A Procedure for Application of the Three-Omega Method to Measurement of Gas Thermal Conductivity

A non-linear least-squares curve-fitting procedure is proposed to analyze three-omega voltage data from a fine wire in a gas sample using the three-omega method. The method uses both three-omega components of the voltage arising from a sinusoidal heating current to determine the thermal conductivity of the surrounding medium. The proposed procedure is tested against simulated data and some experimental data for air at atmospheric pressure. Treating the technique as an absolute method and assuming a known sample heat capacity, the thermal conductivity of air has been measured at room temperature to within 11% of a reference value. Practical application of the method may require a calibrated effective wire length and wire diameter. An average wire temperature rise of around 10 K to ensure the three-omega components is enough for accurate measurement.