Hydrodynamic Phonon Transport Perpendicular to Diffuse-Gray Boundaries

TL;DR

This study investigates heat transfer in phonon-hydrodynamic materials between non-hydrodynamic contacts, revealing how boundary resistance dominates at small scales despite high bulk conductivity, with implications for thermal management.

Contribution

It introduces an integral-equation approach to model phonon transport in hydrodynamic materials, highlighting boundary resistance effects and bridging ballistic and diffusive regimes.

Findings

Boundary resistance dominates at small scales.

Bulk thermal conductivity approaches infinity in hydrodynamic limit.

Solution converges to ballistic limit when boundary distance is small.

Abstract

In this paper, we examine the application of an ideal phonon-hydrodynamic material as the heat transfer medium between two non-hydrodynamic contacts with a finite temperature difference. We use the integral-equation approach to solve a modified phonon Boltzmann transport equation with the displaced Bose-Einstein distribution as the equilibrium distribution between two boundaries perpendicular to the heat transfer direction. When the distance between the boundaries is smaller than the phonon normal scattering mean free path, our solution converges to the ballistic limit as expected. In the other limit, we find that, although the local thermal conductivity in the bulk of the hydrodynamic material approaches infinity, the thermal boundary resistance at the hydrodynamic/non-hydrodynamic interfaces becomes dominant. Our study provides insights to both the steady-state thermal characterization of phonon-hydrodynamic materials and the practical application of phonon-hydrodynamic materials for thermal management.