Effective Thermal Сonductivity Сoefficient of Multi-phase Composite With Spherical Inclusions

Composites consisting of a matrix and variform inclusions are widely used as structural and functional materials in a variety of instrumental devices. There are a large number of works devoted to the study of the thermal conductivity of composites. However, given in these papers formulas, as a rule, are deduced as a result of experimental data processing applying to a specific material, or by a priori indicating of temperature distribution and heat flow in models of heterogeneous body structure. The paper presents a mathematical model of heat transfer in a multi-phase composite with dispersed inclusions of spherical shape (generally, in the form of a hollow sphere), that is a base to determine the effective thermal conductivity coefficients of said composite. The estimation of a possible error of the received results with the use of dual variational formulation of the problem of stationary heat conduction was done. The results can be used to predict the effective thermal conductivity coefficients of multi-phase composites dispersed with modified particles, nanostructured in particular.

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