EFFECTIVE ANISOTROPY OF THERMAL CONDUCTIVITY FOR COMPOSITES: STATISTICAL ANALYSIS
Journal Title: Вісник Кременчуцького національного університету імені Михайла Остроградського - Year 2017, Vol 1, Issue 104
Abstract
Purpose. The main focus of this work is to study the effective thermal conductivity variation of binary composites with random arrangement of thermal-insulated inclusions for the case of different directions of applied temperature gradient. The statistical characteristics of the observed variation are determined either. Methodology. This problem is considered on two-dimensional models. The inclusions placement in simulated material was set using a random number generator. The effective thermal conductivity was found by the Fourier equation numerical solution with the method of the top progressive relaxation. The size of the square inclusions, their concentration and the minimum distance between them were varied in the models. A large number of tests were performed for each set of the inclusions arrangement parameters. Results. It is shown that the values of the effective thermal conductivity of the simulated material don’t coincide for different directions of heat fluxes. The statistical distribution’s average value of the difference between the effective thermal conductivities along two mutually perpendicular directions equals zero. The standard deviation value of this distribution depends on the size of the inclusions, their concentration and the distance between them. This value is also proportional to the standard deviation of the effective thermal conductivity distribution. Originality. We called the difference between the effective thermal conductivities along two mutually perpendicular directions the “effective anisotropy of thermal conductivity”. The nature of the effective anisotropy of thermal conductivity is purely statistical. The measure of the thermal conductivity effective anisotropy can be the standard deviation of the effective thermal conductivity distribution. Practical value. The study of two-dimensional models of composite materials shows that it is possible to control the statistical spread of composites effective thermal conductivity in different directions by choosing the shape, size and density of the inclusions package.
Authors and Affiliations
I. Zaginaylo, А. Pysarenko, D. Spiridonov
Keywords
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