Transition to ballistic regime for heat transport in helium II

• Published in: Physics letters. A 2014-07, Vol.378 (34), p.2471-2477
• Main Authors: Sciacca, Michele, Sellitto, Antonio, Jou, David
• Format: Article
• Language: English
• Subjects: Ballistic phonons; Liquid helium; Micropores; Quantized vortices; Quantum turbulence; Thermal conductivity
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2014.06.041

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. •Heat transport in counterflow helium in the ballistic regime.•The one-fluid model based on the Extended Thermodynamics is used.•The transition from the Landau regime to the ballistic regime.•The transition from quantum turbulence to ballistic regime.