Local stability analysis of an irreversible Carnot heat engine

The local stability of an irreversible Carnot heat engine has been studied based on the linearization technique for dynamical systems and local stability analysis. At two steady-states of the maximum power output and the maximum efficiency the expressions of the relaxation time of an irreversible Carnot heat engine are derived. It is found that the relaxation time is a function of the heat-transfer coefficient α and β, heat capacity C, temperatures of the heat reservoirs TH and TL, the degree of internal irreversibility ϕ and the internal heat conductance k. The influence of heat resistance, internal irreversibility and heat leak on the relaxation time is discussed. Phase portraits for the trajectories are presented in some representative cases. The results obtained here are more general and useful for the realistic irreversible heat engine than endoreversible heat engine.