Influence of multi-irreversibilities on the performance of a Brayton refrigeration cycle working with an ideal Bose or Fermi gas

An irreversible cycle model of the quantum Brayton refrigeration cycle using an ideal Bose or Fermi gas as the working substance is established. Based on the theory of statistical mechanics and thermodynamic properties of ideal quantum gases, expressions for several important performance parameters such as the cooling rate, coefficient of performance and power input, are derived. The influence of the degeneracy of quantum gases, the internal irreversibility of the working substance and the finite-rate heat transfer between the working substance and the heat reservoirs on the optimal performance of the cycle is investigated. By using numerical solutions, the cooling rate of the cycle is optimized for a set of given parameters. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal boundaries of the coefficient of performance and power input are given. The optimally operating region of the cycle is determined. The expressions of some performance parameters for some special cases are derived analytically.