The Kanari model is traditionally treated as an empirical relation to fit observations on the effective thermal conductivity of composites. By applying the integration embedding method, we demonstrate that this model provides an extension of the Halpin-Tsai and Fricke models to highly filled composites, and the only adjustable parameter in the governing equation is expressed in terms of the aspect ratio of filler particles and their aggregates. These assertions are confirmed by the analysis of observations on several polymer composites. POLYM. ENG. SCI., 2019. (c) 2019 Society of Plastics Engineers