Heat conduction in micro-structured materials

The numerical simulations of heat transfer in dielectric thin films with a micro-hole are conducted. Temperature profiles in the micro-structured materials were calculated using the equations of phonon radiative transfer (EPRT) in two dimensions based on the Boltzmann transport theory. It is well known that the classical Fourier law and the hyperbolic heat equation cannot be used to solve the heat transport at the microscopic area. In this study, we have investigated the effects of the hole size and the Knudsen number on the thermal conductivity of the micro-structured materials. When the hole size and the Knudsen number are increased, ballistic phonon transport becomes dominant. The modeling results show that it is possible to make micro-structured materials with thermal conductivity totally different from that suggested by the intrinsic properties.