  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.
