Investigación

Maximum efficiency of an irreversible heat engine with a distributed working fluid and linear phenomenological heat transfer law

Lingen Chen^*, Shaojun Xia, and Fengrui Sun

Postgraduate School, Naval University of Engineering, Wuhan 430033, P.R. China, Fax: 0086–27–83638709. Tel: 0086–27–83615046 *e–mail address: , lingenchen@hotmail.com , lgchenna@yahoo.com.

Recibido el 4 de enero de 2010
Aceptado el 9 de marzo de 2010

Abstract

Maximum efficiency of an irreversible heat engine with a distributed working fluid, in which the heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law , is studied in this paper by using finite–time thermodynamics based on Orlov and Berry's workⁱ. Two kinds of efficiencies are defined, and the problems are divided into three cases. Optimal control theory is used to determine the upper bounds of efficiencies of the heat engines for various cases. Numerical examples of the two efficiencies for the irreversible heat engine with lumped–parameter model working between variable temperature reservoirs are provided, and the effects of changes of the reservoir's temperature on the maximum efficiency of the heat engine are analyzed. The obtained results are also compared with those obtained by Orlov and Berryⁱⁱ with Newtonian heat transfer law .

Keywords: Finite–time thermodynamics; linear phenomenological heat transfer law; heat engine; distributed working fluid; maximum efficiency; optimal control.

Resumen

En este artículo se estudia la eficiencia máxima de un motor térmico irreversible con un fluido de trabajo distribuido, en el cual las transferencias térmicas entre el fluido de trabajo y los depósitos térmicos obedecen la ley fenomenológica linear de transferencia térmica, usando la termodinámica del finito–tiempo basada en el trabajo de Orlov y Berryⁱ. Se definen dos clases de eficiencias, y los problemas se dividen en tres casos. La teoría de control óptima se utiliza para determinar los límites superiores de las eficiencias de los motores térmicos para varios casos. Se proporcionan ejemplos numéricos de las dos eficiencias de motor térmico irreversible con el modelo del amontonar–parámetro trabajando entre los depósitos de temperatura variable, y se analizan los efectos de los cambios de temperatura del recipiente en la eficacia máxima del motor térmico. Los resultados obtenidos también se comparan con los obtenidos por Orlov y Barryⁱⁱ con la ley neutoniana del transferencia térmica .

Descriptores: Termodinámica de tiempos finitos; ley lineal fenomenológica de transferencia de calor; motor térmico; fluido de trabajo distribuido; eficiencia máxima; control óptimo.

PACS: 05.70.Ln; 05.60.Cd; 05.70.–a

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Acknowledgements

This paper is supported by The National Natural Science Foundation of P. R. China (Project No. 10905093), 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 reviewer for his careful, unbiased and constructive suggestions, which led to this revised manuscript.

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