Interfacial thermal resistance in phonon hydrodynamic heat conduction

Two-dimensional materials are usually predicted to have ultrahigh thermal conductivity because of the numerous phonon normal scatterings, which might cause hydrodynamic heat conduction. In addition, boundary and interface are significant in the polycrystalline structure and material contacts. Therefore, this article investigates the thermal behaviors at the boundary and interface in phonon hydrodynamics. Monte Carlo simulation is adopted to study the heat conduction phenomena in Poiseuille hydrodynamics and Ziman hydrodynamics. The concept of a boundary temperature step is defined to depict the temperature decline behaviors at the boundary in steady hydrodynamic heat conduction. Interfacial thermal behaviors can be treated as a combination of the boundary effects and phonon transmission effects, where the interface properties can be described by the interface transmissivity and the specular reflectivity. Moreover, the inverse temperature difference at the interface is observed, which means that the heat is transported from low temperature to high temperature, implying that the definition of temperature in phonon hydrodynamic heat conduction ought to be further investigated. Then, two theoretical models are proposed to describe these phenomena, namely, the particle propagation model and the dual boundary flux model. The particle propagation model tries to trace the propagation and evolution of phonons with simpler rules, and it finds that the heat flux reduction originates from the backward phonons that are scattered by the normal scattering process. The dual boundary flux model divides the whole boundary heat flux into the hydrodynamic heat flux and the diffusive heat flux, and the boundary temperature step appears in the transition between these two fluxes. These two models are compared with the results obtained by Monte Carlo simulations.