Local stability analysis of a non-endoreversible refrigerator

The purpose of this paper is to present a local stability analysis of a non-endoreversible refrigerator operating at the minimum input power P for given cooling load R absorbed from the cold reservoir, in the isothermal couplings of the working fluid with the heat reservoirs TH and TL(TH > TL) through a couple of thermal conductors, both having the same heat conductance α and using I to describe internal dissipations of the working fluid. A non-endoreversible refrigerator 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 relaxation times that are a function α, I, R, TL and the heat capacity C. We can exhibit qualitatively the behavior of solutions of the system by sketching its phase portrait. One eigenvector in a phase portrait is the non-zero constant vector, and the other is a function of α, I, R, TH and TL. Finally, we discuss the local stability and energetic properties of the non-endoreversible refrigerator.