Metal Foams: A Design Guide

186 Metal Foams: A Design Guide
Table 13.1 Non-dimensional parameters for
cellular metal heat dissipation
Heat flux Q D Q/ks[T1 T0]
Prandtl number
Reynolds number
Cell wall thickness
Pr D a/˛a
Re Q D vfL/ a
Qd D d/L
Foam thickness Qb D b/L
Nusselt number
Thermal conduction
Nu D Biks/ka
QKf D p Power dissipation
ka/ks
QP D 1pvfbL2 / a 3 a
˛a D thermal diffusivity of cooling fluid.
13.4 Pressure drop
As the heat transfer coefficient increases, so does the pressure drop across
the medium. The latter can sometimes be the limiting factor in application,
because of limitations on the available pumping power. The pressure drop 1p
has the general form
Pressure drop, ∆p/L
1p/L D ⊲1/a⊳[ m a a/⊲1 ˛⊳ 2 m ]v
8
7
6
5
4
3
2
1
30 ppi
m = 0.37
0
0 1 2 3
Exit velocity, (m/s)
2 m m
f d
20 ppi
m = 0.43
10 ppi
m = 0.44
4 5
⊲13.13⊳
Figure 13.3 The pressure drop per unit length of flow plotted against the
exit velocity for Duocel foams, from which the power dissipated in pumping
the fluid can be estimated