Abstract
In this paper, a unit-cell model for determination of the effective thermal and electrical conductivity, respectively, of highly porous, closed-cell metal foams is presented. Hereby, (i) a large contrast between the transport properties of the conducting, solid material phase and the pore space is assumed, and (ii) thin, interconnected spherical shells of the solid material phase in a simple cubic arrangement are considered as a geometrical model. The unit-cell model prediction is compared to (i) literature data and (ii) well-established homogenization schemes from the effective medium theory.
Highlights
Metal foams are versatile engineering materials characterized by tunable stiffness and strength, superior damping performance, etc., their ever-increasing application in, e.g., automotive and transport industry
We focus on the transport properties of metal foams with closed-cell morphology
We further restrict our consideration to the case of a large contrast between conductivity of the solid material phase and the pore space,1 i.e., negligible conductivity in the pore space
Summary
Metal foams are versatile engineering materials characterized by tunable stiffness and strength, superior damping performance, etc., their ever-increasing application in, e.g., automotive and transport industry. As the underlying field equations for electrostatics and steady-state heat conduction are similar (see Table 1), the outcome of homogenization schemes derived for either one of the problems may be applied to the other one. This is the case for classical effective media and effective field, respectively, homogenization schemes [an excellent review of these methods can be found in Sevostianov and Kachanov (2013)]. A comparison with the homogenization schemes from the effective medium/field theory described above (see Eqs. 3 and 4, underlying spherical pore shape) shows that data approximately lie between the model response for the Maxwell–Euken expression and the differential scheme, respectively.
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