Extracting liquid thermophysical properties inside stainless-steel microtubes using the 3ω method

This paper examines the feasibility of using an AC Joule-heated stainless-steel (SS304) suspended microtube as a combined heater/thermometer to identify the thermal conductivity $$\:{k}_{l}$$ and volumetric heat capacity $$\:{\left(\rho\:{c}_{p}\right)}_{l}$$ of nanoliter-scale liquids, including electrically conducting liquid metals. The analysis builds on the 3ω technique, wherein a sinusoidal drive at frequency f produces temperature oscillations at 2ω and a third-harmonic voltage V3ω carrying the sample’s thermal signature. A first-order axial heat-flow model is formulated for a circular microtube and extended to treat two electrical boundary conditions inside the tube: (A) a conformal inner insulator (no electrical shunting through the liquid) and (B) direct electrical contact to a conductive liquid, which creates a parallel electrical path and modifies both Joule power and effective temperature coefficient of resistance. This study outlines an identification workflow for { $$\:{k}_{l}$$ , $$\:{\left(\rho\:{c}_{p}\right)}_{l}$$ } from the complex V3ω(f), discuss implementation constraints, and present representative spectra computed for real liquids and for a high-k liquid metal (NaK). The results indicate that, after calibration, the insulated case can recover { $$\:{k}_{l}$$ , $$\:{\left(\rho\:{c}_{p}\right)}_{l}$$ } from frequency response alone, and that even when the liquid is electrically conducting, the degradation in signal can be modeled and corrected if the parallel conduction is characterized.