An analytical model for thermal conductivity of composites with nanoparticles in a matrix is developed based on the effective medium theory by introducing the intrinsic size effect of thermal conductivity of nanoparticles and the interface thermal resistance effect between two phases. The model predicts the percolation of thermal conductivity with the volume fraction change of the second phase, and the percolation threshold depends on the size and the shape of the nanoparticles. The theoretical predictions are in agreement with the experimental results.(Some figures in this article are in colour only in the electronic version)Nanocomposites have a wide range of applications in the fields of optoelectronics, thermoelectrics, sensors, etc, due to their novel structure and properties [1][2][3], such as nonlinear optical properties of granular metal-dielectric composites [2] and the large enhancement of effective thermal conductivity of a fluid with the addition of a small amount of carbon nanotubes [3]. With continuous miniaturization of semiconductor and microelectronic devices, thermal transport and heat management problems have begun to attract a great deal of attention [4,5].Some devices such as computer processors and integrated circuits need high thermal conductivity, which is favorable for getting the heat away. On the other hand, for thermal barriers and thermoelectric devices, low thermal conductivity is desired. Studies have found that thermal conductivity of nanowires and thin films is size-dependent, it is lower than the corresponding bulk value [6]. However, there are not many theoretical studies on the thermal conductivity of nanocomposites, despite its importance in applications [1,3].The effective medium theory (EMT) is often used to study the physical properties of composites, such as dielectric constant [2], thermal conductivity and electrical conductivity [7]; the percolation of electrical conductivity is usually found, but there are few reports on the percolation of thermal conductivity. The role of interface thermal resistance (ITR) in the thermal conductivity of nanocomposites was emphasized in recent studies [8,9], which improves the theoretical results based on the EMT, but the related work seems to be discussed only for the dilute limit [9]. Moreover, the intrinsic size effect of the thermal conductivity of nanoscale structures was not considered for composites based on the EMT. The study based on the Boltzmann transport equation considered both the interface and the size effects, but no percolation of thermal conductivity was found for nanocomposites [8]. In this paper, a general theoretical model about the effective thermal conductivity of nanocomposites in the whole range of volume fractions of the second phases is proposed based on the EMT by introducing both the intrinsic size effect and the ITR effect. The model predicts the percolation of the thermal conductivity for composites with nanoparticles or nanorods of smaller size.Based on quantum scattering theory and the Green's f...