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

Author： Barranco-Jiménez Marco A. Páez-Hernández Ricardo T. Reyes-Ramírez Israel Guzmán-Vargas Lev

Publisher： MDPI

E-ISSN： 1099-4300|13|9|1584-1594

ISSN： 1099-4300

Source： Entropy, Vol.13, Iss.9, 2011-08, pp. : 1584-1594

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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 = T 2 / T 1 ( T 1 > T 2 ), the cost function f 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 f and R, the stability properties are characterized by a rapid decay along the fast eigendirection as f increases and R decreases. Finally, we discuss our results in the context of energetic properties.