Indian Journal of Pure & Applied Physics Vol. 54, May 2016, pp. 313-320 A mathematical model for thermal conductivity of homogeneous composite materials John Constantine Venetis & Emilio Paul Sideridis* National Technical University of Athens, Greece Received 6 July 2015; revised 24 November 2015; accepted 5 January 2016 In this paper, a mathematical model to find the thermal conductivity of a large category of polymer homogeneous composite materials is performed. This type of composites contains ideal spherical particles encircled by an inhomogeneous interphase region, whereas the matrix is considered as isotropic. The thermal conductivity of the interphase is formulated as a continuous single-valued function of the radius of a spherical model. In this context, it is evident that the concept of boundary interphase is a useful manner for a quantitative description of the adhesion efficiency between matrix and filler since it is well known that there is a considerable effect of this phase on the thermo-mechanical properties of the composite. On the other hand, the particle distribution which can be considered as the influence of neighboring particles and their possible interaction should affect the thermal conductivity of the overall material. Keywords: Thermal conductivity, Particulate composites, Particle distribution, Interphase 1 Introduction Metal particles added in polymeric matrices produce composites of greater density, improved electrical conductivity, better thermal conductivity and consequently improved behavior at high operating temperatures and above all, highly improved mechanical properties. In many theoretical models describing the thermo- mechanical behavior of composites the adhesion efficiency at the interface of inclusion and matrix was considered as perfect. This is a reasonable assumption when such complicating factors as imperfect wetting (leading to the presence of air bubbles), or the presence of impurities at the interface can be neglected. In reality, around an inclusion embedded in a matrix a rather complex situation develops consisting of areas of imperfect bonding, mechanical stresses due to shrinkage, high stress gradients or even stress singularities due to the geometry of the inclusion, voids, microcracks, etc. In this case the composite will consist of three phases. The third one may also arise during thermal treatment of the material, because of component. Thus, third phase is what we call interphase and obviously is inhomogeneous. The interphase having different thermo-mechanical properties and visco-elastic behavior than the polymeric matrix, considerably affects the respective behavior of the composite. The various theoretical models that have been proposed 1-18 to predict the mechanical properties of composites have emphasized particular parameters. The filler-volume fraction and the mode of packing were the parameters studied in the model presented in Refs 1-3 while the importance of the particle size on the final properties of the composites was discussed in Refs 4-8 . The effect of the filler-matrix adhesion on the mechanical behavior of composites has been discussed in a series of models performed in Refs 8-12 . In the past years there has been a lot of research work carried out for the determination of elastic and thermal constants of particulate composites and for the investigation of the effect of various parameters such as filler-matrix interaction. Particularly, in Ref. 19 , Torquato obtained accurate approximate relationships for the effective elastic moduli of composite materials, whereas in Ref. 20 a new approach for bounding the effective moduli was developed. The effective elastic constants of solids containing random arrangements of spherical inclusions were considered by O’Rourke et al. 21 Kachanov and Sevostianov 22 discussed the proper quantitative characterization of microstructures and effective properties. The effective elastic constants of particulate composites by considering an inhomogeneous interphase were predicted by Wang and Jasiuk 23 . Khan and Muliana 24 introduced a micromechanical model for predicting thermal expansion coefficient of composites having solid spherical particle reinforcements. Sevostianov 25 —————— *Corresponding author (E-mail: siderem@mail.ntua.gr)