Modified 3ω conductivity technique for measurements of thermal conductivity in cryogenic fluids

Abstract

An instrument based on a modification to the 3-omega thermal conductivity technique that allows precise measurement of thermal properties in fluids is presented. Existing hot-wire techniques have difficulty measuring thermal conductivity because of the effects of natural convection distorting the measurement, however the standard 3-omega technique has been used extensively in the measurement of the properties of solids with great success. To address the challenge posed by natural convection in fluids, we modify the boundary condition of the 3-omega device configuration to be finite in extent, thereby restricting fluid motion and enabling a direct high-precision measurement of a fluid’s thermal conductivity. This modified scenario also presents an opportunity for a simultaneous measurement of the thermal diffusivity of the fluid. The behavior of the device is described with the reformed boundary conditions to show how a simultaneous measurement is made. By applying a constant temperature finite boundary condition, the solution characteristic in the frequency domain gains features that allow for simultaneous measurements of the fluid thermal conductivity and diffusivity. Given the density of the fluid, measured separately, the specific heat of the fluid can be calculated. The effects of the thermal properties of the measurement wire influence the measurement characteristic, and only when the wire thermal properties are sufficiently small compared to those of the fluid can a simultaneous measurement be made. Due to limitations in the dynamic reserve of the measurement devices, a setup is described that allows the signal of interest to be extracted and a precise measurement to be made with minimal distortion. Initial data on the thermal conductivity of helium is presented in the 4-300K temperature range. Preliminary specific heat data is also presented. Limitations on the device’s thermal properties prevent a specific heat measurement above 70K. This data is compared with reference fluid properties databases to validate the device performance.