The transient hot strip on-a-chip method to measure the thermal conductivity λ of fluids is based on the micro hot strip sensor with ultrasmall dimensions requiring very low sample volumes of less than 5 µL. The corresponding micro-electromechanical systems (MEMS) chip has dimensions of 4.22 mm × 3.22 mm × 0.6 mm and only consists of a trench that is traversed by a micro-bridge carrying a nickel (hot) strip with dimensions of 2000 µm × 6 µm × 0.5 µm. In accordance with the transient hot wire (THW) method, the strip acts as Joule heater and resistance thermometer. A typical measurement run lasts only around 250 µs for a gas like, e.g., methane, and less than 100 ms for a liquid like, e.g., water. This implies that a run is terminated before free convection can set on and from then on perturb the test result. To control the µHS sensor, just a high-frequency (HF) function generator is required, a fast data acquisition and a laptop. The transient hot wire model can be applied due to the small width of the strip. Here, this model is used as a basic module of the parametrical identity (PI) model. The PI model compares a given set of observations with the underlying model, identifies the degree of mutual agreement, and, if necessary, furnishes two correction factors for an optimal adjustment of the model to the observations. In this way, all significant (bias) influences can be covered without having to be individually determined in advance, which facilitates the assessment of the measurement uncertainty. The result obtained here for the relative expanded uncertainty (coverage factor <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$k = 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>) of λ amounts to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${{U\left( \lambda \right)} \mathord{\left/ {\vphantom {{U\left( \lambda \right)} \lambda }} \right. \kern-0pt} \lambda } = 1{\text{ \% }}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mrow> <mi>U</mi> <mfenced close=")" open="("> <mi>λ</mi> </mfenced> </mrow> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <mrow> <mi>U</mi> <mfenced close=")" open="("> <mi>λ</mi> </mfenced> </mrow> <mi>λ</mi> </mpadded> </mphantom> </mfenced> </mrow> <mi>λ</mi> </mrow> <mo>=</mo> <mn>1</mn> <mrow> <mspace width="0.333333em" /> <mtext>\%</mtext> <mspace width="0.333333em" /> </mrow> </mrow> </math></EquationSource> </InlineEquation> for liquids and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">${{U\left( \lambda \right)} \mathord{\left/ {\vphantom {{U\left( \lambda \right)} \lambda }} \right. \kern-0pt} \lambda } = 1.8{\text{ \% }}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mrow> <mi>U</mi> <mfenced close=")" open="("> <mi>λ</mi> </mfenced> </mrow> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <mrow> <mi>U</mi> <mfenced close=")" open="("> <mi>λ</mi> </mfenced> </mrow> <mi>λ</mi> </mpadded> </mphantom> </mfenced> </mrow> <mi>λ</mi> </mrow> <mo>=</mo> <mn>1.8</mn> <mrow> <mspace width="0.333333em" /> <mtext>\%</mtext> <mspace width="0.333333em" /> </mrow> </mrow> </math></EquationSource> </InlineEquation> for gases. These values are confirmed by experiments on the reference liquid toluene and on gaseous methane at 296 K and 0.1 MPa, for which the measurement data agree very well with corresponding reference values in literature.

Transient Hot Strip On-a-Chip Method for the Measurement of Thermal Conductivity: Uncertainty Assessment

期刊论文
发表日期：

2026年5月28日

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Ulf Hammerschmidt

摘要

The transient hot strip on-a-chip method to measure the thermal conductivity λ of fluids is based on the micro hot strip sensor with ultrasmall dimensions requiring very low sample volumes of less than 5 µL. The corresponding micro-electromechanical systems (MEMS) chip has dimensions of 4.22 mm × 3.22 mm × 0.6 mm and only consists of a trench that is traversed by a micro-bridge carrying a nickel (hot) strip with dimensions of 2000 µm × 6 µm × 0.5 µm. In accordance with the transient hot wire (THW) method, the strip acts as Joule heater and resistance thermometer. A typical measurement run lasts only around 250 µs for a gas like, e.g., methane, and less than 100 ms for a liquid like, e.g., water. This implies that a run is terminated before free convection can set on and from then on perturb the test result. To control the µHS sensor, just a high-frequency (HF) function generator is required, a fast data acquisition and a laptop. The transient hot wire model can be applied due to the small width of the strip. Here, this model is used as a basic module of the parametrical identity (PI) model. The PI model compares a given set of observations with the underlying model, identifies the degree of mutual agreement, and, if necessary, furnishes two correction factors for an optimal adjustment of the model to the observations. In this way, all significant (bias) influences can be covered without having to be individually determined in advance, which facilitates the assessment of the measurement uncertainty. The result obtained here for the relative expanded uncertainty (coverage factor $k = 2$ $k = 2$ ) of λ amounts to ${{U\left( \lambda \right)} \mathord{\left/ {\vphantom {{U\left( \lambda \right)} \lambda }} \right. \kern-0pt} \lambda } = 1{\text{ \% }}$ $U (λ) /) λ = 1 \%$ for liquids and ${{U\left( \lambda \right)} \mathord{\left/ {\vphantom {{U\left( \lambda \right)} \lambda }} \right. \kern-0pt} \lambda } = 1.8{\text{ \% }}$ $U (λ) /) λ = 1.8 \%$ for gases. These values are confirmed by experiments on the reference liquid toluene and on gaseous methane at 296 K and 0.1 MPa, for which the measurement data agree very well with corresponding reference values in literature.