Design of nested Halbach cylinder arrays for magnetic refrigeration applications Paulo V. Trevizoli n , Jaime A. Lozano, Guilherme F. Peixer, Jader R. Barbosa Jr. POLO – Research Laboratories for Emerging Technologies in Cooling and Thermophysics, Department of Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, SC, Brazil article info Article history: Received 14 May 2015 Received in revised form 24 June 2015 Accepted 11 July 2015 Available online 14 July 2015 Keywords: Nested Halbach cylinder Magnetic refrigeration Active magnetic regenerator Design procedure Experimental validation abstract We present an experimentally validated analytical procedure to design nested Halbach cylinder arrays for magnetic cooling applications. The procedure aims at maximizing the magnetic flux density variation in the core of the array for a given set of design parameters, namely the inner diameter of the internal magnet, the air gap between the magnet cylinders, the number of segments of each magnet and the remanent flux density of the Nd 2 Fe 14 B magnet grade. The design procedure was assisted and verified by 3-D numerical modeling using a commercial software package. An important aspect of the optimal design is to maintain an uniform axial distribution of the magnetic flux density in the region of the inner gap occupied by the active magnetocaloric regenerator. An optimal nested Halbach cylinder array was manufactured and experimentally evaluated for the magnetic flux density in the inner gap. The analy- tically calculated magnetic flux density variation agreed to within 5.6% with the experimental value for the center point of the magnet gap. & 2015 Elsevier B.V. All rights reserved. 1. Introduction Magnetic refrigeration at room temperature is an emerging technology with numerous developments in magnetocaloric working materials [1,2], magnetic circuits [3] and active magnetic regenerator (AMR) design [4]. Different types of magnetic field sources have been used in magnetic cooling prototypes through- out the years [5,6]. The pioneering prototypes of Brown [7] and Zimm et al. [8] used superconducting coils to generate the mag- netic field. Permanent magnets, which are more frequent in recent prototypes, have been considered more advantageous due to the relatively small energy cost to generate an average-to-high mag- netic flux density (generally 1.0 T > ). From a thermodynamic cycle perspective, permanent magnet arrangements allow for a recovery of the work needed to magnetize the solid refrigerant, which in- creases the theoretical potential for large efficiency of magnetic refrigeration. Additionally, permanent magnet circuits require lit- tle maintenance to confine the magnetic flux lines into a volume region without generating electromagnetic perturbations in the surroundings. These characteristics make this class of magnetic circuits more attractive for small scale AMRs. Different designs of permanent magnet circuits have been de- veloped for AMR coolers, such as the C-shaped Halbach [9,10], Halbach cylinder [11], nested Halbach cylinders [12,13], rotor– stator [14], and the coaxial permanent magnet circuit [15]. A re- view of magnet designs for magnetic refrigeration was carried out by Bjørk et al. [3]. The performance of AMR systems depends on a synergistic coupling between the designs of the regenerator and the magnetic circuit. Parameters such as the regenerator aspect ratio and bed geometry, mass of magnetocaloric material, number of re- generators, magnetic field volume, magnetic field waveform and magnetic field intensity have to be considered simultaneously to achieve an optimum compromise between size, cost and effi- ciency. With this in mind, Bjørk et al. [15] proposed the following figure of merit to characterize permanent magnet designs for magnetic refrigeration: ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ B B 1 cool high 2/3 low 2/3 Field Magnet Λ τ = 〈 〉 −〈 〉 ϑ ϑ () ⁎ where B high 〈 〉 is the volumetric average high magnetic flux density, B low 〈 〉 is the volumetric average low magnetic flux density, Field ϑ is the total volume where the magnetic field is applied, Magnet ϑ is the volume of permanent magnet raw material, for instance, Nd 2 Fe 14 B, and τ ⁎ is the fraction of the cycle period during which the magnet is used. cool Λ quantifies the potential of a magnetic circuit for magnetic refrigeration applications. An ideal magnet for an AMR prototype should guarantee a high magnetic field variation (higher magnetocaloric effect), a large volume of generated magnetic field Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jmmm Journal of Magnetism and Magnetic Materials http://dx.doi.org/10.1016/j.jmmm.2015.07.023 0304-8853/& 2015 Elsevier B.V. All rights reserved. n Corresponding author. E-mail address: trevizoli@polo.ufsc.br (P.V. Trevizoli). Journal of Magnetism and Magnetic Materials 395 (2015) 109–122