A local stability analysis of an endoreversible Carnot refrigerator, working at the maximum objective function of the product of the cooling rate R and the coefficient of performance ε, is presented. The endoreversible Carnot refrigerator consists of a reversible Carnot refrigerator that exchanges heat with the heat reservoirs TH through the thermal conductance α and with the cold reservoirs TL through the thermal conductance β. In addition, the working fluid has the same heat capacity C in the two isothermal branches of the cycle. By linearization and stability analysis, we find that the relaxation times are a function of α, β, the heat capacity C and τ=TL /TH; that the endoreversible Carnot refrigerator is stable for every value of α, β, C and τ; that after a perturbation, the system state exponentially decays to the steady state with either of two different relaxation times; that both relaxation times are proportional to α/2C; and that one of them is a monotonically increasing function τ and the other is almost independent of τ. Finally, the phase portraits for the trajectories after a small perturbation over the steady-state values of internal temperatures are presented.
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