Research Papers: Conduction

Temperature Solution for Transient Heat Conduction in a Thin Bilayer Between Semi-Infinite Media in Thermal Effusivity Measurement

[+] Author and Article Information
Leendert van der Tempel

Philips Research,
5656 AE Eindhoven, The Netherlands
e-mail: Leendert.van.der.Tempel@Philips.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 22, 2015; final manuscript received December 10, 2015; published online March 1, 2016. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 138(5), 051301 (Mar 01, 2016) (8 pages) Paper No: HT-15-1357; doi: 10.1115/1.4032434 History: Received May 22, 2015; Revised December 10, 2015

A series expansion and an approximation have been derived for the temperature in the general case of transient heat conduction in two thin layers between two semi-infinite media at different uniform initial temperatures. The temperature accuracy and thermal effusivity measurement accuracy have been mapped to establish a window of operation for direct thermal effusivity measurement by the modified transient plane source (MTPS) method. The presented temperature series enables quick thermal analysis of thermally thick and semithick samples without factory correction/calibration.

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Fig. 1

One-dimensional geometry

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Fig. 2

Heater/sensor of C-Therm® TCi Thermal Analyzer with Pt spiral at the origin x = 0. The sample is placed on top. In the test case, a thick Pyrex backing is placed on top of the sample.

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Fig. 3

Laplace transformed temperature distribution

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Fig. 4

Laplace transformed temperature Θ(s,0), geometric series expansion Θm(s,0), and rational approximation Θ̃(s,0) at zero depth multiplied by s3/2

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Fig. 9

Relative heating rate error of series (19), approximation (22), and the asymptotic approximation in Ref. [5] and asymptote (1), compared to an accurate 1DT Comsol numerical model including the overglaze and water interlayers for 1 s measurement time

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Fig. 7

Absolute truncation and approximation error of the temperature at the origin x = 0 for the test case. Figure 4 shows the Laplace transformed counterpart.

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Fig. 5

Temperature evolution in thermal effusivity measurement of 0.1 mm thick PC

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Fig. 6

Absolute maximum temperature error versus the computational work, i.e., number of function evaluations for the test case

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Fig. 8

Absolute temperature error (K) of series expansion (19) compared to an accurate 1DT Comsol numerical model including the overglaze and water interlayers

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Fig. 10

Absolute relative estimation bias of the thermal effusivity due to series (19). The absolute relative measurement accuracy of the thermal effusivity of 56 samples is marked by ○. The outlier is a 2 cm thick SrTiO3 sample.

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Fig. 11

Repeatability of 16 thermal effusivity repeat measurements elaborated by the series (19) or by the asymptotic approximation in Ref. [5] versus the thermal thickness of 56 samples. Lines are cubic Padé fits.



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