Investigation of the thermal conductivity of composite materials with a spherical filler

Abstract

In the light of the disadvantages of existing methods for determining the thermal conductivity of composite materials, the major practical issue is the need for creating more advanced calculation methods that take into account the geometry of the dispersed inclusions and their properties, i.e., those capable of evaluating the heat-conducting parameters of the composite with consideration of the properties of its components and their relative positions. In this paper, the analytical formulas, containing the ratio of the thermal conductivity coefficients of the base material and the filler, are derived for calculating the thermal conductivity of composite. The proposed model uses averaging of parameters at the "matrix-dispersed inclusion" phase boundary. We consider several well-known models developed by domestic and foreign researchers in recent years, which allows us to calculate the coefficient of thermal conductivity of such composites. The results of comparison of these models with the analytical dependence obtained in this paper are presented, and its applicability intervals are specified for different ratios of the inclusion thermal conductivity coefficient and the matrix material. The main goal is to fill the lack of information on thermal conductivity of spherical filler composites. The model considered in this paper is based on a change in the thermal resistance at the phase boundary. Since most materials used in industry contain inclusions with different geometric characteristics, then it is necessary to use the equivalent volume method - the reduction of various geometric inclusions to a given spherical one - which makes it possible to determine a change in the thermal conductivity coefficient for different physical and geometric values of the matrix material and filler. Various dependences of the change in the thermal conductivity coefficient of composite materials on the volume content of the spherical inclusion are compared with the numerical and experimental results. The analytical dependence given in this paper is consistent with the experimental and numerical results for relatively small values of the thermal conductivity coefficient and the inclusion diameter.