Transition to ballistic regime for heat transport in helium II

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 regim...

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Bibliographic Details
Published in:arXiv.org 2014-05
Main Authors: Sciacca, Michele, Sellitto, Antonio, Jou, David
Format: Article
Language:English
Subjects:
Capillaries
Fluid dynamics
Fluids
Heat flux
Heat transfer
Helium
Liquid helium
Parallel plates
Slip flow
Superfluidity
Thermal conductivity
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Summary: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, are 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 \(\ell\) 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 \(R^2\) (Landau regime) to another one proportional to \(R\ell\) (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates.
ISSN:2331-8422
DOI:10.48550/arxiv.1405.3596