Effective Thermal Conductivity of Composites with Contact Thermal Resistance between the Inclusions and the Matrix
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ctive Thermal Conductivity of Composites with Contact Thermal Resistance between the Inclusions and the Matrix I. V. Lavrova, A. A. Kochetygova, V. V. Bardushkina, A. P. Sychevb, *, and V. B. Yakovleva, c aNational
Research University of Electronic Technology, Moscow, Russia Federal Research Centre the Southern Scientific Centre, Russian Academy of Sciences, Rostov-on-Don, Russia c Institute of Nanotechnology of Microelectronics, Russian Academy of Sciences, Moscow, Russia *e-mail: [email protected]
b
Received December 18, 2019; revised December 26, 2019; accepted January 14, 2020
Abstract—A method is proposed for predicting the effective thermal conductivity of a matrix composite with several types of spherical inclusions, in the case of contact thermal resistance at the matrix–inclusion boundary. The method is based on generalized effective-field approximation for a inhomogeneous medium containing inclusions that have an outer shell. As an example, calculations are presented for a matrix tribocomposite with two types of inclusions. Keywords: effective thermal conductivity, contact thermal resistance, composites, matrix, spherical inclusions, shell model, Maxwell-Garnett approximation, generalized effective-field approximation DOI: 10.3103/S1068798X20080134
Composites are widely used in structural components and machine parts. In addition to their mechanical properties (including their tribological properties), their thermal behavior is of great interest—in particular, their thermal conductivity. In the operation of composite components, specific temperature fields and heat-flux distributions are established. That may significantly change the functional properties of inhomogeneous materials. For example, friction gives rise to nonuniform heating of zones near the surface and in the volume of frictional elements. That intensifies the diffusion and segregation processes in such materials and hence may significantly change their physical and mechanical properties [1]. Increase in effective thermal conductivity of the composite is able to decrease the temperature gradient associated with friction and also lower the value of temperature. Therefore, it is of interest to predict the thermal conductivity of composites, which depends on their composition and structure. Thermal contact between the inclusions and matrix in composites is not ideal, as established in [2‒6]. When heat flux passes through nonuniform materials, a temperature jump is observed at the boundary between media with different properties. That may be attributed to thermal contact resistance at the boundary. P.L. Kapitsa discovered this phenomenon in investigating the heat transfer in liquid helium
[7]; consequently, thermal contact resistance is known as Kapitsa resistance. In the stationary case, the equations describing the temperature distribution in a medium resemble those describing the distribution of the electric field. Therefore, the methods used to predict the dielectric parameters and electrical conductivity of a inhomogeneous material may
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