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

• Published in: Entropy (Basel, Switzerland) Vol. 13; no. 9; pp. 1584 - 1594
• Main Authors: Barranco-Jiménez, Marco A., Páez-Hernández, Ricardo T., Reyes-Ramírez, Israel, Guzmán-Vargas, Lev
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2011
• Subjects: endoreversible heat engine; local stability; thermo-economics
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e13091584

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.