Environmental Engineering Reference
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For both the spheres and the parallel plates the cost decreases with an increasing
magnetic
eld change from 1.5 to 2 T. The increase in the COP will lead to a higher
relative cost (due to the decrease of the cooling power with the increase of the
COP). For the case of longer regenerators (i.e. L = 15 cm for packed beds and all
the considered lengths for parallel plates), slightly better results can be obtained
with a magnetic
eld change.
However, shorter regenerators lead to higher relative costs for the 3 T magnetic
eld change of 3 T compared to a 2 T magnetic
eld changes (e.g. 3 T)
and for longer regenerators with spheres, there is a substantial increase in the
relative cost at higher COPs.
In 2011, another comprehensive economic evaluation was performed by Bj
eld, compared to the 2 T
eld. Moreover, at high magnetic
ø
rk
et al. [
38
]. Furthermore, the authors de
ned an expression for the mass of the
magnet and the magnetocaloric material that is required for a magnetic refrigerator.
This was determined by numerical modelling for both parallel plate and packed-
sphere-bed regenerators as a function of the temperature span and cooling power.
For the purpose of the study the magnetocaloric material gadolinium was consid-
ered to have a constant adiabatic temperature change with in
nitely linearly graded
properties (i.e. ideally layered).
They introduced a new
gure of merit for the permanent magnet assembly,
de
ned as [
38
]:
2
V
field
V
mag
l
0
H
B
rem
M
¼
ð
9
12
Þ
:
where V
field
is the volume of the air gap where there is a constant applied magnetic
l
0
H, and V
mag
is the volume of permanent magnets which have a remanence
magnetic
eld,
ux density B
rem
.
The authors further stated that the maximum value of M
¼
fl
25 and denoted
such a magnet assembly as M
25
. Based on Eq. (
9.12
) the authors provided another
expression that holds for devices in which the magnetocaloric material is contin-
uously utilized:
0
:
2
1
2
l
0
H
B
rem
m
mc
q
mag
m
mag
¼
ð
9
13
Þ
:
ð
1
e
Þ
q
mc
M
In Eq. (
9.13
) the m
mc
represents the total mass of the magnetocaloric material,
the term 1
ð
e
Þ
represents the volume fraction of the magnetocaloric material
in the AMR, and
q
mc
represent the densities of the permanent magnets and
the magnetocaloric material, respectively. In an economic analyses, Bj
q
mag
and
rk et al. [
38
]
considered the cost of the magnet material to be 40 US$/kg and the cost for the
magnetocaloric material to be 20 US$/kg. The manufacturing costs of the magnet
assembly and the manufacturing costs of the regenerator were not included, nor
were the costs related to the motor drive, regulation and control, and other auxil-
iaries. However, the aim of the study was to optimize (
ø
nd the minimum) the costs
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