Local stability analysis of a thermoeconomic model of a Curzon-Ahlborn heat engine with a Dulong-Petit heat transfer law working at different regimes of performance

In recent works [1, 2], we reported a local stability analysis of a thermo-economic model of an irreversible heat engine working at different regimes of performance and considering a linear heat transfer law (the Newton law case). In those works, we showed that the relaxation times are function of α, C, τ = T₂/T₁, with T₁≤T₂ being the temperatures of the external heat reservoirs and the parameters f and R; that is, they depend on the materials that separate the working fluid from the reservoirs (through α); on the working fluid (through C, heat capacity); on the reservoirs temperatures (through τ); on fractional fuel costs (through f, which is associate to various energy sources from renewable energy until natural gas and on the internal irreversibilities (through R). In those works, we considered three regimes of performance: Maximum Power output, Maximum Efficient power [3] and the Ecological function regime [4]. In this work, we present a local stability analysis of a thermoeconomic model of an irreversible heat engine but considering a heat transfer law of the Dulong-Petit type. In our study we also consider three regimes of performance: Maximum Power output, maximum Efficient Power and maximum ecological function. We show that the relaxation time under maximum ecological function conditions is lesser than the relaxation times under both maximum power and maximum efficient power. Besides, we observe that the stability of the system improve as τ increases whereas the steady-state energetic properties of the engine declines for all cases of energy sources.