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Revista mexicana de física

Print version ISSN 0035-001X

Rev. mex. fis. vol.56 n.2 México Apr. 2010




Optimal ratios of the piston speeds for a finite speed endoreversible Carnot heat engine cycle


Huijun Feng, Lingen Chen*, and Fengrui Sun


Postgraduate School, Naval University of Engineering, Wuhan 430033, P.R. China.


*Corresponding author.
Fax: 0086–27–83638709,
Tel: 0086–27–83615046,


Recibido el 22 de junio de 2009
Aceptado el 11 de enero de 2010



The performance of an endoreversible Carnot heat engine cycle is analyzed and optimized using the theory of finite time thermodynamics based on Agrawal and Menon'si model of finite speed of the piston on the four branches and Curzon and Ahlborn'sii model of finite rate of heat transfer. The finite speeds of the piston on the four branches are further assumed to be different, which is unlike the model of constant–speed of the piston on the four branches. The analytical formula between power and efficiency of the cycle is derived for a fixed cycle period. There exist optimal ratios of the finite piston speeds on the four branches. The effects of the temperature ratio of the heat reservoirs on the dimensionless power versus efficiency of the cycle and isothermal expansion ratio are obtained by numerical examples.

Keywords: Finite time thermodynamics; endoreversible Carnot heat engine; finite speed of the piston; finite rate of heat transfer; power; efficiency.



Se analiza y optimiza el funcionamiento cíclico de un motor endoreversible de Carnot, utilizando la teoría termodinámica de tiempo finito basada en el modelo de Agrawal y Menoni de velocidad finita del pistón en los cuatro cilindros, y en el modelo de rapidez finita de transporte de calor de Curzon y Ahlbornii. También se supone que las velocidades del pistón en los cuatro cilindros son diferentes. Se deduce la fórmula analítica de la potencia y la eficiencia para un período del ciclo. Resultan cocientes óptimos para las velocidades finitas del pistón en los cuatro cilindros. Se obtienen, mediante ejemplos numéricos, los efectos del cociente de temperatura de los focos térmicos sobre la potencia versus la eficiencia del ciclo y el coeficiente de dilatación isotérmica.

Descriptores: Termodinámica de tiempo finito; motor endoreversible de Carnot; velocidad finita del pistón; potencia; eficiencia.


PACS: 05.70.–a; 05.30–d





This paper is supported by Program for New Century Excellent Talents in University of P.R. China (Project No: NCET–04–1006) and the Foundation for the Author of National Excellent Doctoral Dissertation of P.R. China (Project No: 200136). The authors wish to thank the reviewers for their careful, unbiased and constructive suggestions, which led to this revised manuscript.



i. D.C. Agrawal and V.J. Menon, Eur. J. Phys. 30 (2009) 2951.        [ Links ]

ii. Curzon and Ahlborn, Am. J. Phys. 43 (1975) 22.        [ Links ]

1. I.I. Novikov, Atommaya Energiya 3 (1957) 409.        [ Links ]

2. P. Chambdal, Les Centrales Nucleases (Paris: Armand Colin, 1957) p. 41.        [ Links ]

3. F.L. Curzon and B. Ahlborn, Am. J. Phys. 43 (1975) 22.        [ Links ]

4. B. Andresen, Finite Time Thermodynamics. Physics Laboratory II (University of Copenhagen, 1983).        [ Links ]

5. A. De Vos, Endoreversible Thermodynamics of Solar Energy Conversion (Oxford: Oxford University Press, 1992).        [ Links ]

6. A. Bejan, J. Appl. Phys. 79 (1996) 1191.        [ Links ]

7. M. Feidt, Thermodynamique et Optimisation Energetique des Systems et Procedes, 2nd Ed. (Paris: Technique et Documentation, Lavoisier, 1996).        [ Links ]

8. R.S. Berry et al., Thermodynamic Optimization of Finite Time Processes (Chichester: Wiley, 1999).        [ Links ]

9. L. Chen, C. Wu, and F. Sun, J. Non–Equilib. Thermodyn. 24 (1999) 327.        [ Links ]

10. L. Chen and F. Sun, Advances in Finite Time Thermodynamics: Analysis and optimization (New York: Nova Science Publishers, 2004).        [ Links ]

11. W. Muschik and K.H. Hoffmann, J. Non–Equilib. Thermody. 31 (2006) 293.        [ Links ]

12. M. Feidt, Int. J. Exergy 5 (2008) 500.        [ Links ]

13. S. Petrescu, M. Costea, M. Feidt, and O. Malancioiu, Proc. Birac, Bucuresti, Romania (2000) 22.        [ Links ]

14. S. Petrescu, M. Costea, and M. Feidt, Optimization of a Carnot cycle engine by using finite speed thermodynamics and the direct method Proc. ECOS'2001, Istanbul, Turkey, July, 2001, Vol. I, pp. 151–161.        [ Links ]

15. S. Petrescu, M. Feidt, and M. Costea, Optimization of Carnot cycle engine with internal and external irreversibilities by using thermodynamics with finite speed Proc. of the 8th Francophone Congress Recent Progress on Process Design, CFGP' 2001, Nancy, A. Storck, J. Boudrant, T. Tondeur, eds., Tech & Doc, Paris, France, Vol. 15–2001, No. 83, pp. 149–156, 2001.        [ Links ]

16. S. Petrescu, M. Costea, C. Harman, and M. Costea, Optimization of the irreversible Carnot cycle engine for maximum efficiency and maximum power through use of finite speed ther–modynamic analysis Proc. ECOS'2002, Berlin, Germany, July 3–5, 2002, Vol. II, pp. 1361–1368.        [ Links ]

17. S. Petrescu, C. Harman, M. Costea, and M. Feidt, Thermodynamics with finite speed versus thermodynamics in finite time in the optimization of Carnot cycle Proc. of the 6th ASME–JSME Thermal Engineering Joint Conference, Hawaii, March16–20, 2003.        [ Links ]

18. M. Feidt, M. Costea, C. Petre, and S.Petrescu Appl. Thermal Engineering 27 (2007) 829.        [ Links ]

19. D.C. Agrawal and V.J. Menon, Eur. J. Phys. 30 (2009) 295.        [ Links ]

20. D.C. Agrawal, Eur. J. Phys. 30 (2009) 587.        [ Links ]

21. M. Mozurkewich and R.S. Berry J. Appl. Phys. 53 (1982) 34.        [ Links ]

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