Heat Conduction in Composites: Homogenization and Macroscopic Behavior

Abstract

The review article discusses methods of macroscopic averaging of heat conduction in composite materials that lead to models of homogenized, macroscopic behavior of these media. It is shown that essentially two continuum models are in use: 1) the effective medium and 2) the mixture. The ensemble averaging technique allows one to derive the constitutive relations for both models assuming Fourier-like conduction on the microstructure level of a composite. These constitutive relations contain effective, macroscopic properties of the composite material which can be forecast when properties of individual constituents, the form of thermal interaction at constituent interfaces, amount of each material and its distribution are known. For weakly varying mean temperature fields, thermal behavior of the composite is essentially the same as homogeneous media but, for stronger variation, a non-classical behavior is observed. This non-classical behavior can be associated either with space nonlocality and memory phenomena or with wall effects and, in some cases, with influence of local heat sources on the effective properties. Most of these effects are not well known and need further detailed studies. The article includes 158 references.

Computation of the Effective Conductivity of Unidirectional Fibrous Composites With an Interfacial Thermal Resistance

“…Effects of a ¢nite interfacial conductance also are illustrated in Figure 6, where we show (grayscale) contour plots of the periodic temperature ¢eld w h for a hexagonal cell for the concentration cˆ0. 3 and two values of the reference Biot number, Bi rˆ1 0 ¡1 (Figure 6a) and Bi rˆ1 0 1 (Figure 6b). The jump of w h at the interface G is seen to be clearly less pronounced for the larger value of Bi r .…”

“…One of the most important macroscopic thermal properties of composite materials is the effective thermal conductivity, which depends on the conductivities, relative amounts, geometries, and spatial distributions of the constituent phases. A recent comprehensive review of heat conduction in composites is presented by Furma·ski [3].…”

“…One of the most important macroscopic thermal properties of composite materials is the effective thermal conductivity, which depends on the conductivities, relative amounts, geometries, and spatial distributions of the constituent phases. A recent comprehensive review of heat conduction in composites is presented by Furma·ski [3].Most manufacturing processes of composite materials do not ensure a perfect thermal contact between the constituent phases [1, 2, 5^8]. Therefore, in practice, the effective conductivity also depends on the interfacial thermal resistance, or contact resistance, between the continuous phase (the matrix) and the dispersed phase.…”

Coordination number for random distribution of parallel fibres

“…In the first case the upper limit of the integral was assumed to be λ = 1.5 [7,11,14] and in the second case it was made equal to the distance corresponding to the location of the first minimum of the pair distribution function [9,2]. The numerical procedure for calculation PDF function follows the one suggested in literature [20,4]. Around every cylindrical particle, a set of bins with the thickness ∆r are created and particles inside each bin are counted.…”

Probabilistic Elastic Characteristics of the Periodic Fiber Composites

“…(Π) (12) where the characteristic function χ p (xO is given as M-max ^Kmax + 8μ" (16) and any periodic stress boundary conditions.…”