Calculation of the Optimal Magnetic Duty Cycle for a Graded Coaxial Magnet of a Rotary Type Magnetic Refrigerator

In the design of a rotary-type magnetic refrigerator, a high field of a coaxial magnet is desired. Typically, a high-field design can be achieved with a small duty cycle, which might not be optimized from the viewpoint of the thermal hydraulics of a magnetic refrigerator. In this work, a numerical simulation analysis of a graded coaxial magnet designed using a COMSOL program for a rotary-type active magnetic refrigeration (AMR) system was performed. The magnet structures are based on neodymium–iron–boron permanent magnets with thin gadolinium (Gd) and gadolinium-terbium alloy (Gd-Tb) plates as AMR materials. For a rotary-type magnetic cooling system, from the thermal–hydraulic point of view, the best duty cycle of a coaxial magnet should be 50% if the magnetic field can be kept constant during the period of duty cycles. However, the simulation calculation shows a serious reduction in the magnetic field strength at higher duty cycles, resulting in lower magnetic cooling efficiency. After considering the thermos-hydraulic part, the optimized duty cycle is around 30% in the case of a temperature span of 8 K between the hot and cold ends on a rotary-type magnetic cooling system. By applying graded Gd-Tb alloy along the flow direction, the performance of magnetic refrigeration improves significantly. Compared to a pure Gd AMR system, it is demonstrated that more than three times the increase in the cooling capacity can be achieved.