Effective thermal conductivity of functionally graded particulate composites

H.M. Yin, G.H. Paulinoa), and W.G. Buttlar

Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue,  IL 61801

L.Z. Sun

Department of Civil and Environmental Engineering and Center for Computer-Aided Design, The University of Iowa, Iowa City, IA 52242

A multi-scale modeling method is proposed to derive effective thermal conductivity in two-phase graded particulate composites. In the particle-matrix zone, a graded representative volume element is constructed to represent the microstructure at the neighborhood of a material point. At the steady state, the particle’s averaged heat flux is solved by integrating the pair-wise thermal interactions from all other particles. The homogenized heat flux and temperature gradient are further derived, through which the effective thermal conductivity of the graded medium is calculated. In the transition zone, a transition function is introduced to make the homogenized thermal fields continuous and differentiable. By means of temperature boundary conditions, the temperature profile in the gradation direction is solved. When the material gradient is zero, the proposed model can also predict the effective thermal conductivity of uniform composites with the particle interactions. Parametric analyses and comparisons with other models and available experimental data are presented to demonstrate the capability of the proposed method.

Submitted toJournal of Applied Physics for Publication (March 24, 2005)