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Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine

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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
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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
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Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas del IPN, Av. IPN 2580, L. Ticomán, México D.F. 07340, México
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Author to whom correspondence should be addressed.
Entropy 2011, 13(9), 1584-1594; https://doi.org/10.3390/e13091584
Received: 29 June 2011 / Revised: 3 August 2011 / Accepted: 17 August 2011 / Published: 29 August 2011
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. View Full-Text
Keywords: thermo-economics; local stability; endoreversible heat engine 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.

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