Magnetic Field Sources - Magnetocaloric Energy Conversion: From Theory to Applications - page 64

Z

NI ¼ HdL ¼ H iron L iron þ H gap L gap ð 3 : 93 Þ

closed path

where L iron and L gap are the path lengths in the iron and in the air gap, respectively.
It follows:

!

L iron þ

B
l 0

BL gap
l gap ¼

L iron
l iron þ

L gap
l gap

NI ¼ M B ð 3 : 94 Þ

More comprehensive analyses can be made analytically; however, for particular
electromagnet designs normally a 2D numerical tool is used for solving the rst

design ideas, whereas 3D software (e.g. Comsol, Ansys Multiphysics) can serve for
the optimization and more detailed information on the operation of a magnet. This
also holds for permanent-magnet assemblies and their design.
The magnetic

eld in electromagnets can vary between a few mT up to 2 T, or
even more. Of course, at high magnetic elds the electromagnets become very large

in volume and mass. Furthermore, in almost all cases, high magnetic

eld elec-
tromagnets require additional cooling of the coil, which heats up due to the Joule
heating caused by the electric resistance of the wire. High magnetic eld electric

magnets also do not apply an iron core, and at very high magnetic elds, these

magnets operate as pulsed magnets. Moreover, the ratio between the useful mag-
netizing energy and the energy lost by Joule heating is rather small, indicating that
electromagnets cannot by successfully applied in magnetic refrigeration devices.
However, these kinds of magnets can be applied in testing devices, either for
magnetocaloric materials or for the characterization of magnetocaloric regenerators.
In such electromagnets the size of the air gap (between poles) can usually be
adjusted by a screw mechanism, thus producing an alternating magnetic

eld.
For additional reading on the basic engineering of magnetism, besides the
already cited topics, we recommend Purcell and Morin [ 17 ].
A much more interesting application is that of superconducting magnets.
However, their potential market application in magnetic refrigeration is restricted to
rather large units, since this would affect the cost of the device. This issue is also
discussed in the Chap. 9 . However, one has to be aware that the operating costs of
superconducting magnets can represent less than 5 % of that of an equivalent
resistive magnet. An additional advantage compared to equivalent resistive magnets
is in their compactness and durability. However, since the superconductivity of
materials is strongly restricted by the critical magnetic eld (see subsequent text),

the strongest superconducting magnets cannot perform such a high magnetic ux

density as counter, resistive Bitter magnets. But most probably, such high magnetic

fl

elds (e.g. far above 10 T) will not be applied in any market application of the
magnetic refrigeration or heat pumping near room temperature.
Since the costs of the R&D in this special domain of magnetic refrigeration can
be at least an order higher compared to permanent-magnet-based magnetic