Effect of geometrical shape of the working substance Gadolinium on the performance of a regenerative magnetic Brayton refrigeration cycle

Based on Mean Field Theory (MFT), the entropy of magnetic material Gadolinium (Gd), which is a function of the local magnetic field and temperature, is calculated and analyzed. This local magnetic field is the sum of the applied field H ₀ plus the exchange field H _W=λM and the demagnetizing field H _d=-NM, where the demagnetizing factor N depends on the shape of magnetic materials. Hereby, the impacts of the demagnetizing factor N on the magnetic entropy, magnetic entropy change and main thermodynamics performance of a regenerative magnetic Brayton refrigeration cycle using Gd as the working substance are investigated and evaluated in detail. The results obtained underline the importance of the shape of the working substance used in magnetic refrigerators for room-temperature application; elongated materials provide better thermodynamics performance such as higher COP and net heat absorption. It is pointed out that for low external fields, the magnetic refrigerator ceased to be functional if flat materials were used.