Active Magnetic Regeneration - Magnetocaloric Energy Conversion: From Theory to Applications - page 121

Table 4.3 The friction factor number correlations used in the packed-bed AMR models
Friction factor correlation Note Conditions

of
validation

Used in the
AMR model by

Source

2

Based on
d and not
d h

For smooth
particles

Engelbrecht
[ 41 ]

Kaviany
[ 65 ]

90 1 e

ð Þ

9 1 e
e 3

f F ¼ þ 0 :

Re e 2

For all Re
numbers

2

Based on
d and not
d h

For smooth
particles

Engelbrecht
[ 41 ], Li et al.
[ 53 ]

Rohsenow
et al. [ 89 ]

f F ¼ 75 1 e

ð Þ

þ 0 : 9375 1 e
e 3

Re e 2

For all Re
numbers

plate AMR was constructed of plates with a thickness and spacing of 0.25 mm
(porosity of 0.5), while the packed-bed AMR had spheres with a diameter of
0.25 mm (porosity of 0.39).
It is clear from Fig. 4.14 that the majority of the Nusselt number correlations for
fully developed laminar

ow do not depend on the Reynolds number, but only on
the boundary conditions. The exception here is the correlation from Nickolay and
Martin [ 84 ], which is also valid for developing

fl

ow (which usually occurs in the
AMR); therefore, it is more correct than others and used by most authors of the
(1-D) parallel-plate AMR model (see Table 4.4 ).
In the case of the packed-bed AMR, the difference between the different cor-
relations is quite signi

fl

cant, as shown in Fig. 4.15 . However, the most widely used
by the authors of packed-bed AMR models is the correlation from Wakao and
Keguei [ 71 ]. Figure 4.16 shows the Fanning friction factor correlation for a parallel-
plate AMR and two very similar AMR correlations for the packed-bed AMR, which
are the most widely used in the models.
It should be underlined that there are no well-established heat transfer correla-
tions for the fl ow through porous media in the low Reynolds number fl ow regime

and for high operating frequencies (oscillating fl ow), as is usually the case during

'

the AMR eld has to be further investigated in order to develop

more reliable correlations [ 43 ].

s operation. This

4.3.4 Improved Modelling of an AMR (Modelling
of the Additional Loss Mechanisms in an AMR)

The above-presented mathematical model of the AMR is based on certain
assumptions (neglected loss mechanisms) for which it was shown that it might have
a signi

s operation and its cooling characteristics [ 92 ].
This section thus shortly discusses the impact and deals with the inclusion of the
following additional AMR loss mechanisms: the demagnetization

cant in fl uence on the AMR '

ow
maldistribution ; the parasitic heat losses to the surroundings and the hysteresis
losses of the magnetocaloric material into the AMR mathematical model.

eld ; the

fl