Analysis of Thermodynamic Cycles of Heat Pumps and Magnetic Refrigerators Using Mathematical Models

This paper proposes a critical review of the different aspects concerning magnetic refrigeration systems, and performs a detailed analysis of thermodynamic cycles, using mathematical models found in the literature. Langevin’s statistical mechanical theory faithfully describes the physical operation of a refrigeration machine working according to a magnetic Ericsson cycle. Results of mathematical and real experimental models are compared to deduce which best describes the Ericsson cycle. The theoretical data are not perfectly consistent with the experimental data; there is a maximum deviation of about 30%. Numerical and experimental data confirm that very high Coefficient of Performance (COP) values of more than 20 can be achieved. The analysis of the Brayton cycle consisted of finding the mathematical model that considers the irreversibility of these machines. Starting from the thermodynamic properties of magnetocaloric materials based on statistical mechanics, the efficiency of an irreversible Brayton regenerative magnetic refrigeration cycle is studied. Considering the irreversibility in adiabatic transformations, the lower limit of the optimal ratio of two magnetic fields is determined, obtaining a valid optimization criterion for these machines operating according to a Brayton cycle. The results show that the Ericsson cycle achieves a higher Coefficient of Performance than the Brayton cycle, which has a higher cooling capacity as it operates with a larger temperature difference between the magnetocaloric material and source.