Homogenization of thermal conductivity in a periodic structure

TRISO particle is used for a high temperature gas cooled reactor. There are few billions of TRISO particles in a reactor core. It is necessary to develop a homogenization model for compact level or block level calculation. It is widely accepted to obtain a (flux-) volume average of inverse of diffusion coefficient such as the neutron diffusion coefficient or the thermal conductivity as an analogy to the neutron transport cross section. However there are large difference in the averaged conductivity when the structure is highly heterogeneous. Cho's method gives a quite reasonable result for practical application. However, Cho's method is not accurate in the sense that a Monte Carlo method is based on the Fredholm integral equation, and a diffusion equation cannot be converted into a Fredholm equation rigorously