Active Magnetic Regeneration - Magnetocaloric Energy Conversion: From Theory to Applications - page 122

Table 4.4 The Nusselt number correlations used in the parallel-plate AMR models
Nusselt number correlation Note Conditions of validation Used in the

AMR
model by

References

1 = 3 : 592

0.1 < Gz <10 6

3 : 592

ð Þ d h

L RePr

Tu ek

et al. [ 17 ],
Nielsen
et al. [ 83 ]

š Nickolay

and Martin
[ 84 ]

Gz ¼

Nu ¼ 7 : 541 3 : 592 þ 1 : 841Gz 1 =ðÞ

For fully developed laminar fl ow

1 = 3 : 592

3 : 592

d h

For developing laminar fl ow Petersen

et al. [ 82 ]

ð Þ

Gz ð x Þ¼

x RePr

1 =ðÞ

541 3 : 592 Nu x ðÞ¼ 7 : þ 1 : 841Gz ð x Þ

Nu ¼ 7 : 54 For a fully developed laminar ow and a

constant heat transfer wall temperature (the
latter is not actually the case in the AMR)

fl Chiba et al.

[ 48 ]

Bejan
et al. [ 85 ]

0
@

1
A

1 2 : 61R þ 4 : 97R 2
5 : 119R 3

R is the aspect
ratio of the fluid
channel

For fully developed laminar flow Nikkola

et al. [ 47 ]

Kandlikar
et al. [ 86 ]

þ 2 : 702R 4
0 : 548R 5

Nu ¼ 7 : 541

! 1 = 2

2

R is the aspect
ratio of the fluid
channel

For developing laminar flow Risser

et al. [ 44 ]

Bavie ' re
et al. [ 87 ]

1 = 2

x
d h Re

1
Pr

2

Nu ¼ 0 : 41 þW

0
@

1
A

0853R 2 1 2 : 0421R þ 3 :

2 : 4765R 3 þ 1 : 0578R 4

0 : 1861R 5

W ¼ 8 : 235