Fig. 2
Data analysis for 3-omega method adapted for use with needle-form sensor. a) Representative in-phase temperature maps of temperature-sensing portion of sensor and surrounding sample from the 3-D comsol model used in analysis, shown for high and low frequency, \(\omega\), and sample thermal conductivity, k. Thermal conductivities are representative of the lowest and highest conductivities measured in this study (0.28 \(\hbox {W/m}^{\circ }\hbox {C}\) and 2.27 \(\hbox {W/m}^{\circ }\hbox {C}\)); For ease of visualization, frequencies are representative of the lowest and center frequencies used in measurement (\(\omega /2\pi\)=2.001 Hz and 18.95 Hz). The central linear shape in each image is the 2-mm sensing portion of the needle-form sensor, and the surrounding area is the measured sample. b) Data from a typical measurement using the needle-form 3-omega sensor (water, \(21^{\circ }\hbox {C}\), expected k = 0.601 \(\hbox {W/m}^{\circ }\hbox {C}\)28). Points represent the measured voltage converted to the average temperature rise of the metal line within the needle, with error bars representing the propagated error of the measurement. Solid lines represent the best fit provided by the comsol model. Similar plots for each sample and details on propagated error are included in the Supplementary Information. The model fit is in excellent agreement with the experiment across all frequencies, and returns a best-fit value of k that is within 3% of the literature value.
