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Research Papers

Measurement Sensitivity Analysis of the Transient Hot Source Technique Applied to Flat and Cylindrical Samples

[+] Author and Article Information
Jason Ostanek

Naval Surface Warfare Center,
Philadelphia Division,
5001 South Broad Street,
Philadelphia, PA 19112

Krishna Shah, Ankur Jain

Mechanical and Aerospace
Engineering Department,
The University of Texas at Arlington,
500 West First Street,
Arlington, TX 76019

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received January 26, 2016; final manuscript received June 15, 2016; published online September 8, 2016. Assoc. Editor: Steve Q. Cai. This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Thermal Sci. Eng. Appl 9(1), 011002 (Sep 08, 2016) (12 pages) Paper No: TSEA-16-1022; doi: 10.1115/1.4034178 History: Received January 26, 2016; Revised June 15, 2016

The transient source measurement technique is a nonintrusive, nondestructive method of measuring the thermal properties of a given sample. The transient source technique has been implemented using a wide variety of sensor shapes or configurations. The modern transient plane source (TPS) sensor is a spiral-shaped sensor element which evolved from transient line and transient hot strip (THS) source techniques. Commercially available sensors employ a flat interface that works well when test samples have a smooth, flat surface. The present work provides the basis for a new, cylindrical strip (CS) sensor configuration to be applied to cylindrical surfaces. Specifically, this work uses parameter estimation theory to compare the performance of CS sensor configurations with a variety of existing flat sensor geometries, including TPS and THS. A single-parameter model for identifying thermal conductivity and a two-parameter model for identifying both thermal conductivity as well as volumetric heat capacity are considered. Results indicate that thermal property measurements may be carried out with greater measurement sensitivity using the CS sensor configuration than similar configurations for flat geometries. In addition, this paper shows how the CS sensor may be modified to adjust the characteristic time scale of the experiment, if needed.

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Figures

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Fig. 1

Sketches of various transient heat source sensors. CS, GCS, and SCS sensor configurations are unique to the present work. Also shown are the coordinate system definitions and representative heat flow vectors depicting the mathematical model to be used for each sensor. (a) Transient hot strip (THS), (b) transient plane source (TPS), (c) guarded THS, (d) 1D finite slab, (e) cylindrical strip (CS), and (f) guarded CS.

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Fig. 2

Schematic drawings (not to scale) of solution domain and boundary conditions and verification data comparing analytical solutions (lines) with numerical solutions (symbols). The analytical solutions used for each sensor configuration are indicated in Table 2. (a) THS, (b) TPS, (c) GTHS, GTPS, (d) 1D finite slab, (e) CS, SCS, and (f) GCS.

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Fig. 5

Measurement sensitivity analysis for GTPS/GTHS configuration: temperature rise (a), sensitivity coefficients (b), covariance matrix components (c), and D-optimality criteria (d)

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Fig. 9

Comparison of CS, SCS, and GCS sensors, showing the progression of increasing the portion of heated area (shaded). CS sensor with H/W = 15 (a), SCS1 with H/W = 4 (b), SCS2 with H/W = 2 (c), and GCS with H/W = 1 (d).

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Fig. 8

Measurement sensitivity analysis for GCS geometry: temperature rise (a), sensitivity coefficients (b), covariance matrix components (c), and D-optimality criteria (d)

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Fig. 7

Measurement sensitivity analysis for CS geometry: temperature rise (a), sensitivity coefficients (b), covariance matrix components (c), and D-optimality criteria (d)

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Fig. 6

Measurement sensitivity analysis for TPS geometry: temperature rise (a), sensitivity coefficients (b), covariance matrix components (c), and D-optimality criteria (d)

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Fig. 4

Measurement sensitivity analysis for a 1D finite slab: temperature rise (a), sensitivity coefficients (b), covariance matrix components (c), and D-optimality criteria (d)

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Fig. 3

Measurement sensitivity analysis for THS geometry: temperature rise (a), sensitivity coefficients (b), covariance matrix components (c), and D-optimality criteria (d)

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Fig. 10

Effect of separation distance between adjacent heater strips using the CS/SCS sensor. Decreasing separation distance results in reduced sensitivity to λ (a) as well as reduced sensitivity to simultaneous estimation of λ and ρ·Cp (b). (a) Single-parameter model and (b) two-parameter model.

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