Optimization of the performance characteristics in an irreversible magnetic Ericsson refrigeration cycle

A general model of an irreversible Ericsson refrigeration cycle employing paramagnetic materials as the working substance is presented, in which multi-irreversibilities such as finite-rate heat transfer, regenerative loss, heat leak, efficiency of regenerator and internal irreversibility resulting from magnetic working substances are taken into account. On the basis of the general thermodynamic properties of paramagnetic materials and the optimal-control theory, the optimal mathematical expressions of cooling load, coefficient of performance and power input of the irreversible Ericsson refrigeration cycle using paramagnetic materials as the working substance are derived. By means of a numerical approach, the influence of the heat leak, the internal irreversibility, the efficiency of regenerator, the ratio of the magnetic fields on the cyclic performance characteristics of the refrigeration cycle are revealed and discussed in detail. Some important performance bounds, e.g. the maximum cooling load and the corresponding coefficient of performance, the maximum coefficient of performance and the corresponding cooling load, are determined and evaluated. Furthermore, several special cases may be deduced from the primary results in this paper. The conclusions obtained in the present paper are more general and useful than those existing in literature and can provide some new important information for the optimal design and performance improvement of magnetic refrigerators.