Effective phonon mean-free path and slip heat flow in rarefied phonon hydrodynamics

• Slip heat flow in nanowires is considered.
• Length scale of non-local terms in heat transport is discussed.
• Microscopic view of slip heat flux is emphasized.
• Specular and diffusive collisions contribution to thermal conductivity is clarified.

Non-local effects in generalized heat-transport equations provide a mesoscopic approach to phonon hydrodynamics. In contrast to usual phonon hydrodynamics with non-slip heat flow, we consider, in analogy to rarefied gas dynamics, a slip heat flow along the walls. This way the effective thermal conductivity behaves as Kn−1Kn−1 instead of as Kn−2Kn−2, which is the behavior in usual phonon hydrodynamics, Kn being the Knudsen number, i.e., the ratio between the mean-free path of the heat carriers and a characteristic size of the system. Here we revisit previous formulations to provide a more explicit and clearer interpretation of the differences between the effective mean-free path in the non-local term of the generalized transport equation for q, and that in the thermal conductivity.