Metal Foams: A Design Guide

182 Metal Foams: A Design Guide
h
Cooling
fluid
q
d
T o
b
Q
vf Fluid velocity
r
~
Relative density
v f
Te
h Local heat transfer coefficient
Figure 13.1 An open-cell foam sandwiched between two conducting plates.
Fluid flow from left to right transfers heat from the foam, which has a high
surface area per unit volume
surface area depends inversely on d and the heat conduction cross-section
increases with / s. Counteracting this is the increase in the pressure drop
needed to force the fluid through the foam as the surface-area-to-volume ratio
increases. Accordingly, for any application there is an optimum cellular structure
that depends explicitly on the product specification. These issues are
explored more fully below.
13.2 Heat transfer coefficient
The cellular metal is envisaged as a system that transfers heat from a hot
surface into a fluid. Thermal performance is characterized by an effective heat
transfer coefficient, Hc, which is related to the heat flux, per unit area, q, from
the hot surface in the standard manner (e.g. Holman, 1989):
q D Hc1T ⊲13.1⊳
where 1T is a representative temperature drop, roughly equal to the temperature
difference between the hot surface and the incoming fluid. A more precise
definition is given later. The goal is to develop a cellular system with large Hc
that also has acceptable pressure drops and occupies a small volume (compact).
The determination of the heat transfer coefficient, Hc, can be approached
in several self-consistent ways. The one presented in this chapter regards