In this paper, we present the magnetic refrigeration by magnetocaloric effect, for which the magnetic flux distribution has been modified in the Halbach cylinder. The insertion of a soft magnetic rod in the bore led to the alternating magnetic field with two regions of high flux density for magnetization and two regions of low flux density for demagnetization of magnetocaloric materials in the annular gap. The two-dimensional numerical simulations by the finite element method using COMSOL Multiphysics and Poisson SUPERFISH demonstrated the substitution effect of neodymium-iron-boron permanent magnets by soft magnetic low-carbon steels. The optimized soft magnetic cross-sectional area of 0.04 m(2) in the Halbach cylinder gave the maximum flux density of 2 T in the air gap, comparable to the peak field of existing prototypes. The flux density is further increased and became the largest when the ratio of external to internal radius of the cylinder is at the maximum. The cooling performance is also affected by the size of the cylinder, and the substantial value is obtained in a practical design with reserved air gap for magnetocaloric materials.
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