Bounds on the Transverse Effective Conductivity of Computer-Generated Fiber Composites

Abstract

Using trial functions that are motivated by single-body calculations, we have derived bounds on the effective transverse thermal conductivity of a fiber composite. These bounds incorporate both fiber area fraction information and some information of the configurational statistics. Simplified expressions for the bounds are obtained for the limits of widely differing conductivity values for the constitutent phases, and of a dilute suspension. The bounds are made specific for a given computer-generated fiber composite and these specific bounds are compared with the best available bounds that require area fraction information alone. The conclusions reached are that configuration statistics are significant for effective property calculations for moderately dense composites for component conductivity values that differ by some one to two orders of magnitude, or greater. Further, the bounds based on the single-body calculation are reasonably close for component conductivity values that differ by some two orders of magnitude, or less.