Comparison of three 3ω techniques: (a) Standard 3ω – heater is built on solid substrate. The fluid to be sensed is above the heater. The outer probes drive a 1ω current and the inner probes sense a third-harmonic voltage signal 3ω. (b) Solid-wire 3ω – has the 1ω current driven through the length of the wire and 3ω voltage sensed across the length of the wire. The fluid to be measured surrounds the fiber. (c) Metal-coated 3ω – employs a glass fiber as a backbone for a nanometer thick metal coating. The voltage and current is applied similar to solid metal wire, with the fluid surrounding the metal coating.
Fraction of zero time-average periodic heating entering fluid-under-test (air). For a metal-coated fiber (25 μm diameter glass fiber coated with 100 nm of platinum) more of the heat enters the fluid-under-test than with solid metal wire 3ω. Thermoproperties were taken for Pyrex and air at standard temperature and pressure. The analytical model for metal-coated and solid-wire 3ω are developed in a later section.
(a) “Sputtering lathe” – glass fibers are strung across spool which rotated during metal deposition to ensure circumferentially even coating. Glass fibers are adhered to the spool with Kapton tape. (b) Metal-coated fiber cross-section scanning electron microscope image.
3ω electronic schematic: Current source provides a 1ω current to the series circuit consisting of the metal-coated filament and the calibration resistor. The calibration resistor is adjusted such that it equals the average sense filament resistance. The voltages across the metal-coated filament and calibration resistor are buffered by an instrumentation amplifier and fed into a lock-in amplifier. The lock-in determines the magnitude and phase of the third-harmonic (3ω) voltage, thereby measuring the magnitude and phase of the metal coating's temperature.
Normalized amplitude and phase versus frequency for various fluids (Argon – dark blue cross, Air – light blue triangle, Helium – red square, Deionized H20 – green circles) with corresponding analytical fits shown as similarly colored lines. The experimental and accepted thermal conductivities are shown in Table I. The data was normalized by dividing a given fluid's ΔTs by its maximum ΔT. This normalization is optional, but removes the need for measuring the heater's coefficient of thermoresistance. A least-squares minimization was then used to fit experimental data to analytical model.
A simulated plot of change in phase between thermal boundary conductance of 107 and 108 W/m2 K in metal-coated 3ω (solid green) and solid metal 3ω (dashed red). The greater separation between metal-coated 3ω curves indicates greater sensitivity to thermal boundary conductance than solid metal 3ω. Simulated experiment has heater surrounded by mercury with a thermal boundary conductance across metal-mercury interface.
Comparison of accepted thermal conductivity values (Refs. 20 and 25) to experimental values obtained with this experiment on benchmark fluids. Experiments performed at atmospheric pressure at 300 K.
Properties and dimensions of experimental setup assumed for the predictions of thermal conductivity shown in Table I. Accepted values of ρ and c were used for each fluid sample (Refs. 20 and 25).
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