Appl Phys A (2010) 99: 223–228 DOI 10.1007/s00339-009-5503-9 Effective thermal conduction in composite materials Bashir M. Suleiman Received: 23 March 2009 / Accepted: 10 November 2009 / Published online: 9 December 2009 © Springer-Verlag 2009 Abstract The problem of determining the bounds and/or estimating the effective thermal conductivity (λ eff ) of a composite (multiphase) system given the volume fractions and the conductivities of the components has been inves- tigated. A comparison between the measured data and the results predicted by theoretical models has been made for seven heterogeneous samples. The tested models include those of the effective medium theory (EMT), Hashin and Shtrikman (HS) bounds, and Wiener bounds. These mod- els can be used to characterize macroscopic homogeneous and isotropic multiphase composite materials either by de- termining the bounds for the effective thermal conductiv- ity and/or by estimating the overall conductivity of the ran- dom mixture. It turns out that the most suitable one of these models to estimate λ eff is the EMT model. This model is a mathematical model based on the homogeneity condition which satisfies the existence of a statistically homogeneous medium that encloses inclusions of different phases. Nu- merical values of thermal conductivity for the samples that satisfy the homogeneity condition imposed by the effective medium theory are in best agreement with the experimen- tally measured ones. 1 Introduction Various numerical and analytical approaches have been de- veloped to deal with the problem of estimating the effec- tive or average conductivity of a composite material (λ eff ) B.M. Suleiman ( ) Department of Applied Physics, College of Sciences, P.O. Box 27272, University of Sharjah, Sharjah, United Arab Emirates e-mail: bashir@sharjah.ac.ae given the geometry of the composite and conductivities of the components [1–3]. The effective thermal conduction in inhomogeneous media (composite materials) is of increas- ing importance both in recent technological applications and in research [4, 5]. Examples such as using polymer fibers to strengthen concrete slabs or embedding a conducting net- work in a polymer matrix to produce conducting polymers are evidence of the need to understand the thermal and/or electrical conduction of heterogeneous media. In this work, a comparison between the measured data and the results from predictions of theoretical models has been done for several heterogeneous samples. The tested models include those of the effective medium the- ory (EMT) [6], Hashin and Shtrikman (HS) bounds [7], and Wiener bounds [8]. The EMT model depends on the exis- tence of a statistically homogeneous medium surrounded by inclusions of different phases (homogeneity condition). Within these models there are two ways to estimate λ eff , either by using exact mathematical formulas to evaluate the bounds (range) within which the conductivity must lie, or by using models based on approximate mathematical ex- pressions. It should be mentioned that bounds can also be constructed in hierarchies which become narrower as the amount of structural information included grows. However, the higher order of these bounds is extremely difficult to calculate since it involves n-point correlation functions [9]. This paper deals with three aspects: The first one is the pos- sibility of using the utility of Wiener and/or Hashin and Shtrikman bounds to obtain a narrower range and to pre- dict a good estimate that matches the real value of the effec- tive thermal conductivity. The second one is to use Wiener bounds as a preliminary indicator to validate the homogene- ity condition of the investigated samples. The third one is to compare the experimental data of the effective thermal conductivity with the corresponding theoretical estimation