Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes

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10 Citazioni (Scopus)

Abstract

The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter–Mellink regime). To do so, we use an expression for the quantum vortex line density L in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity as a function of the heat flux, and we discuss in detail the corresponding size dependence.
Lingua originaleEnglish
pagine (da-a)1835-1851
Numero di pagine17
RivistaZeitschrift fur Angewandte Mathematik und Physik
VolumeND
Stato di pubblicazionePublished - 2014

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Effective Conductivity
Thermal Conductivity
Heat Flux
Helium
Heat flux
heat flux
Thermal conductivity
thermal conductivity
helium
Vortex
Vortex flow
vortices
Dependent
Thermal gradients
Friction
temperature gradients
friction
Directly proportional
Roots
Fluxes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics
  • Physics and Astronomy(all)

Cita questo

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title = "Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes",
abstract = "The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter–Mellink regime). To do so, we use an expression for the quantum vortex line density L in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity as a function of the heat flux, and we discuss in detail the corresponding size dependence.",
author = "Mongiovi', {Maria Stella} and Michele Sciacca and Jou and Sciacca",
year = "2014",
language = "English",
volume = "ND",
pages = "1835--1851",
journal = "Zeitschrift fur Angewandte Mathematik und Physik",
issn = "0044-2275",
publisher = "Birkhauser Verlag Basel",

}

TY - JOUR

T1 - Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes

AU - Mongiovi', Maria Stella

AU - Sciacca, Michele

AU - Jou, null

AU - Sciacca, null

PY - 2014

Y1 - 2014

N2 - The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter–Mellink regime). To do so, we use an expression for the quantum vortex line density L in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity as a function of the heat flux, and we discuss in detail the corresponding size dependence.

AB - The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter–Mellink regime). To do so, we use an expression for the quantum vortex line density L in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity as a function of the heat flux, and we discuss in detail the corresponding size dependence.

UR - http://hdl.handle.net/10447/104441

M3 - Article

VL - ND

SP - 1835

EP - 1851

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

ER -