EFFECTIVE MACROSCOPIC DESCRIPTION FOR HEAT-CONDUCTION IN HETEROGENEOUS MATERIALS

The macroscopic thermal behaviour of heterogeneous materials is studied using the ensemble averaging technique. The non-local constitutive relations for heat conduction are derived. They relate the ensemble averaged heat flux and energy density to the ensemble averaged temperature of the medium. All the effective properties appearing in the relations are defined with help of the newly introduced, so-called microstructure functions. The asymptotic behaviour of the heterogeneous media for slowly varying average temperature fields was investigated. Possible applications of the theory are presented in two examples analytical results could be easily obtained.