Numerical Simulation of the Heat Conductivity of Randomly Inhomogeneous Two-Dimensional Composite Materials

Numerical Simulation of the Heat Conductivity of Randomly Inhomogeneous Two-Dimensional Composite Materials consists of six sections. The introduction and second section present a wide variety of theoretical and empirical models for heat transport in two-component composites and their governing scientific principles. In particular, the methods of homogenization and the representative volume element are examined. The third section is devoted to the numerical methods in heat conduction processes in composites. In this section, the choice of the finite difference method and the Monte Carlo method for numerical experiments on the study of heat transfer in two-component composites was confirmed. The fourth section describes the computational model for two-component composite material with different values of the matrix and filler thermal conductivity. The study assumes a random placement of inclusions in the composite matrix with the following parameters: The concentration and size of inclusions, and the minimum distance between the inclusions. The fifth section deals with the distribution statistics of the effective heat conductivity. General forms of the effective thermal conductivity distributions and their transformation have been obtained when the parameters of the inclusions placement have been changed. Moreover, the influence of the placement heat-insulating inclusions on the parameters of the effective thermal conductivity distributions has also been discussed. The Monte Carlo simulation has been used to obtain the statistics of the effective anisotropy of the thermal conductivity distributions and its relationship to the effective thermal conductivity distributions statistics. The local heat fluxes statistics and pattern maps of local heat fluxes through a randomly inhomogeneous material with a heat-conducting matrix and heat-insulating inclusions have been analyzed in the sixth section. Numerical experiments reveal the influence of the number and extent of induced heat-conducting channels on the effective thermal conductivity of the material. Special attention has been paid to an area with a shortage of induced heat-conducting channels, or the so-called dark matrix. Multimodal distributions of the local heat flux density, as well as the binding of two distribution modes to heat-insulating inclusions and induced thermal conductive channels have been described. The third mode of distribution was tied to a dark matrix on the heat-insulating inclusions map. This section also presents the statistical distributions of angles between the direction of local heat fluxes and the temperature macro gradient as well as the transformation of the character of distribution when changing the parameters of placement for inclusions.