Analytical solution of concentric two-pole Halbach cylinders as a preliminary design tool for magnetic refrigeration systems

Highlights: •An analytical model for concentric two-pole Halbach cylinders is presented. •A rectified cosine-like magnetic profile is generated in the air gap. •Interactions between two large cylinders result in low average energy density. •There are optimal values of the air gap height to maximize magnet efficiency. •Larger inner magnets are more robust to generate desired magnetic field variations. - Abstract: This work presents a parametric analysis of the performance of nested permanent magnet Halbach cylinders intended for applications in magnetic refrigeration and heat pumping. An analytical model for the magnetic field generated by the cylinders is used to systematically investigate the influence of their geometric parameters. The proposed configuration generates two poles in the air gap between the cylinders, where active magnetic regenerators are positioned for conversion of magnetic work into cooling capacity or heat power. A sample geometry based on previous designs of magnetic refrigerators is investigated, and the results show that the magnetic field in the air gap oscillates between 0 to approximately 1 T, forming a rectified cosine profile along the circumference of the gap. Calculations of the energy density of the magnets indicate the need to operate at a low energy (particular the inner cylinder) in order to generate a magnetic profile suitable for a magnetic cooler. In practice, these low-energy regions of the magnet can be potentially replaced by soft ferromagnetic material. A parametric analysis of the air gap height has been performed, showing that there are optimal values which maximize the magnet efficiency parameter ${\Lambda }_{\text{cool}}$. Some combinations of cylinder radii resulted in magnetic field changes that were too small for practical purposes. No demagnetization of the cylinders has been found for the range of parameters considered.