Modeling of Phonon Thermal Conductivity of Two Dimensional Nano and Micro Composites in the Longitudinal Direction

The three important length scales in composites made from nano/micro wires and fibers are: 1) the ratio of inter fiber distance and mean free path of the phonons in the host medium 2) the ratio of the diameter of the fiber or the wire and the mean free path of the phonons in the host medium and 3) the ratio of the diameter of the fiber and the mean free path of phonons in the fiber. Modeling of longitudinal thermal conductivity of two-dimensional nano and micro composites has not been attempted in the literature. This paper develops analytical modeling for the longitudinal thermal conductivity of nano and micro composites by solving the Boltzmann transport equation (BTE) for phonons. The paper shows the scattering of phonons in the host medium by the fiber boundaries play a very important role in deciding the thermal conductivity of nano and micro composites. The model is in good agreement with data on thermal diffusivity of Bismuth Telluride nanowire/ Alumina composite.