Local stability analysis of a thermoeconomic model of a Curzon-Ahlborn heat engine with a Dulong-Petit heat transfer law

In a recent work [1], we studied the thermoeconomics of a Novikov power plant model in terms of the maximization of a benefit function defined by the ratio of the plant's power output and the total cost involved in the plant's performance. In that work, we use different heat transfer laws: the so called Newton's law of cooling, the Stefan-Boltzmann radiation law, the Dulong-Petit's law and another phenomenological heat transfer law. We also have calculated the optimal efficiency in terms of the temperature ratio τ = T₂/T₁ (T₁ > T₂, being the temperatures of the external heat reservoirs) and a parameter f (fractional fuel cost), which is associated to several energies resources, considering energy sources where de investment is the preponderant cost (f 0) until energy source where the fuel is the predominant cost (f 1). In this work, we present a local stability analysis of a thermoeconomic model of an irreversible heat engine working at maximum power conditions and considering a heat transfer law of the Dulong-Petit type. We show that the relaxation times are function of τ, f and R, (a parameter which comes from the Clausius inequality and measure the degree of the internally irreversibilities of the system). Our results generalize other results obtained in the literature [2]. We show that the stability of the system improve as increases τ whereas the steady-state energetic properties of the engine declines for all cases of energy sources treated here.