Effective Thermal Conductivity Coefficient of the Composite with Non-Ideal Contact between Spherical Inclusions and the Matrix

A mathematical model of thermal energy transfer in the composite with inclusions of spherical shape (generally, in the form of hollow balls) is constructed. The possibility of the non-ideal contact between the inclusions and the matrix is taken into consideration. The estimates of the effective thermal conductivity coefficient of this composite are obtained including evaluations with application of dual formulation of the variational problem regarding the stationary heat conduction in an inhomogeneous solid. The parametric analysis is performed which makes it possible to find the range of application of the obtained estimates that can be used for predicting an effective thermal conductivity coefficient of composites, in particular those modified with nanostructured components.

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