Two-sided estimate of effective thermal conductivity coefficients of a textured composite with anisotropic ellipsoidal inclusions

Based on the developed mathematical model of the heat energy transfer in a composite with anisotropic inclusions having a shape of triaxial ellipsoids, the method of calculation of two-sided estimates for components of the effective thermal conductivity tensor of the textured composite is proposed. This technique uses the dual variational formulation of the problem of stationary thermal conductivity in an inhomogeneous body. A case of anisotropic inclusions having the shape of triaxial ellipsoids that main axes of the thermal conductivity tensor coincide with their axes is considered. An example of calculation of two-sided estimates for a conical texture of the composite is given. The results obtained can be used to estimate the possible error in prediction of the effective thermal conductivity coefficients for composites modified with nanostructural elements (including carbon nanotubes). Mathematics Subject Classification (2010). Primary 80M30; Secondary 74E25