Environmental Engineering Reference
In-Depth Information
In Petersen et al. [
82
], a direct comparison of 1-D and 2-D models for a parallel-
plate AMR is shown. The authors concluded that both models show an excellent
qualitative and quantitative agreement between the cooling and heating powers for
thin regenerator channels. However, the results of the two models diverge as the
thickness of the regenerator plates is increased. The comparison between the model
results for the COP values did not show the same degree of agreement. The reason for
this is that the magnetic work and the COP are derived from the cooling and heating
powers and small differences in either result in large deviations between the estimated
COP values of the models. The cause of the discrepancy between the models at larger
channel thicknesses is due to the effect of the perpendicular temperature gradients,
primarily in the
uid as well as in the solid. These are not accounted for by the 1-D
model. They concluded that the 1-D model is valid (regarding the 2-D model) when
the channels are smaller than about 0.5 mm, which is necessary for an ef
fl
cient AMR
with good heat transfer characteristics, as shown in Sect.
4.4
.
4.3.3 Heat Transfer and Fanning Friction Factor
Correlations
Most 1-D models rely on correlations for the convective heat transfer and friction
factor coef
cients. The use of the appropriate correlations is crucial for an accurate
AMR model. As explained by
Š
arlah and Poredo
š
[
42
], a 10 % higher heat transfer
coef
cient can yield a 4.4 % higher temperature span of the AMR. In this section,
the most widely applied correlations for the convective heat transfer and friction
factor coef
cients are reviewed and compared through the Nusselt number and the
Fanning friction factor number correlations, respectively.
Here, the Reynolds number, the Nusselt number and Fanning friction factor are
de
ned as:
q
v
d
h
¼
ð
4
:
20
Þ
Re
g
a
d
h
k
Nu
¼
ð
4
:
21
Þ
d
h
2 v
ðÞ
q
D
p
L
f
F
¼
ð
4
:
22
Þ
2
ˁ
ʵ
ʷ
ʱ
λ
ʔ
where
,v,
,d
h
,
,
,
,
p, L are the
fl
uid density, internal (pore) velocity of the
fl
uid
thermal conductivity, pressure drop along the AMR and its length, respectively.
The Reynolds number de
uid, porosity, hydraulic diameter, dynamic viscosity, heat transfer coef
cient,
fl
),
which is valid for the packed bed structures. However, the Reynolds number of the
parallel-plate is usually de
ned in Eq.(
4.20
) includes the external velocity (v
ʵ
ned with the internal velocity. For details see the
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