MODELLING OF HEAT CONDUCTIVITY OF COMPOSITE MATERIALS WITH BALL INCLUSIONS

Abstract

A number of papers deals with the heat conductivity of composite materials: Zarubin et al used new approaches to the problem of evaluation of the effective heat conductivity coefficients of composite material with ball inclusions. We used variational analysis for a simplified model in a vicinity of inclusion. Contemporary computers allow implementing another approach to solving the problem of the effective heat conductivity: it may be modelled by the Brownian motion of virtual heat particles. The main idea is to obtain the exact formula for the heat conductivity for a homogeneous material and subsequently obtain a statistical evaluation of this formula for a composite material.In the present paper we compare two methods for finding the effective heat conductivity coefficients of composite materials by modeling the process of heat conduction via the Brownian motion of virtual heat particles. We consider a composite with ball inclusions of a material with heat conductivity and heat capacity coefficientsdiffering from those of the matrix material. In a computational experiment, we simulate the process of heatconduction through a flat layer of the composite material, which has been heated on one side at the initial moment. In order to find the confidence interval for the effective heat conductivity coefficient, we find, by means of statistics, either the displacement of the center of heat energy, or the probability of a virtual particle to pass through the layer during a certain time. We compare our results with theoretical assessments suggested by other authors.