Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 54

2

M sat
2

ð mag ¼ l 0 BH ð 3 : 65 Þ

Note that real magnets do not exhibit such perfect loops as in the case of
Eq. ( 3.65 ). Their energy product is always smaller than the upper ideal limit.
Namely, the soft iron (used to guide the magnetic fl ux), has a nite magnetic

permeability. Furthermore, there will always be some magnetic ux leakage into the

environment of the magnet (or magnet assembly). Therefore, for a real magnet
assembly certain correction factors can be applied. These can be de

fl

ned as the

leakage coef cient K 1 (Eq. 3.66 ) and the loss factor K 2 (Eq. 3.67 ), respectively [ 14 ].

magnet flux
useful flux ¼

B mag A mag
B gap A gap [

K 1 ¼ 1 ð 3 : 66 Þ

magnet magnetomotive force
useful magnetomotive force ¼

H mag L mag
H gap L gap [

K 2 ¼ 1 ð 3 : 67 Þ

By following the expressions in Eqs. ( 3.66 ), ( 3.67 ) and ( 3.62 ), which represents
the load line, can now be written as:

A gap l mag
A mag l gap

B mag
l 0 H mag ¼

K 1
K 2

ð 3 : 68 Þ

Let us consider two different characteristics of magnets, as presented in Buschow
and de Boer [ 15 ] (Fig. 3.14 a, b).
In the rst case (Fig. 3.14 a) the usual characteristics for permanent magnets

based on rare-earth materials (e.g. Nd B) are shown. In this particular case, the

intrinsic coercivity H ci can be much larger than the remanence and exceeds the

Fe

- -

eld
that corresponds to the maximum energy product (BH) max and the coercivity H c .
This kind of magnet will be able to resist very high magnetic elds, which can be as

high as triple value of the eld at the (BH) max .

Fig. 3.14 The magnetic fl ux density and the magnetization curve as a function of the

demagnetization eld strength. The maximum energy product as a function of the magnetic fl ux

density. a Rare-earth permanent magnets (i.e. Nd Fe

-

B), b Al Ni Co magnets