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^(-1) instead of as Kn^(-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.
Effective phonon mean-free path and slip heat flow in rarefied phonon hydrodynamics
Carlomagno, IsabellaWriting – Original Draft Preparation
;SELLITTO, ANTONIO
Writing – Original Draft Preparation
;
2015
Abstract
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^(-1) instead of as Kn^(-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.