**3.9 The G2Elab prototypes**

238 Trends in Electromagnetism – From Fundamentals to Applications

Fig. 10. 3D structure form of the Cooltech magnetic refrigerator, some details in further pictures, photography of the assembly and the open Halbach type of magnet (Vasile and

how the magnetic field is produced in the magnetocaloric material (Yu, 2010).

Fig. 11. A rotary magnetic refrigerator of the joint collaboration action between Cooltech

In France at Cooltech Applications, Bour et al. built a reciprocating prototype as it is shown in Fig. 12. The AMR bed was composed of 37 parallel plates of Gadolinium of 0.6 mm thickness, showing a spacing of the heat transfer fluid channels of 0.1 mm and 0.2 mm, respectively. The Halbach arrays, which produced a magnetic field intensity between 0.8 T and 1.1 T in the air gap, consisted of an assembly of three sets of NdFeB magnets of 50 mm thickness. The French experts obtained experimentally the evolutions of the average temperatures at the hot end and the cold end reservoirs for different initial temperatures and operation frequencies. The device

Applications and INSA in France (Muller et al., 2007).

led to a maximum temperature span of 16.1 K (Yu, 2010).

A rotary magnetic refrigerator prototype was developed in collaboration between the National Institute of Applied Sciences INSA of Strasbourg and the company Cooltech Applications in France (Muller et al., 2007). The system was composed by a rotary magnet assembly and of four static blocks of magnetocaloric material performed by gadolinium. The maximum magnetic field was 1.3 T and water was the working fluid. Unfortunately, there is no more information available. However, from Fig. 11, one may easily verify the manner

Muller, 2005, 2006).

The first device constructed at G2Elab (Grenoble Electrical Engineering Laboratory) is an alternating device type as shown in Fig. 13. The regenerator is composed of parallel plates of gadolinium with 1 mm in thickness and 50 mm in length. The magnetic field is produced by a permanent magnet (Halbach cylinder) creating a magnetic field of 0.8 T. The fluid used is water. Its circulation is ensured by a peristaltic pump operating in both directions (Clot, 2002). The pneumatic actuator produces the movement of the refrigerant blocs and provides magnetization / demagnetization phases. The controller is programmed to manage the Halbach cylinder and the flow of fluid to perform the four phases of the cycle. The system is closed and there is no exchange with the outside. It was designed to study the Active Magnetic Regenerative Refrigeration (AMRR) cycles and exploit different materials.

Fig. 13. The G2Elab first device (Clot, 2002).

A second prototype was developed at G2Elab (Allab, 2008), (Bouchekara, 2008), (Dupuis, 2009). This structure is quite similar to a rotating machine. It is also similar to some existing prototypes (Okamura, 2005, 2007). It consists of a permanent magnet which forms the rotor and of a stator made of magnetic yoke and four refrigerant beds (see Fig. 14).

The yoke is composed of four poles which are aimed to better conduct the magnetic flux within the refrigerant bed. The magnetization and demagnetization phases are obtained by a simple rotation of the permanent magnet. The beds undergo an active magnetic regenerative refrigeration AMRR cycle and operate two by two in the opposite way.

Magnetic Refrigeration Technology at Room Temperature 241

Heat exchanges play an important role in magnetic refrigeration systems, both in the cold production cycles, and in the interaction with external environments, including the substance to be cooled. Thus, a thermal study is needed to determine the performance of a magnetic refrigeration system and optimize it. The aim of this section is to focus on the

Most of heat exchanges operating in the magnetic refrigeration are via convection. The convection represents transfer processes performed by the motion of fluids (Bianchi, 2004). In a solid (index 's') in contact, with a fluid (index 'f'), the flow through the wall (index 'w')

> *s f p ws f*

> > ( )*s f* ( ) *wM wM*

where : ( )*<sup>s</sup> wM <sup>T</sup>* is the temperature of the solid at a point 'M' of the wall and ( )*<sup>f</sup> wM*

where: <sup>2</sup> *h W Km* represents the coefficient of heat transfer by convection or simply the

Using the first law of thermodynamics, by subtracting the mechanical energy, we get the balance of internal energy that gives us the heat equation governing the temperature field at

*<sup>p</sup>* V.grad V.grad ( ) grad *<sup>T</sup> <sup>p</sup> <sup>C</sup> T T T P div T*

β

. V. *<sup>p</sup>* grad ( ) grad *<sup>T</sup> <sup>C</sup> T P div T*

the dissipation function and *P* [*W* ] is the local thermal power produced or absorbed. For low viscosity fluids and isochors (Janna, 2000), the energy equation reduces to:

<sup>∂</sup>

*kg m* is he volume density, *Cp J kg K* ( ) is the specific heat, V [*m s*] is the

 λ

( ) *<sup>s</sup> <sup>f</sup>*

<sup>∂</sup> <sup>∂</sup> + = + + +Φ+ ∂ ∂ (22)

According to Newton, there is a linear relationship between the density of heat flow

temperature difference Δ= − *TT T <sup>s</sup> <sup>f</sup>* between the solid (*Ts* ) and the fluid (*Tf* ):

ϕ

*t T*

*t*

ρβ

ρ

ϕ

∂ ∂ = = ∂ ∂ (19)

*T T* = (20)

=Δ = − *h T hT T* (21)

 λ

+ =+ <sup>∂</sup> (23)

[1 *K*] is the coefficient of dilatation, Φ [*W* ] is

*T*

ϕand

*W mK* ( ) is the thermal conductivity

*T T n n*

λ

 λ

λ

whereas, the continuity of temperatures can be given by:

represents the temperature of the fluid at this point.

**4. Thermal study** 

can be written as:

convection coefficient.

where: <sup>3</sup> ρ

any point in the domain (Janna, 2000)

velocity of the fluid, *p* [ ] *Pa* is the pressure,

thermal modeling of magnetic AMRR systems.

where : n is the normal to the wall and

Fig. 14. The second prototype of the G2Elab, Components of the prototype (left) and the Prototype in its actual environment (right) (Bouchekara, 2008).
