Entrance, slip, and turbulent effects in heat transport in superfluid helium across a thin layer

We explore how the expression for the thermal resistance of a porous layer in superfluid helium in laminar counterflow conditions can be generalized for thin layers with several pores. We analyze different situations, i.e., narrow pores with radius comparable to the phonon mean free path, in which s...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2020-04, Vol.71 (2), Article 57
Main Authors: Saluto, Lidia, Jou, David
Format: Article
Language:English
Subjects:
Counterflow
Engineering
Entrances
Fluid dynamics
Fluid flow
Fluids
Heat flux
Heat transfer
Helium
Liquid helium
Mathematical Methods in Physics
Porosity
Slip
Superfluidity
Theoretical and Applied Mechanics
Thermal energy
Thermal resistance
Thin films
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Summary:We explore how the expression for the thermal resistance of a porous layer in superfluid helium in laminar counterflow conditions can be generalized for thin layers with several pores. We analyze different situations, i.e., narrow pores with radius comparable to the phonon mean free path, in which slip effects along the walls must be incorporated and thermal resistance is slightly reduced, and thin layers with length of the pores comparable to the so-called entrance length, in such a way that Poiseuille parabolic flow is not achieved and thermal resistance becomes dependent on the heat flux. Furthermore, we deal with the contribution to the thermal resistance of a turbulent layer of quantized vortices produced at the exit of the pores.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-020-1277-x