Magnetic refrigeration uses magnetic field changes to provoke a phase transition in solid Magneto-Caloric Materials (MCM). Then, using a Heat Transfer Fluid, a Brayton-like refrigeration cycle can be produced. Developing these kind of refrigerators is usually costly, due to the amount of rare earth materials needed for the permanent magnet and the MCM. In order to aid in better designing such machines, a 3D DNS solver was developed. The solver includes the simulation of four different physical phenomena: the magnetic field, fluid velocity field, temperature field, and the Magneto-Caloric Effect. To produce an efficient solver, collateral coupling mechanisms were studied and deemed negligible, including the temperature dependency of the HTF (water) viscosity, and the influence of the magnetic permeability on the internal magnetic field of Gadolinium. The resolution of the physical phenomena was benchmarked separately and then the performance of the cycle solver was compared to a measured prototype. The solutions given by the new 3D DNS solver provide a more accurate description of the temperature field than the 2D solver available in the literature. The authors argue that this is probably partially due to the detailed simulation of the magnetic field (not accounted in 2D codes). The produced numerical solver is aimed to serve as a tool in the design process of magnetic refrigerators. By simulating conceptual magnetic regenerators, it is expected that the new prototypes experience a qualitative jump
