Effective thermal conductivity of particulate composites for time-varying temperature fields

Abstract

A homogeneous conductive medium containing random sets of identical spherical inclusions is considered. The self-consistent effective medium method is used for solution of the homogenization problem and calculation of the effective thermal conductivity parameters of the composite. For time-varying fields, the effective conductivity parameters are non-local operators with respect to time. The effective medium method allows reducing the homogenization problem to solution of a system of non-linear equations for the Laplace transforms of the kernels of these operators. An efficient numerical algorithm of solution of this system is proposed. Examples of construction of these operators for the composites with copper and glass phases are considered. The Green functions of the corresponding effective media are compared with the Green function of the media with static effective parameters of thermal conductivity.