Environmental Engineering Reference
In-Depth Information
cooling energy q
Rmax
and the maximum speci
c heating energy q
Hmax
that can be
obtained in the magnetic thermodynamic cycle (this case is shown for a Brayton-
like cycle). Despite the fact that the regenerative process can be applied to increase
the temperature span, this must not be misunderstood as the maximum speci
c
cooling power (because of the heat regeneration).
In the case that all the irreversible losses are neglected, the theoretical speci
c
cooling energy per mass or volume of magnetocaloric material for the case of the
Brayton-like AMR cycle can be de
ned using the following equation:
ð
Þ
sT
R
þD
T
ad
ð
dem
Þ
Z
ð
¼
Þ¼
ð
4
:
1
Þ
q
R
H
0
T ds
sT
ðÞ
where T
R
denotes the lowest temperature of the magnetocaloric material in the
cycle. In the case of a heat pump, the theoretical speci
c heating energy per mass or
volume of magnetocaloric material for the case of the Brayton-like AMR cycle is
equal to:
sT
ðÞ
Z
q
H
H
[
0
ð
Þ¼
T ds
ð
4
:
2
Þ
ð
Þ
sT
H
D
T
ad
ð
mag
Þ
The difference in both capacities dened in Eqs. (
4.1
-
4.2
) is equal to the the-
oretical work of the AMR cycle:
ð
Þ
sT
H
D
T
ad
ð
mag
Þ
;
H
¼
0
sT
H
;
ð
Z
H
0
Þ
Z
[
w
¼
Tds
Tds
ð
4
:
3
Þ
ð
Þ
sT
R
;
H
¼
0
ð
Þ
sT
R
þD
T
ad
ð
dem
Þ
;
H
[
0
where T
H
represents the highest temperature of the magnetocaloric material within
the cycle.
Note that Eqs. (
4.1
4.3
) are also valid for the case where regeneration is per-
formed, but it does not account for the overlapping of the internal cycles. They
could be generally applied for the characterization of magnetocaloric materials in
AMRs if the overlapping is neglected or included afterwards.
For a rapid (engineering) estimation, it is convenient to simplify (linearize)
Eq. (
4.1
) as:
-
ð
Þ
sT
R
þD
T
ad
ð
dem
Þ
D
Z
2 T
R
þ D
T
ad dem
s
T
ðÞ
ð
Þ
ð
¼
Þ¼
ð
4
:
4
Þ
q
Rmax
H
0
T ds
2
sT
ðÞ
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