Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 89

Fig. 3.48 A 3D Halbach array designed at the University of Applied Sciences of Western
Switzerland [ 44 , 63 , 64 ]

3.5 Evaluation of Different Magnet Assemblies Designed
or Constructed for Magnetic Refrigeration

The following section provides information about the gure of merit for the design
of a permanent-magnet assembly. This can also be considered as the of

the design of magnets for magnetic refrigeration. Most of the work that regards this
issue was conducted for magnetic refrigeration at room temperature by Bj

“ ef ciency ”

ø rk [ 65 ],

Bj ø rk et al. [ 66 ] and Roudaut et al. [ 67 ].

Bj ø rk also proposed the most recognized gure of merit for a magnetic eld

source in magnetic refrigeration. Namely, he introduced the so-called ʛ cool , which

was de ned using the following relation [ 65 , 66 ]:

V field
V magnets

2
3

2
3
low

K cool ¼ ð l 0 H Þ

high l 0 H

ð Þ P field ð 3 : 95 Þ

eld is generated at
some moment. The volume as the sum of all the permanent magnets in the magnet
assembly is represented by the V magnets . The terms (

In Eq. ( 3.95 ), the V eld represents the volume where a high

2/3 2/3

ʼ 0 H) high and ( ʼ 0 H) low represent

the volume average of the applied magnetic eld in the high- eld region (mag-

netization) and in the low- eld region (demagnetization), respectively. The P eld

parameter represents the fraction of time when the magnet is in use.
This gure of merit can be applied especially for the design of devices that are

based on the Brayton-like AMR cycle. Namely, in other thermodynamic cycles, the
transition magnetic

eld) should be considered as well and
should not be averaged (see the chapter on AMRs and different thermodynamic

eld (from high to low