An analysis for effective thermal conductivity on unidirectional fiber composites

Abstract

The validity of two methods of calculating effective thermal conductivity of composite materials is examined by comparing the numerical solutions for the effective thermal conductivity calculated through application of these two methods to unidirectional fiber compos ites. Mathematical model and the assumptions associated with them are outlined first. Then, the approach, which is referred to as the direct approach, on which the two methods are based, is explained. In this approach, the effective thermal conductivity of a composite material is simply defined as the relation between the averaged temperature gradient and the averaged heat flux over the smallest volume representing all the characteristics of the composite material. Both of the methods compared are based on the direct approach and differ from each other according to the boundary conditions imposed. Imposed conditions are, namelr, the homogeneous boundary conditions, and the prescribed temperature and insulated surface boundary conditions over the unidirectional fiber composites in which fibers are distributed in rectangul ar and staggered array forms. In thi swork, those methods, in which homogeneous boundary conditions are incorporated are referred to as homogeneous-methods, and those in which the other boundaryconditions are used are referred to as flux methods.