Local stability analysis of a class of endoreversible heat pumps

Abstract

The purpose of this paper is to present a local stability analysis of an endoreversible heat pump operating at the minimum input power P for given heating load qH to the high-temperature reservoir, for different thermal conductances α and β, in the isothermal couplings of the working fluid with the heat reservoirs TH and TL(TH>TL). An 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 a function of α, β, qH, TH, 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 α, β, qH, TH, and TL. Finally, we discuss the local stability and energetic properties of the endoreversible heat pump.