A mixture theory for heat conduction in heterogeneous media

A mixture theory based on the ensemble-averaging technique is proposed for studying the thermal behaviour of heterogeneous media. Balance equations with partial heat fluxes and interaction terms are introduced for a two-component medium. Relations between these quantities and the ensemble-averaged (mean) temperatures of separate components are derived. The limits of application of widely used postulates of proportionality of the interaction term of difference in mean temperature of components is discussed. The effective conductivities of components in the mixture and the interaction coefficient are introduced and related to the so-called microstructure functions, which are functions of the microgeometry of the medium and the thermal properties of its components. Examples of the application of the theory to the calculation of the mean properties of a heterogeneous medium are presented.