<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{k}_{l}\)</EquationSource> </InlineEquation> and volumetric heat capacity <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:{\left(\rho\:{c}_{p}\right)}_{l}\)</EquationSource> </InlineEquation> of nanoliter-scale liquids, including electrically conducting liquid metals. The analysis builds on the 3<i>ω</i> technique, wherein a sinusoidal drive at frequency <i>f</i> produces temperature oscillations at 2<i>ω</i> and a third-harmonic voltage <i>V</i><sub>3ω</sub> 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 {<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:{k}_{l}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\:{\left(\rho\:{c}_{p}\right)}_{l}\)</EquationSource> </InlineEquation>} from the complex <i>V</i><sub>3ω</sub>(<i>f</i>), discuss implementation constraints, and present representative spectra computed for real liquids and for a high-<i>k</i> liquid metal (NaK). The results indicate that, after calibration, the insulated case can recover {<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\:{k}_{l}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\:{\left(\rho\:{c}_{p}\right)}_{l}\)</EquationSource> </InlineEquation>} 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.</p>

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

  • Jungchul Lee

摘要

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 V 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 V(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.