engine with Fourier heat transport","volume":"44","author":"Schwalbe","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1515\/jnet-2017-0051","article-title":"General properties for an Agrawal thermal engine","volume":"43","year":"2018","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1515\/jnet-2017-0047","article-title":"From finite time to finite physical dimensions thermodynamics: The Carnot engine and Onsager\u2019s relations revisited","volume":"43","author":"Feidt","year":"2018","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1515\/jnet-2018-0007","article-title":"Finite time thermodynamics: Realizability domain of heat to work converters","volume":"44","author":"Zaeva","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1515\/jnet-2018-0021","article-title":"Optimal control of an endoreversible solar power plant","volume":"43","author":"Schwalbe","year":"2018","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wu, Z.X., Chen, L.G., and Feng, H.J. (2018). Thermodynamic optimization for an endoreversible Dual-Miller cycle (DMC) with finite speed of piston. Entropy, 20.","DOI":"10.3390\/e20030165"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3165","DOI":"10.3390\/en12163165","article-title":"Endoreversible trigeneration cycle design based on finite physical dimensions thermodynamics","volume":"12","author":"Dumitrascu","year":"2019","journal-title":"Energies"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Meng, Z.W., Chen, L.G., and Wu, F. (2020). Optimal power and efficiency of multi-stage endoreversible quantum Carnot heat engine with harmonic oscillators at the classical limit. Entropy, 22.","DOI":"10.3390\/e22040457"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"de Vos, A. (2020). Endoreversible models for the thermodynamics of computing. Entropy, 22.","DOI":"10.3390\/e22060660"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Masser, R., Khodja, A., Scheunert, M., Schwalbe, K., Fischer, A., Paul, R., and Hoffmann, K.H. (2020). Optimized piston motion for an alpha-type Stirling engine. Entropy, 22.","DOI":"10.3390\/e22060700"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1986","DOI":"10.1073\/pnas.78.4.1986","article-title":"Finite-time thermodynamics: Engine performance improved by optimized piston motion","volume":"78","author":"Mozurkewich","year":"1981","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1063\/1.329894","article-title":"Optimal paths for thermodynamic systems. The ideal Otto cycle","volume":"53","author":"Mozurkewich","year":"1982","journal-title":"J. Appl. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2125","DOI":"10.1063\/1.335977","article-title":"Optimal paths for thermodynamic systems. The ideal Diesel cycle","volume":"58","author":"Hoffmann","year":"1985","journal-title":"J. Appl. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/7\/720\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:44:18Z","timestamp":1760175858000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/7\/720"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,29]]},"references-count":40,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,7]]}},"alternative-id":["e22070720"],"URL":"https:\/\/doi.org\/10.3390\/e22070720","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,6,29]]}}}