Local stability characteristics of a non-endoreversible heat engine working in the optimum region

The local stability of a non-endoreversible heat engine working between the maximum power output and the maximum efficiency is analyzed based on stability criteria for almost linear systems. A non-endoreversible heat engine system that is modeled by the differential equation may depend on the numerical values of certain parameters that appear in the equation. From the local stability analysis we find that a critical point of an almost linear system is a stable node. After a small perturbation the system state exponentially decays to steady-state with either of two characteristic relaxation times that are a function of the thermal conductance α, heat capacity C, temperatures of the heat reservoirs TH and TL, internal irreversible factor I, and a parameter θ measuring the degree of lying close to the maximum efficiency. The behavior of solutions of the system is exhibited qualitatively by sketching its phase portrait. Several special cases are discussed in detail so that some important conclusions relative to local stability of an irreversible heat engine in the literature may be derived from the present paper. Finally, we discuss the local stability and energetic properties of the non-endoreversible heat engine.