Thermal Conductivity Modeling of Axisymmetric Nanowires Using Phonon Boltzmann Model Equation

Energy transport in semiconductor is basicly by atomic or crystal vibrations, These vibrations travel within material waves. The energy is quantized and each quantam is called a phonon. On a macroscopic scale, the heat transfer in semiconductor mainly obey the Fourier law. However, on a microscopic scale the heat transfer will no longer follow the Fourier law. Instead, the equation of phonon radiative transfer (EPRT) is developed to study the heat transfer under microscopic scale.
EPRT is a nonlinear equation with intergral and differential terms, which is difficult to solve directly. If we simplify the collision term by Bhatnagar-Gross-Krook Equation, the equation will be easy to solve.
This article is mainly about the heat transfer in the symmetric semiconductor nanowires with different material arrangement under cylindrical coordinates. Several geometries are studied including : single layer nanowires, tubular nanowires, core-shell nanowires, multi-layer nanowires, and composite nanowires. The discrete ordinate method is used for angular discretization; and upwind scheme is used for spatial discretization. The results show that the effective thermal conductivity changes not only with the radius and the length of the nanowires, but also with the boundary thermal resistance.