Metal Foams: A Design Guide

q *(MW/m 2)
15
10
Power density
fixed ∆p*(8 kPa)
0.4
0.5
∆p*
5 0.3 ρ/ρs 0.2
0
100 200 300 400
∆p
q max
d (mm)
Air Pump
⋅
V
Case studies 231
Heat sink
Pump
Figure 17.15 Maximum on-chip thermal performance using mesocell metal
heat sinks
mance coefficients (Figure 17.15). These characteristics overlay with the pressure
drop in the heat sink, also given in Table 17.1.
Equating the pressure drop with the operating characteristics results in an
explicit flow rate for each heat sink (Figure 17.15): that is, for given cell
size, relative density and thickness. With this defined flow rate, a specific heat
flux, q, can be accommodated by the design. Accordingly, for a prescribed
fan, the heat sink exhibits a heat flux domain wherein the relative density
and cell size are the variables. One such domain is indicated in Figure 17.15,
calculated for bhs D 3cm and bsi D 0.5 cm. Note that there is a ridge of high
heat flux coincident with an optimum cell size. At a cell size smaller than
this optimum, the pressure drop is excessive: conversely, at a larger cell size,
the diminished heat transfer limits the performance. Along the ridge, there
is a weak dependence of heat flux on relative density in the practical range
( / s D 0.2–0.5).
By selecting cellular materials that reside along the heat flux ridge, the
requirements for the fan can be specified, resulting in a relationship between
⋅
V *