Exact Solutions and Bounds for the Thermal Conductivity Coefficient of a Dispersed Medium

Exact solutions for the thermal conductivity coefficient of a two-phase dispersed medium are obtained using the most general physical principles of locality and symmetry. Two solutions define the well-known Hashin–Shtrikman bounds. The third solution, invariant under the phase inversion transformation, significantly narrows the Hashin–Shtrikman boundaries; this is confirmed by comparison with numerous experiments by other authors. It has been shown that taking into account the remote interaction of dispersed particles at their increased concentration only slightly (less than 3%) affects the result.