Thermal transport properties of the helium near the superfluids transition II. Dilute 3He-He mixtures in the superfluid phase

Measurements of the average thermal conductivity k/sub exp/ is identical to hQ/ΒT and of the thermal relaxation time Γ to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of 3He in 4He. Here h is the cell height, Q is the heat flux, and ΒT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2 x 10-9 < x (3He) < 3 x 10-2 and with heat fluxes 0.3 < q < 160 μ w/cm2. Assuming the boundary resistance R /sub b/, measured for x < 10-5, to be independent of x over the whole range of x, a calculation is given for k/sub exp/. for Q smaller than a well-defined critical heat flux Q /sub c/ (X) proportional to X/sup 0.9/, k/sub exp/. for Q of Q and can be identified with the local conductivity K/sub eff/, which is found to be independent of the reduced temperature ε = (T - T/sub lambda/)/ T/sub lambda/ for -ε ≤ 10-2 from the prediction extrapolated value at T/sub lambda/ is found to depart for X ≤ 10-3 from the prediction k/sub lambda/ proportional to X-1, tending instead to a weaker divergence k/sub lambda/ proportional to X/sup -a/ with a≅ 0.8. A finite conductivity as X tends to zero is not excluded by the data, however. For Q > Q/sub c/ (X) a nonlinear regime is entered. for X ≤ 10-6, the measurements with the availavle temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime for X ≥ 2 x 10-7. the results for K /sub exp/ (Q), Q/sub c/ (X), and k /sub eff/ (XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations