131 Introduction

The thermal conductivities of metal foams (see Table 4.1(b)) are at least an order of magnitude greater than their non-metallic counterparts, so they are generally unsuited for simple thermal insulation though they can provide some fire protection. The thermal conductivities of closed-cell foams are, however, lower than those of the fully dense parent metal by a factor of between 8 and 30, offering a degree of fire protection in, for instance, an automobile bulkhead between engine and passenger compartment. More important, open-cell metal foams can be used to enhance heat transfer in applications such as heat exchangers for airborne equipment, compact heat sinks for power electronics, heat shields, air-cooled condenser towers and regenerators (Antohe et al., 1996; Kaviany, 1985). The heat-transfer characteristics of open-cell metal foams are summarized in this chapter.

Examples of the use of metfoams for thermal management can be found in the case studies of Sections 16.4, 16.5, 16.6 and 16.8.

Figure 13.1 illustrates a prototypical heat-transfer configuration. Heat sources are attached to thin conducting substrates between which is bonded a layer of open-celled foam of thickness b and length L. A fluid is pumped at velocity vf through the foam, entering at temperature T0 and exiting at temperature Te. An idealization of the foam structure is shown below: the relative density is p = pc/ps and the diameter of the cell edges is d. The local heat-transfer coefficient at the surface of a cell edge is h. There are three guiding design principles.

1. High conductivity ligaments are needed that transport the heat rapidly into the medium: the preference is for metals such as Cu or Al.

2. A turbulent fluid flow is preferred that facilitates high local heat transfer from the solid surface into the fluid.

3. A low-pressure drop is needed between the fluid inlet and outlet such that the fluid can be forced through the medium using a pumping system with moderate power requirements making low fluid viscosity desirable.

Heat transfer to the fluid increases as either the ligament diameter, d, becomes smaller or the relative density, p/ps, increases because the internal

Cooling fluid d

vf Fluid velocity

~ Relative density h Local heat transfer coefficient q

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 d h surface area depends inversely on d and the heat conduction cross-section increases with p/ps. 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.

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