NON-CLASSICAL FILM FREE CONVECTION IN SUPERFLUID LIQUID HELIUM II NEAR THE λ-POINT

1974 ◽  
Author(s):  
R. C. Amar ◽  
S. C. Soloski ◽  
Traugott H. K. Frederking
1966 ◽  
Vol 88 (4) ◽  
pp. 343-349 ◽  
Author(s):  
W. J. Rivers ◽  
P. W. McFadden

Free-convection heat transfer from a solid surface to liquid Helium II in the presence of a film of either liquid Helium I or helium gas is analyzed mathematically. The analysis includes two heater shapes, a vertical flat plate and a horizontal circular cylinder, each with an isothermal surface. The integral forms of the boundary-layer equations are used to describe the heat transfer and fluid flow processes that occur within the film. The velocity and temperature profiles within the film are approximated by fourth degree polynomials whose coefficients were evaluated by applying a system of boundary conditions which were derived in the usual fashion but are based on assumed discontinuities in both the velocity and temperature profiles at the film-Helium II interface. Calculated results, which include the film thickness, the heat transfer coefficient, and the mass flow in the film, are presented and discussed.


Author(s):  
J. O. Wilhelm ◽  
A. D. Misener ◽  
A. R. Clark ◽  
John Cunningham McLennan

It is a well-known fact that liquid helium changes from one form of liquid to another at a temperature of 2.19º K, under its own vapour pressure at that temperature. The liquid above this temperature is spoken of as helium I, and below it, as helium II. This temperature is known as the λ point. The apparent difference between these two forms of the liquid is that helium I visibly boils as it is being evaporated in a way similar to ordinary liquids, but immediately this temperature is passed boiling stops and the liquid appears to be absolutely quiescent, although the temperature is progressively reduced by continued evaporation. Many properties of these two forms of liquid helium have been studied, but apparently up to the present the viscosity has not been determined. In order to keep the liquid helium at a given temperature below 4.2º K, its boiling point, it is necessary to allow it to boil under reduced pressure, consequently the formation of bubbles excludes any possibility of using a capillary viscosimeter method. The necessity of operating the liquefying system under reduced pressure also allows small amounts of impurity to leak in; these traces of impurity condense over the liquid helium and drop as fine particles through the liquid. This has to be considered in designing the apparatus.


An apparatus is described for detecting single quanta of superfluid circulation round a fine wire in liquid helium II. The wire is stretched down the centre of a cylindrical vessel containing helium, and the circulation may be established by rotating the whole apparatus about the axis of the wire and cooling from above the λ-point. The wire can be set into transverse vibration, and the circulation round it can then be obtained from the rate of precession of the plane of vibration. The technique proves to be sufficiently sensitive for the measurement of circulations of order h/m with an accuracy of about 3%. The method in its present form measures only an average of the circulation along the length of the wire, and it is found that this average is not quantized. Apparent circulations equal to a fraction of a quantum are attributed to quantized vortices that are attached to only a fraction of the length of the wire, and this interpretation has been confirmed by showing that an apparent circulation of exactly h/m has much greater stability than any other value. In this way the quantization of superfluid circulation in units of h/m has been experimentally verified. Observations made in the course of this work show clearly that superfluid circulations (including free vortex lines) can persist indefinitely even when the rotation of the apparatus is stopped. Values have also been obtained for the circulation round the wire as a function of the angular velocity of rotation, and it is shown from these that the energy of a free vortex line in the helium surrounding the wire may perhaps be considerably smaller than has hitherto been supposed.


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

1948 ◽  
Vol 74 (9) ◽  
pp. 1148-1156 ◽  
Author(s):  
F. London ◽  
P. R. Zilsel

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