Heat transfer in conductors of cylindrical cross-section with diffusive boundary scattering

We present a theoretical study of heat transfer properties in three-dimensional cylindrical conductors of finite lengths in the ballistic regime of phonon propagation. The phonon emission is considered to be radiative and its interactions with the lateral boundary is assumed to be completely diffusive. The main goal of this study is to determine the temperature profile and the features of its formation for the generalized case of a conductor of finite length. A matrix numerical solution of the integral equation for the particle energy flux is obtained and an approximate analytical solution of this equation is proposed. The heat flux and thermal conductivity coefficient are determined; and the significant difference between our results and those of the generally accepted formulation in the Knudsen regime and the Casimir model is discussed.