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Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine
Departamento de Formación Básica, Escuela Superior de Cómputo del IPN, Av. Miguel Bernard Esq. Juan de Dios Bátiz, U.P. Zacatenco, México D.F. 07738, México
Área de Física de Procesos Irreversibles, Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa Tamps., México D.F. 02200, México
Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas del IPN, Av. IPN 2580, L. Ticomán, México D.F. 07340, México
* Author to whom correspondence should be addressed.
Received: 29 June 2011; in revised form: 3 August 2011 / Accepted: 17 August 2011 / Published: 29 August 2011
Abstract: In this work we present a local stability analysis of the thermo-economic model of an irreversible heat engine working at maximum power conditions. The thermo-economic model is based on the maximization of a benefit function which is defined by the ratio of the power output and the total cost involved in the plant’s performance. Our study shows that, after a small perturbation, the system decays exponentially to the steady state determined by two different relaxation times. In particular, we show that the relaxation times are function of the temperature ratio τ = T2/T1 (T1 > T2), the cost function ƒ and the parameter R (a parameter related to the degree of internal irreversibilities). We observe that the stability of the system improves as τ increases whereas for changes in ƒ and R, the stability properties are characterized by a rapid decay along the fast eigendirection as ƒ increases and R decreases. Finally, we discuss our results in the context of energetic properties.
Keywords: thermo-economics; local stability; endoreversible heat engine
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Barranco-Jiménez, M.A.; Páez-Hernández, R.T.; Reyes-Ramírez, I.; Guzmán-Vargas, L. Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine. Entropy 2011, 13, 1584-1594.
Barranco-Jiménez MA, Páez-Hernández RT, Reyes-Ramírez I, Guzmán-Vargas L. Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine. Entropy. 2011; 13(9):1584-1594.
Barranco-Jiménez, Marco A.; Páez-Hernández, Ricardo T.; Reyes-Ramírez, Israel; Guzmán-Vargas, Lev. 2011. "Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine." Entropy 13, no. 9: 1584-1594.