Environmental Engineering Reference
In-Depth Information
[
92
,
110
] that they have a signi
cant effect when modelling a real AMR device (and
predicting its performance). There are two general approaches for including the
thermal interactions with the surroundings into the AMR model: directly into
the governing equations [
47
,
50
] or through an iterative thermal analysis where the
estimated loss of cooling power for particular operating conditions (through
Eq.
4.25
) is used as an input for the model [
92
,
110
]. The direct approach applies
additional terms in the AMR governing equations (Eqs.
4.5
and
4.6
):
1
R
loss
A
loss
V
q
loss
¼
ð
T
AMR
T
surr
Þ
ð
4
:
25
Þ
where R
loss
is the lumped thermal resistance of the regenerator housing (and other
isolations if applied), A
loss
is the outer area of the AMR and T
surr
is the ambient
temperature. The parasitic loss term can be applied either to the solid or to the
fl
uid
equation (where T
AMR
is the average temperature of the
uid and solid at a certain
location and time) or to both simultaneously (where T
AMR
is T
f
for the
fl
uid
equation and T
s
for the solid equation, respectively) as shown by Nikkola et al. [
47
].
Both approaches for the inclusion of the heat losses to the surroundings apply
only a lumped thermal resistance and do not include a regenerator housing and its
thermal mass into the numerical scheme through an additional domain and gov-
erning equation. To the best of our knowledge no such AMR model exists so far.
However, Nielsen et al. [
111
] presented a heat regenerator model with an included
regenerator wall (and its governing equation) in the numerical scheme. They ana-
lysed the impact of the housing wall on the packed-bed regenerator
'
s performance
under the conditions usually applied in the AMR and showed that its performance
can be signi
fl
cantly reduced for a Reynolds number below 10 and a thermal con-
ductivity of the housing material above 10 Wm
−
1
K
−
1
.
4.3.4.4 Hysteresis Losses
A hysteresis behaviour during the magnetization and demagnetization process
(magnetic hysteresis) and during heating and cooling (thermal hysteresis) is
observed in most of the known
rst-order magnetocaloric materials (e.g. Mn
Fe,
-
La
Si). It was shown that hysteresis behaviour can drastically reduce the
magnetocaloric effect under the cyclic conditions applied in the AMR as well as the
AMR performance [
112
,
113
]. To the best of our knowledge, there is no AMR
model that directly applies the hysteresis of the magnetocaloric material. For details
about the effect of the material hysteresis on the magnetic refrigeration cycle
associated with the non-equilibrium thermodynamics and its modelling through the
Preisach model approach see [
114
,
115
].
Fe
-
-
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