On the field fluctuations in a random dispersion

Abstract

In this note the variances of the basic random fields - temperature and heat flux - in a dilute dispersion of spheres with a small volume fraction $c \ll 1$, subjected to a constant macroscopic temperature gradient are studied. The basic result is an estimate on the $c^2$-term of these variances, which includes the well-known $c^2$-term of the effective conductivity, extensively studied in the literature.