Investigación

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,
e–mail: lgchenna@yahoo.com; lingenchen@hotmail.com

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

Abstract

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.

Resumen

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

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Acknowledgments

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.

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