Hydrodynamic heat conduction based on eigenvalues and eigenvectors of the normal collision operator

Abstract Although the Guyer-Krumhansl equations has opened up the study of phonon hydrodynamics in ultra-low temperature and low dimensional non-metallic crystals, it still cannot explain the high thermal conductivity of low dimensional non-metallic materials in adiabatic environments. In this work, the analytical solution of the linear Boltzmann transport equation with the Callaway approximation is obtained by expanding the nonequilibrium distribution function into a series of the orthogonal eigenvectors of the normal-process collision operator. By assuming the normal scatterings dominate the heat conduction in an anisotropic non-metallic crystal allowing the different branches of the phonon frequency spectrum having different group velocity, the macroscopic energy and momentum balance equations are developed for describing the phonon hydrodynamic transport. For an isotropic and dispersionless system, these balance equations reduce to the improved Guyer-Krumhansl equations. The thermal conductivity in these balance equations includes not only the contribution of the resistive scatterings, but also the contribution of the normal scatterings. Therefore, the improved Guyer-Krumhansl equations is capable for explaining the high thermal conductivity of suspended graphene, which is validated by the experimental results. Finally, the improved Guyer-Krumhansl equations is employed to derive the occurrence condition of the second sound in suspended single-layer graphene.