Mathematics – Group Theory
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phdt.........8o&link_type=abstract
Thesis (PH.D.)--DUKE UNIVERSITY, 1994.Source: Dissertation Abstracts International, Volume: 56-02, Section: B, page: 0866.
Mathematics
Group Theory
Scientific paper
The thermal transport properties of liquid helium have been studied both above and below the lambda line at saturated vapor pressure (SVP) using a time-varying heat flux, Q(t) = Qoegp(iwt) . Above the superfluid transition, helium behaves as a simple fluid and the temperature within the fluid is determined by the heat equation. The thermal conductivity, kappa, and the thermal diffusivity, DT, of the normal fluid are then both obtained by the 1-D temperature response, DeltaT(z,w), where z is the position in the fluid along the direction of heat flow and w is the frequency of the oscillating heat amplitude. Previous transient heat flux experiments which measure the thermal relaxation of the fluid towards equilibrium assume the dominance of a single slowest mode. The fully developed AC technique, however, yields distinct and precise measurement of the separate time scales in the system, leading to a more detailed description of thermal transport. The technique allows for the first direct measurement of the thermal boundary resistance, Rb, at the fluid-to-metal interface above the superfluid transition. Such a technique is invaluable to testing Renormalization Group Theory predictions for the behavior of the boundary resistance in the normal-phase. Data was also obtained above the critical heat in the normal fluid, where diffusive processes give way to convective heat transport. Below Tlambda , previous DC measurements have indicated a dependence on the fluid layer thickness, d, for the effective thermal conductivity, kappaeff , at low ^3He impurity concentrations, X. This suggests an intrinsic length scale of the fluid not predicted by the standard models for superfluid dynamics. In the superfluid phase, the time varying temperature response, Delta T(z,w), yields simultaneous information on kappaeff and Diso, analogous to measurements of kappa and D T above T_λ. AC measurements are a valuable technique for measuring the boundary resistance. Below Tlambda, a divergent anomaly is observed in the DC component of R_ {b} as the superfluid transition is approached. The AC technique yields the first measurements on the dynamic response of Rb. A resonant-like peak is found in the thermal response of Rb in the same temperature regime as the Q-dependent anomaly detected in DC measurements. Measurements on a superfluid mixture of impurity concentration, X = 1.2 times 10^{ -4} demonstrate the presence of an additional thermal resistance, R_0, that is independent of the fluid layer thickness d. A model is presented that characterizes the AC thermal response in terms of kappaeff, Diso, R_ {b}, R_0 and a corresponding diffusivity, D_0, for the additional resistance.
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