**5.2 Structure B: Halbach cylider**

The structure B is a Halbach cylinder (Fig. 20). It is a magnetized cylinder composed of 'N' segments of ferromagnetic material producing (in the idealized case) an intense magnetic field confined entirely within the cylinder with zero field outside. This second structure can be used in an AMRR system. The MCE material, which can be in the form of plates stacked in a cylinder, is guided by a linear motor or actuator to create the phases of magnetization (material located inside the cylinder) and the demagnetization phase (material located 244 Trends in Electromagnetism – From Fundamentals to Applications

(a) (b)

From the definition of the MCE, it is obvious that the performance of a magnetic refrigeration system depends mainly on the efficiency of the MCE material and the strength of the magnetic field. Thus the study of magnetic field sources dedicated to magnetic refrigeration systems is of a paramount importance. In this section we will pay a particular

The field sources described throughout this section are built with permanent magnets (Neodymium Iron Boron) with a remanent magnetization of 1.46 *Br* = T and a magnetic

ensure a better heat exchange between the MCE material and the exchanging fluid, other forms are considered (plates, powder, etc). The yoke, when it exists, is made of XC10 steel.

This first structure is suitable for linear magnetic refrigeration systems with direct cycles. It consists of two magnets (to create the magnetic field), a soft magnetic material yoke (to canalize the magnetic flux) and a block of MCE material (to create the cold) as shown in Fig. 19 (a). The MCE material has a linear alternating movement along the 'y' axis (to achieve magnetization and demagnetization phases). The magnetic characteristics (induction and magnetic force profiles) are shown in Fig. 19 (b) and Fig. 19 (c) while Fig. 19 (d) represents

The structure B is a Halbach cylinder (Fig. 20). It is a magnetized cylinder composed of 'N' segments of ferromagnetic material producing (in the idealized case) an intense magnetic field confined entirely within the cylinder with zero field outside. This second structure can be used in an AMRR system. The MCE material, which can be in the form of plates stacked in a cylinder, is guided by a linear motor or actuator to create the phases of magnetization (material located inside the cylinder) and the demagnetization phase (material located

*<sup>r</sup>* = . The MCE material used is gadolinium with isotropic magnetic

*<sup>r</sup>* = . In this study, MCE solid blocks are considered. However, in actuality to

Fig. 18. Temperature profiles given by the AMRR numerical model.

attention to the design of these sources using the finite element method.

**5. Magnetostatic study** 

permeability of 1.064 μ

**5.1 Structure A: monobloc linear system** 

**5.2 Structure B: Halbach cylider** 

the distribution of the magnetic induction B in Tesla.

permeability 2 μ

Fig. 19. Geometry and magnetic characteristics of the Structure A.

outside the cylinder). The opposite way works also; i.e. the material remains fixed and the magnet is connected to the linear motor. In this case, the magnetic behavior is the same as in the first case.

Fig. 20. Cylindre d'Halbach made of eight segments.

Magnetic Refrigeration Technology at Room Temperature 247

magnetizations of the first cylinder are in opposition with those of the second cylinder the

=180° ) and the demagnetization phase is achieved.

θ

Fig. 22. Double Halbach cylinder (The two cylinders are opposed in this figure).

The structure D presented here has a configuration adapted to rotary magnetic refrigeration systems with a direct thermal cycle. It has two magnets to create the field; a yoke of soft material to canalize the magnetic flux and N MCE material blocks for the creation of the cold (Fig. 23). Table 4 below shows the parameter values used in our simulation for the

Parameters *R*<sup>1</sup> *ml Lm me al La <sup>a</sup> e e*

Values [mm] 100 50 50 20 50 50 20 3

Table 4. The dimensions used in the simulation of the rotating multiblock system.

magnetic field produced is low (

**5.2.2 Structure D: rotating multiblock system** 

Fig. 23. Geometry of the rotating multiblock system.

rotating multiblock system.

We modeled this structure with the commercial software 'Flux 3D'. The parameters used in this simulation are given in Table 3.


Table 3. The dimensions of the Halbach cylinder used in the simulation.

Fig. 21 (a) shows the induction at the center of the material according to the movement. It shows clearly the phases of magnetization and demagnetization produced by this structure. Fig. 21 (b) represents the magnetic forces exerted by the cylinder on the block of MCE material. The distribution of the magnetic induction is shown in Fig. 21 (c).

Fig. 21. Magnetic characteristics of the Structure B.

#### **5.2.1 Structure C: double Halbach cylinder**

Structure C is a double Halbach cylinder; two cylinders are concentric and have the same number of segments (Fig. 22). Using this structure for magnetic refrigeration systems allows having the phases of magnetization and demagnetization simply by rotating one of the cylinders while the active material remains stationary at the center of the structure. The magnetic field produced at the center is the sum of the two fields produced by each cylinder. When the magnetizations of the first cylinder segments are in the same direction of those of the second cylinder, the magnetic field produced is high and the magnetization phase is achieved (this position is taken as a reference, i.e.θ= 0° ). However, when the 246 Trends in Electromagnetism – From Fundamentals to Applications

We modeled this structure with the commercial software 'Flux 3D'. The parameters used in

Parameters *Rext R*int *Rm l* Values [mm] 65 25 22 50

Fig. 21 (a) shows the induction at the center of the material according to the movement. It shows clearly the phases of magnetization and demagnetization produced by this structure. Fig. 21 (b) represents the magnetic forces exerted by the cylinder on the block of MCE

Z0=0(mm)

Z0=50(mm) (c) The distribution of the magnetic induction.

= 0° ). However, when the

Table 3. The dimensions of the Halbach cylinder used in the simulation.

material. The distribution of the magnetic induction is shown in Fig. 21 (c).

Z0 (mm)

Z0 (mm)

Structure C is a double Halbach cylinder; two cylinders are concentric and have the same number of segments (Fig. 22). Using this structure for magnetic refrigeration systems allows having the phases of magnetization and demagnetization simply by rotating one of the cylinders while the active material remains stationary at the center of the structure. The magnetic field produced at the center is the sum of the two fields produced by each cylinder. When the magnetizations of the first cylinder segments are in the same direction of those of the second cylinder, the magnetic field produced is high and the magnetization

θ

Fig. 21. Magnetic characteristics of the Structure B.

phase is achieved (this position is taken as a reference, i.e.

**5.2.1 Structure C: double Halbach cylinder** 

this simulation are given in Table 3.

(a) Induction (T)

(b) Forces (N)

magnetizations of the first cylinder are in opposition with those of the second cylinder the magnetic field produced is low (θ=180° ) and the demagnetization phase is achieved.

Fig. 22. Double Halbach cylinder (The two cylinders are opposed in this figure).
