Heat Conduction in Composites: Homogenization and Macroscopic Behavior

The review article discusses methods of macroscopic averaging of heat conduction in composite materials that lead to models of homogenized, macroscopic behavior of these media. It is shown that essentially two continuum models are in use: 1) the effective medium and 2) the mixture. The ensemble averaging technique allows one to derive the constitutive relations for both models assuming Fourier-like conduction on the microstructure level of a composite. These constitutive relations contain effective, macroscopic properties of the composite material which can be forecast when properties of individual constituents, the form of thermal interaction at constituent interfaces, amount of each material and its distribution are known. For weakly varying mean temperature fields, thermal behavior of the composite is essentially the same as homogeneous media but, for stronger variation, a non-classical behavior is observed. This non-classical behavior can be associated either with space nonlocality and memory phenomena or with wall effects and, in some cases, with influence of local heat sources on the effective properties. Most of these effects are not well known and need further detailed studies. The article includes 158 references.