A Mixture Theory for Quasi-One-Dimensional Diffusion in Fiber-Reinforced Composites

Abstract

A binary mixture theory is developed for heat transfer in unidirectional fibrous composites with periodic, hexagonal microstructure. The case treated concerns a class of problems for which heat conduction occurs primarily in the fiber direction. Model construction is based upon an asymptotic technique wherein the ratio of transverse-to-longitudinal thermal diffusion times is assumed to be small. The resulting theory contains information on the distribution of temperature and heat flux in individual components. Mixture accuracy is estimated by comparing transient solutions of the mixture equations with finite difference solutions of the Diffusion Equation for an initial boundary value problem. Excellent correlation between “exact” and mixture solutions is observed. The construction procedures utilized herein are immediately applicable to other diffusion problems—in particular, moisture diffusion.