Uncertainty Analysis of the Thermal Bridge Method
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Uncertainty Analysis of the Thermal Bridge Method Yiwen Sun1 · Juekuan Yang1 Received: 24 June 2020 / Accepted: 11 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Thermal bridge method is widely used in thermal conductance measurements of one-dimensional nanostructures. The studies used by thermal bridge method advances our understanding of one-dimensional nanoscale thermal transport. And many efforts have been made to boost the reliability of the thermal bridge method and improve the measurement sensitivity. In this paper, uncertainty analysis is performed on the thermal bridge measurements of a CNT and a CdSe nanowire. Both the Taylor series method and the Monte Carlo method are used to figure out the propagation of the errors in the direct measurements. Our results show that the uncertainty of the thermal conductance decreases as the thermal conductance of the measured sample decreases, which can be attributed to the increase in the temperature drop on the measured sample. This finding indicates that we can reduce the measurement uncertainty by increasing the measured length of the sample or increasing the Joule heating generated on the heat source. Keywords Monte Carlo method · Taylor series method · Thermal bridge method · Uncertainty analysis
1 Introduction Thermal bridge method proposed by Kim et al. [1, 2] has been widely used in the measurements of the thermal conductance of one-dimensional nanomaterials, including carbon nanotubes (CNTs) [1–3], silicon nanowires or nanoribbons [4–8], boron nitride nanotubes [9], vanadium dioxide nanobeams [10], polymer nanofibers [11–14], etc. These studies advance our understanding of one-dimensional nanoscale thermal transport. Since the thermal bridge method is very useful to the research of nanoscale thermal transport, many efforts have been made to improve its accuracy. When the * Juekuan Yang [email protected] 1
School of Mechanical Engineering and Jiangsu Key Laboratory for Design and Manufacture of Micro‑Nano Biomedical Instruments, Southeast University, Nanjing 211189, China
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International Journal of Thermophysics
(2020) 41:146
method was first proposed, a DC current was used both to heat the heat source and to sense the temperature rise of the heat source ΔTh [1]. However, it was found soon that the measurement error in ΔTh dominates the total measurement uncertainty. To improve the accuracy of ΔTh , an AC sensing current was coupled to the DC heating current to detect ΔTh [2]. The introduction of the AC sensing current improves the measurement sensitivity to ~ 1 nW·K−1. Later, in order to eliminate the effect of ambient temperature fluctuation on the measurement of the temperature rise of the heat sink ΔTs , a reference heat sink and Wheatstone bridge circuit were used by Wingert et al. [15]. They demonstrated that the measurement sensitivity was improved to be ~ 10 pW·K−1 after rejecting the common environmental instabilities. Furthermore, Weathers et al. [16]
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