Thermal Conductivity of Superfluid $$^3$$He-B in a Tubular Channel Down to 0.1$$T_\mathrm{c}$$ at the $$^{4}$$He Crystallization Pressure

We studied the thermal conductivity of superfluid $$^{3}$$ 3 He in a 2.5-mm effective diameter and 0.15-m-long channel connecting the two volumes of our experimental assembly. The main volume contained pure solid $$^{4}$$ 4 He, pure liquid $$^{3}$$ 3 He and saturated liquid $$^{3}$$ 3 He–$$^{4}$$ 4 He mixture at varying proportions, while the separate heat-exchanger volume housed sinter and was filled by liquid $$^{3}$$ 3 He. The system was cooled externally by a copper nuclear demagnetization stage, and, as an option, internally by the adiabatic melting of solid $$^{4}$$ 4 He in the main volume. The counterflow effect of superfluid just below the transition temperature $$T_\mathrm{c}$$ T c resulted in the highest observed conductivity about five times larger than that of the normal fluid at the $$T_\mathrm{c}$$ T c . Once the hydrodynamic contribution had practically vanished below $$0.5T_\mathrm{c}$$ 0.5 T c , we first observed almost constant conductivity nearly equal to the normal fluid value at the $$T_\mathrm{c}$$ T c . Finally, below about $$0.3T_\mathrm{c}$$ 0.3 T c , the conductivity rapidly falls off toward lower temperatures.