Thermal Conductivity of Liquid Helium II in Very Narrow Channels

1957 ◽  
Vol 108 (4) ◽  
pp. 911-913 ◽  
Author(s):  
K. R. Atkins

The thermal conductivities of crystals of solid helium at densities between 0⋅194 and 0⋅218 g/cm 3 have been measured at liquid-helium temperatures. In order to interpret the results, the specific heat of solid helium at these densities has been measured from 0⋅6 to 1⋅4° K. The range of densities employed is sufficient to allow the observation of Debye characteristic temperatures varying by 40 %, and of thermal conductivities varying by factors of over 10. It is shown that the conductivity measurements are in accord with the ‘umklapp’ type of thermal resistance derived by Peierls (1929, 1935). Further work was restricted by the difficulty of obtaining good single crystals in narrow tubes, but measurements of the conductivity at one density were obtained down to 0⋅3° K. In this region the conductivity is limited by boundary scattering and is higher than that observed by other authors for liquid helium II at similar temperatures.


Author(s):  
J. F. Allen ◽  
J. Reekie

It has been found by one of the authors (1) in collaboration with Dr H. Jones that a flow of heat in liquid He ii is accompanied by what seems to be a transfer of momentum. The effect can be seen when the channel through which the heat and liquid flow consists of a smooth-walled glass capillary, such as shown in Fig. 1a. Due to the high thermal conductivity of He ii, a considerable part of the heat put into the reservoir is carried down through the capillary to the bath. When a steady heat flow exists, a flow of liquid takes place in the opposite direction, and the level of the liquid in the reservoir is seen to be higher than that in the bath. Smooth capillaries, however, produce a rise in level of only 1 or 2 cm. at most, since the viscosity of the liquid is small and hydrostatic pressure pulls the accumulated liquid in the reservoir back through the capillary. When the heat flow is large, violent surging is observed in the reservoir, but there is no further rise in level.


1955 ◽  
Vol 8 (2) ◽  
pp. 206 ◽  
Author(s):  
PG Klemens

In narrow channels (~10?4 cm) the observed heat transport is considerably larger than calculated by the internal convection theory. It is suggested that, because of the anisotropy of the distribution cf phonons in the channel walls resulting from the temperature gradient, the normal fluid in the immediate vicinity of the walls is not at rest but flows towards the colder region. The magnitude of the resulting heat transport is in reasonable agreement with the observed discrepancy.


A series of experiments has been performed to study the steady flow of heat in liquid helium in tubes of diameter 0.05 to 1.0 cm at temperatures between 0.25 and 0.7 °K. The results are interpreted in terms of the flow of a gas of phonons, in which the mean free path λ varies with temperature, and may be either greater or less than the diameter of the tube d . When λ ≫ d the flow is limited by the scattering of the phonons at the walls, and the effect of the surface has been studied, but when λ ≪ d viscous flow is set up in which the measured thermal conductivity is increased above that for wall scattering. This behaviour is very similar to that observed in the flow of gases at low pressures, and by applying kinetic theory to the problem it can be shown that the mean free path of the phonons characterizing viscosity can be expressed by the empirical relation λ = 3.8 x 10 -3 T -4.3 cm. This result is inconsistent with the temperature dependence of λ as T -9 predicted theoretically by Landau & Khalatnikov (1949).


1950 ◽  
Vol 5 (6) ◽  
pp. 1010-1013 ◽  
Author(s):  
S. Nakajima ◽  
M. Shimizu

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