Heat Transport in LiquidHe3

Abstract

The thermal conductivity of liquid He 3 at a pressure of § atmosphere has been determined experimentally and found to increase slowly from 7X10~5 watt/cm°K at 0.24°K to 16X10" 5 watt/cm°K at 2.7°K with no evidence of superfluidity. Several models of liquid He 3 based on Fermi-Dirac statistics predict a 1/T dependence for the thermal conductivity of He 3 at the lowest temperatures, but no such behavior has been observed down to 0.24°K in the present work. A study of the convective heat transport in the liquid has indicated that the coefficient of thermal expansion becomes negative below about 0.5 °K. A thermal boundary resistance across a copper-liquid He 3 interface has been found which is similar in magnitude and temperature dependence to that found for a copper-superfluid He 4 boundary.

Thermal conductance at the interface of a solid and helium II (kapitza conductance)

“…1 for tin, and 1.06 for indium (Rosenberg, 1963), which would result in a spuriously lower boundary conductance. Since the surfaces of the samples studied by Cheeke (1969) were machined under liquid helium,this mechanism was probably Lee and Fairbank, 1959), and also between two solids (see Syomi, Anderson and Holmstrom, 1968) (Woods, 1965). …”

“…Lower ratios were found for other metals: 1. 3 for mercury (Neeper, Pearce, and Wasilik, 1967), 1. 1 for tin, and 1.06 for indium (Rosenberg, 1963), which would result in a spuriously lower boundary conductance.…”

Thermal conductivity of helium-3 between 3 mK and 300 K

“…Challis and Wilks [1] first measured the liquid conductivity between 1.2 and 3 K. They found the conductivity to increase slowly with increasing temperature throughout the entire range investigated, which was verified by Lee and Fairbank from 0.24 to 2.7 K reported preliminarily in 1957 [2,3] and eventually in 1959 [4]. However, Lee and Fairbank's data were approximately 10% higher than those of Challis and Wilks.…”

“…The low temperature and the small mass of the helium atom require a quantum mechanical treatment of most problems associated with liquid helium. Also, the properties of liquid 4 He and 3 He show dramatic differences, with increasing effects on the properties as the temperature is lowered.…”

“…No equations, tables, or graphs are available in the literature for the thermal conductivity of 3 He in a wide range of temperature and pressure covering the cryogenic applications. The experimental work on the transport properties of 3 He were mostly regarding the liquid phase, due to two basic motivations: 1) to explore the superfluidity of 3 He as discovered with 4 He, and 2) to verify the behavior λ v 1/T as predicted by the Fermi quantum fluid theory. A basic statistical mechanical treatment of transport phenomena in fluid 3 He is a difficult problem, because of the quantum effect which appears to be determined in a significant way by Fermi-Dirac statistics.…”