The thermal conductivity of fluid4He and the ratio of thermal conductivities of solid and fluid4He at the melting point

Abstract

A critical factor in the study of dendritic solidification is the ratio of thermal conductivities of solid and fluid, {beta}, at the melting point. Models of dendritic solidification due to Langer define the relationship of {beta} to such observable features as side arm spacing and tip growth velocity, which have been systematically studied in {sup 4}He systems by Franck and Jung. For most materials, {beta} has a value near 1.0, a notable exception being water, for which {beta} {approx} 4.0. However, for {sup 4}He, it is almost entirely unknown, there being but a single, estimated value at T{sub m} = 1.9 K, P{sub m} = 26 bar, where {beta} {approx} 14.5. The thermal conductivity of solid and fluid {sup 4}He was measured using guarded concentric cylinders since a thick-walled cylindrical pressure cell was mandated by anticipated pressures of up to 2 kbar. The measuring system consisted of concentric beryllium-copper cylinders separated by an annular gap filled with fluid helium. The thermal gradient in the working fluid due to the heated inner cylinder was measured with a differential (Au + 0.07%Fe) vs. Chromel thermocouple. Heated guard cylinders eliminated longitudinal heat loss from the inner cylinder. Data were obtained as the cellmore » was cooled in a controlled temperature dewar.« less