Local stability analysis of a thermo-economic model of a Chambadal-Novikov-Curzon-Ahlborn heat engine

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 T = T2/T1 (T1 > T2), 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 T 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. © 2011 by the authors.