TY - JOUR

T1 - Transition to ballistic regime for heat transport in helium II

AU - Sciacca, Michele

AU - Sellitto, Antonio

AU - Sciacca, Michele

AU - Jou, David

PY - 2014

Y1 - 2014

N2 - The size-dependent and flux-dependent effective thermal conductivity of narrow capillaries filled with superfluid helium is analyzed from a thermodynamic continuum perspective. The classical Landau evaluation of the effective thermal conductivity of quiescent superfluid, or the Gorter–Mellinck regime of turbulent superfluids, is extended to describe the transition to ballistic regime in narrow channels wherein the radius R is comparable to (or smaller than) the phonon mean-free path l in superfluid helium. To do so, we start from an extended equation for the heat flux incorporating non-local terms, and take into consideration a heat slip flow along the walls of the tube. This leads from an effective thermal conductivity proportional to R2 (Landau regime) to another one proportional to Rl (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates.

AB - The size-dependent and flux-dependent effective thermal conductivity of narrow capillaries filled with superfluid helium is analyzed from a thermodynamic continuum perspective. The classical Landau evaluation of the effective thermal conductivity of quiescent superfluid, or the Gorter–Mellinck regime of turbulent superfluids, is extended to describe the transition to ballistic regime in narrow channels wherein the radius R is comparable to (or smaller than) the phonon mean-free path l in superfluid helium. To do so, we start from an extended equation for the heat flux incorporating non-local terms, and take into consideration a heat slip flow along the walls of the tube. This leads from an effective thermal conductivity proportional to R2 (Landau regime) to another one proportional to Rl (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates.

UR - http://hdl.handle.net/10447/99733

UR - http://dx.doi.org/10.1016/j.physleta.2014.06.041

M3 - Article

VL - 378

SP - 2471

EP - 2477

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

ER -