Optimal configuration of heat engines for maximum efficiency with generalized radiative heat transfer law
Lingen Chen*, Hanjiang Song, Fengrui Sun, and Shengbing Wang
Postgraduate School, Naval University of Engineering, Wuhan 430033, P.R. China Fax: 0086–27–83638709 Tel: 0086–27–83615046. *e–mail: lgchenna@yahoo.com, lingenchen@hotmail.com
Recibido el 24 de noviembre de 2008
Aceptado el 7 de diciembre de 2009
Abstract
Optimal configuration of a class of endoreversible heat engines with generalized radiative heat transfer law [q ∞ Δ (Tn] has been determined by this paper. The optimal cycle that maximizes the efficiency of the engines with fixed input energy has been obtained using optimal–control theory, and the differential equations are solved by Taylor series expansion. It is shown that the optimal cycle for maximum efficiency has eight branches including two isothermal branches, four maximum–efficiency branches and two adiabatic branches. The interval of each branch has been obtained, as well as the solutions of the temperatures of heat reservoirs and working fluid. Numerical examples are given for the optimal configurations with n = — 1, n=1, n=2, n=3 and n=4, respectively. The results obtained are compared with each other and with those results obtained for maximum power output.
Keywords: Generalized radiative heat transfer law; endoreversible heat engine; maximum efficiency; optimal configuration; finite time thermodynamics; generalized thermodynamic optimization.
Resumen
En este artículo se determina la configuración óptima de una clase de motor térmico endoreversible con la ley generalizada de transferencia de claro radiativa [q ∞ Δ (Tn]. El ciclo óptimo que maximiza la eficiencia de los motores con una entrada de energía dada se obtiene usando la teoría del control óptimo y las ecuaciones diferenciales son resueltas mediante la expanción en series de Taylor. Se muestra que el ciclo óptimo para máxima eficiencia tiene ocho ramas, incluyendo dos ramas isotérmicas, cuatro de máxima eficiencia y dos adiabáticas. Se muestra el intervalo para cada rama, así como la temperatura del recipiente calorífico y del fluido de trabajo. Los ejemplo numéricos se muestran para la configuración óptima con n= — 1, n=1, n=2, n=3 y n=4. Los resultado obtenidos son comparados unos con otros, y con éstos se obtiene la potencia máxima de salida.
Descriptores: Leyes de transferencia de calor; motores endoreversibles; máxima eficiencia; configuración óptima; termodinámica de tiempos finitos.
PACS: 05.70.–a
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Acknowledgements
This paper is supported by the Program for New Century Excellent Talents in University of P. R. China (Project No 20041006) and The Foundation for the Author of National Excellent Doctoral Dissertation of P. R. China (Project No. 200136).
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