Active Magnetic Regeneration - Magnetocaloric Energy Conversion: From Theory to Applications - page 120

original source of a particular correlation in Tables 4.1 , 4.2 , 4.3 and 4.4 . It should
be noted that for a packed-bed AMR, in most cases the correlations are based on the
particle (sphere) diameter and not the hydraulic diameter. Therefore, this should be
included in Eqs. ( 4.20 )

( 4.22 ) as well (see Tables 4.1 , 4.2 , 4.3 and 4.4 for details).
The hydraulic diameter in Eqs. ( 4.20 )

-

( 4.22 )isde ned as (if not stated differently

-

in Tables 4.1 , 4.2 , 4.3 and 4.4 ):

4V AMR e
A HT

d h ¼ ð 4 : 23 Þ

Tables 4.1 , 4.2 , 4.3 and 4.4 present the Nusselt number and the friction factor
number correlations for the parallel-plate and packed-bed AMR, respectively.
Tables 4.1 , 4.2 , 4.3 and 4.4 also show the conditions for which the particular cor-
relation is valid, the AMR models that apply it and the source where it can be found.
Figures 4.14 , 4.15 and 4.16 show a comparison of the Nusselt number and the
Fanning friction factor number correlations presented in Tables 4.1 , 4.2 , 4.3 and 4.4
for two different AMRs (with outer dimensions of 80 mm (length) × 40 mm
(width)

× 10 mm (height)) and with water as the heat transfer fl uid. The parallel-

Table 4.1 The Fanning friction factor number correlation used in the parallel-plate AMR models
Friction
factor
correlation

Conditions
of validation

Used in the AMR model by Source

f F ¼ 24 = Re For fully devel-

oped laminar
fl

Tu ek et al. [ 17 ], Nikkola et al. [ 47 ],

Chiba et al. [ 48 ], Petersen et al. [ 82 ]

š Keys and

London
[ 88 ] ow

Table 4.2 The Nusselt number correlations used in the packed-bed AMR models
Nusselt number correlation

Note Conditions

of
validation

Used in the
AMR model
by

Source

Nu ¼ 2 þ 1 : 1Re 0 : 6 Pr 1 = 3

Based on d
and not d h

For all Re
numbers

Tu š ek et al.
[ 16 ], Aprea
et al. [ 29 ],
Engelbrecht
[ 41 ], Burdy-
ny and Rowe
[ 46 ], Li et al.
[ 53 ]

Wakao and
Keguei
[ 71 ]

Based on d
and not d h

Re > 50 Engelbrecht

[ 41 ]

Rohsenow
and Hart-
nett [ 89 ]

Nu ¼ 2 þ 1 : 8Re 1 = 2 Pr 1 = 3

j ¼ 0 : 23Re 0 : 3 j is Colburn factor

de ned as:

Re > 20 Dikeos and

Rowe [ 90 ]

Keys and
London
[ 88 ]

Nu ¼ jRePr 1 = 3

¼ 0 : 23Re 0 : 7 Pr 1 = 3

NuPr 1 = 3
Re

j ¼ StPr 2 = 3 ¼

Pr 1 = 3

d e
1