Local and global stability analysis of a Curzon-Ahlborn model applied to power plants working at maximum $k$-efficient power

TL;DR

This paper analyzes the local and global stability of the Curzon-Ahlborn heat engine model operating at maximum k-efficient power, using Lyapunov functions to demonstrate asymptotic stability under linear heat transfer laws.

Contribution

It extends stability analysis to the generalized maximum k-efficient power regime and applies Lyapunov theory to demonstrate stability of the steady-state temperatures.

Findings

Restructured operation conditions improve stability against perturbations.

Lyapunov functions confirm asymptotic stability of the model.

The role of the k parameter influences the evolution of heat flow perturbations.

Abstract

The analysis of the effect of noisy perturbations on real heat engines, working on any steady-state regime has been a topic of interest within the context of Finite-Time Thermodynamics (FTT). The study of their local stability has been proposed through the so-called performance regimes: maximum power output, maximum ecological function, among others. Recently, the global stability analysis of an endoreversible heat engine was also studied taking into account the same performance regimes. We present a study of local and global stability analysis of power plant models (the Curzon-Ahlborn model) operating on a generalized efficient power regime called maximum k-efficient power. We apply the Lyapunov stability theory to construct the Lyapunov functions to prove the asymptotically stable behavior of the steady-state of intermediate temperatures in the Curzon-Ahlborn model. We consider the effect of a linear heat transfer law on the phase portrait description of real power plants, as well as the role of the $k$ parameter in the evolution of perturbations to heat flow. In general, restructured operation conditions show better stability in external perturbations.