Analytical insights into thermophysical properties of nanomaterials

Using the discrete ordinate method, we solve the equations of phonon radiative transfer for thin films analytically, and deduce closed-form expressions for three thermophysical properties including the phonon intensity, heat flux density and effective phonon thermal conductivity. These analytical expressions provide a fast and convenient way to analyze heat conduction behavior in thin films, and thus allowing us to comprehend how the film thickness and bulk phonon mean free path affects the thermophysical properties. Also we extend these expressions from thin films to one period of superlattices, and demonstrate that adjusting the thickness ratio of two layers can control its effective phonon thermal conductivity.