Metal Foams: A Design Guide

Thermal management and heat transfer 185
where cp is the specific heat of the fluid and D 1 0.22⊲ / s⊳. Theexit
temperature may thus be determined by introducing ℓ from equation (13.12)
into (13.11) and setting x D L, whereupon Tf Te.
Expected trends in the heat flux, Q, dissipated by cellular metals (in
W/m 2 ) can be anticipated by using the above formulae. Typically, this is
done using non-dimensional parameters, as plotted in Figure 13.2 with air
as the cooling fluid. The parameters are defined in Table 13.1. The principal
feature is the substantial increase in heat dissipation that can be realized upon
either decreasing the cell edge diameter, d, or increasing the relative density,
/ s. Eventually, a limit is reached, governed by the heat capacity of the
cooling fluid.
Q ∼
Pr κ
∼ 2
f
κ
∼
f = 0.011
1000
800
650
400
200
0 0 0.002
Limiting
heat transfer
0.004
0.006
∼ 0.008
d
0.01 0
Present
materials
0.1
Air
∼
Re = 5000
Pr = 0.72
Nu = 1.0
∼
b = 0.2
0.3
0.2
r
∼
0.5
0.4
0.6
Figure 13.2 The heat flux Q D Q/ks[T1 T0 ] into the fluid, plotted as a
function of the relative density, Q, and the dimensionless cell-edge diameter,
Qd D d/L