Local stability analysis of a non-endoreversible heat pump

The purpose of this paper is to present a local stability analysis of a non-endoreversible heat pump operating at the minimum input power P for given heating load q(H) to the high-temperature reservoir, in the isothermal couplings of the working fluid with the heat reservoirs T-H and T-L(T-H > T-L), both having the same heat conductance alpha and using R to describe internal dissipations of the working fluid. A non-endoreversible heat pump 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 functions of alpha, R, q(H), T-H, 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 nonzero constant vector, and the other is a function of alpha, R, q(H), T-H, and T-L. Finally, we discuss the local stability and energetic properties of the non-endoreversible heat pump.