Simulation of the effective thermal conductivity of fibrous composites taking into account contact thermal resistance between inclusions and matrix


Аuthors

1*, Kochetygov A. A.2**, Bardushkin V. V.3***, Yakovlev V. B.2****

1. National Research University of Electronic Technology, Bld. 1, Shokin Square, Zelenograd, Moscow, Russia, 124498
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
3. Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia

*e-mail: iglavr@mail.ru
**e-mail: aakcht@gmail.com
***e-mail: bardushkin@mail.ru
****e-mail: yakvb@mail.ru

Abstract

The problem of calculating the transverse component of the effective thermal conductivity of a matrix composite with unidirectional cylindrical inclusions in the presence of contact thermal resistance at the boundary between the matrix and inclusions is considered. First, it is shown that the formula obtained by Hasselman for the case of a very low concentration of cylindrical inclusions with contact resistance between them and the matrix is true at a moderate concentration of inclusions. Then, a method is proposed to account for contact thermal resistance at the boundary between the matrix and cylindrical inclusions in the composite, based on the generalized effective-field approximation developed earlier by the authors for a inhomogeneous medium with coated inclusions. In this method, the contact thermal resistance is simulated by a thin inclusion shell with specially selected thickness and thermal conductivity. Based on the developed method, the expression for the transverse component of the effective thermal conductivity of a composite with the same type of cylindrical inclusions is obtained depending on the thermal conductivity of the matrix, shells and cores of inclusions. Model calculations were made for composite with ED-20 as matrix and unidirectional cylindrical inclusions made of aluminium-borosilicate glass. The inclusion radius was assumed to be 1 μm. The transverse component of thermal conductivity of this composite was calculated depending on the relative thickness of the shell at various values of contact thermal resistance, as well as depending on the volume fraction of inclusions. It is shown that the results obtained on the basis of the generalized effective-field approximation for the composite model with inclusions with a shell are in correspondence with the results of calculations according to the Hasselman formula. It has also been shown that with poor contact between the inclusions and the matrix, an increase in the volume fraction of inclusions leads to a decrease in the effective thermal conductivity, despite the higher thermal conductivity of the inclusion material than the matrix.

Keywords:

effective thermal conductivity, interfacial thermal resistance, composite, matrix, coated cylindrical inclusion, generalized effective-field approximation

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