Performance analysis of irreversible quantum Stirling cryogenic refrigeration cycles and their parametric optimum criteria

Abstract

The influence of both the quantum degeneracy and the finite-rate heat transfer between the working substance and the heat reservoirs on the optimal performance of an irreversible Stirling cryogenic refrigeration cycle using an ideal Fermi or Bose gas as the working substance is investigated, based on the theory of statistical mechanics and thermodynamic properties of ideal quantum gases. The inherent regeneration losses of the cycle are analysed. Expressions for several important performance parameters such as the coefficient of performance, cooling rate and power input are derived. By using numerical solutions, the cooling rate of the cycle is optimized for a given power input. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal regions of the coefficient of performance and power input are determined. In particular, the optimal performance of the cycle in the strong and weak gas degeneracy cases and the high temperature limit are discussed in detail. The analytic expressions of some optimized parameters are derived. Some optimum criteria are given. The distinctions and connections between the Stirling refrigeration cycles working with the ideal quantum and classical gases are revealed.