Investigation of the Thermal Conductivity of Composite Materials with a Spherical Filler

In the light of the disadvantages of determining the thermal conductivity coefficient of composite materials, the question arises of creating more advanced calculation methods that take the geometry of dispersed inclusions and their properties into account, i.e., methods for finding the heat-conduction parameters of a composite as a whole with consideration for the properties of its components and their mutual arrangement. An analytical formula for calculating the thermal conductivity of a composite is obtained, which contains the ratio of the thermal conductivities of the base material (matrix) and the filler material. In this case, the model is based on a change in the thermal resistance at the matrix-dispersed inclusion boundary and the use of averaged parameter values here. Several well-known models that have been developed recently by domestic and foreign researchers are considered, which allow calculating the thermal conductivity coefficients of such composites. The results are presented for their comparison with the analytical dependence constructed in this study. The intervals of applicability of this dependence are specified for different ratios of the thermal conductivities of the inclusion materials and the matrix. The main purpose of this research is an attempt to fill the lack of information on the thermal conductivity of composite materials with spherical fillers. Since the materials used in industry mostly contain inclusions with different geometric characteristics, the technique of equivalent volumes is used to reduce various forms of inclusions to the required spherical shape, thus making it possible to find changes in the thermal conductivities of the matrix and filler materials with different physical parameters. The dependences of the thermal conductivity of composite materials on the volume content of spherical inclusions are presented, which were determined numerically according to the proposed model and taken from other researchers. Their comparison shows that with relatively small values of the thermal conductivity coefficient of a spherical-inclusion material and its diameter, the results agree fairly well with each other.