Parametric optimization of an irreversible magnetic Ericsson refrigerator with finite heat reservoirs

An irreversible cycle model of magnetic Ericsson refrigerators is established, in which the finite heat capacities of external heat reservoirs, heat-transfer irreversibility, inherent regenerative losses, additional regenerative losses due to thermal resistances and irreversibility inside the magnetic working substances are taken into account. On the basis of the thermodynamic equations of paramagnetic materials, the performance characteristics of the magnetic Ericsson refrigeration cycle are investigated. By using the method of the optimal control theory, the optimal equations between the cooling load and the coefficient of performance and between the cooling load and the power input are derived. Furthermore, the maximum cooling load and the corresponding coefficient of performance, the minimum power input and the optimally operating temperatures of the cyclic working substance are obtained. The optimal operating region of the magnetic Ericsson refrigerator is determined. The results obtained here are closer to the performance characteristics of practical magnetic refrigerators with finite heat reservoirs than those in literature and are helpful to the optimal design and performance improvement of magnetic Ericsson refrigerators.