**2.3.1 Application of MFT to gadolinium (Gd)**

In this section the theoretical study based on the MFT developed in the previous section is applied to the gadolinium. Table 1 gives the parameters used to calculate the magnetocaloric properties.


Table 1. Parameters used for applying MFT to the gadolinium.

The numerical solution of equations (14), (15) and (16) allows getting the isotherms of magnetization and its evolution as a function of temperature calculated by the method of Weiss as shown in Fig. 2 (a) and Fig. 2 (b). Fig. 2 (c) represents the total heat capacity calculated from the equation (3) for different levels of induction. The magnetic entropy and its variation with temperature are shown respectively in Fig. 2 (d) and Fig. 2 (e). Finally, Fig. 2 (f) shows the magnetocaloric effect calculated by the MFT.

Magnetic Refrigeration Technology at Room Temperature 231

Fig. 3(a) shows the conventional gas compression process that is driven by continuously repeating the four different basic processes shown while Fig. 3 (b) shows the magnetic refrigeration cycle comparison. The steps of the magnetic refrigeration process are analogous to those of the conventional refrigeration. By comparing (a) with (b) in Fig. 3, one can see that the compression and expansion are replaced by adiabatic magnetization and demagnetization, respectively. These processes change the temperature of the material and

heat may be extracted and injected just as in the conventional process.

Fig. 3. Analogy between magnetic refrigeration and conventional refrigeration.

The direct exploitation of the giant MCE around the room temperature is limited by the fact that existing MCE materials do not achieve high temperature differences (Lebouc, 2005). For example, a sample of gadolinium around room temperature produces an MCE of

**2.5 The Active Magnetic Regenerative Refrigeration (AMRR)** 

approximately 10 K in a magnetic field of 5 T.

Fig. 2. Results of the theoretical study applied to Gd.

#### **2.4 Application of MCE to produce cold**

The magnetic cycles are generally composed of the process of magnetization and demagnetization, in which heat is discharged or absorbed in four steps as depicted by Fig. 3. From thermodynamic point of view, the magnetic cooling can be realized by: Carnot, Stirling, Ericsson and Brayton, where the Ericsson and Brayton cycles are believed to be the most suitable for such medium or room temperature cooling. Such cycles are predisposed to yield high cooling efficiency of the magnetic materials (Bouchekara, 2008).

230 Trends in Electromagnetism – From Fundamentals to Applications

of temperature. (d) Magnetic entropy.

(e) Variation of the magnetic entropy. (f) MCE of Gd calculated by the MFT.

The magnetic cycles are generally composed of the process of magnetization and demagnetization, in which heat is discharged or absorbed in four steps as depicted by Fig. 3. From thermodynamic point of view, the magnetic cooling can be realized by: Carnot, Stirling, Ericsson and Brayton, where the Ericsson and Brayton cycles are believed to be the most suitable for such medium or room temperature cooling. Such cycles are predisposed to

yield high cooling efficiency of the magnetic materials (Bouchekara, 2008).

(b) Variation of magnetization versus the temperature.

(a) Variation of magnetization versus the Magnetic field.

(c) Evolution of the total heat capacity as a function

Fig. 2. Results of the theoretical study applied to Gd.

**2.4 Application of MCE to produce cold** 

Fig. 3(a) shows the conventional gas compression process that is driven by continuously repeating the four different basic processes shown while Fig. 3 (b) shows the magnetic refrigeration cycle comparison. The steps of the magnetic refrigeration process are analogous to those of the conventional refrigeration. By comparing (a) with (b) in Fig. 3, one can see that the compression and expansion are replaced by adiabatic magnetization and demagnetization, respectively. These processes change the temperature of the material and heat may be extracted and injected just as in the conventional process.

Fig. 3. Analogy between magnetic refrigeration and conventional refrigeration.
