Abstract

This work reports a custom instrument that employs a modified Ångström's method to measure the thermal diffusivity of foil-like materials in which heat propagates in one dimension. This method does not require a semi-infinite medium assumption as compared to the original Ångström's method, which also has been typically performed in vacuum. However, in this work, temperature measurements are performed in laboratory ambient conditions, which are more convenient for most experiments. To quantify and reduce uncertainties due to temperature fluctuations in noisy ambient conditions, a Bayesian framework and Metropolis algorithm are employed to solve the inverse heat transfer problem and to obtain a probability distribution function for thermal diffusivity. To demonstrate the effectiveness of the custom instrument, the thermal diffusivity of a copper 110 foil (25.0 mm long, 7.0 mm wide, and 76.2 μm thick) was measured in ambient conditions, and the results match well with previous studies performed in vacuum conditions on much longer samples.

References

1.
Cahill
,
D. G.
,
1990
, “
Thermal Conductivity Measurement From 30 to 750 K: The 3 Omega Method
,”
Rev. Sci. Instrum.
,
61
(
2
), pp.
802
808
.10.1063/1.1141498
2.
Parker
,
W. J.
,
Jenkins
,
R. J.
,
Butler
,
C. P.
, and
Abbott
,
G. L.
,
1961
, “
Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity
,”
J. Appl. Phys.
,
32
(
9
), pp.
1679
1684
.10.1063/1.1728417
3.
Zhao
,
D.
,
Qian
,
X.
,
Gu
,
X.
,
Jajja
,
S. A.
, and
Yang
,
R.
,
2016
, “
Measurement Techniques for Thermal Conductivity and Interfacial Thermal Conductance of Bulk and Thin Film Materials
,”
ASME J. Electron Packag.
,
138
(
4
), p.
040802
.10.1115/1.4034605
4.
Park
,
D. G.
,
Kim
,
H. M.
,
Baik
,
S. J.
,
Kim
,
K. H.
,
Ahn
,
S. B.
, and
Ryu
,
W. S.
,
2009
, “
Heat Loss Effects of Laser Flash Method for Low Thermal Diffusivity Materials
,”
Proceedings of the KNS Autumn Meeting
,
Kyungju, Republic of Korea
, Paper No. 41027226.
5.
Xu
,
J.
, and
Fisher
,
T. S.
,
2006
, “
Enhancement of Thermal Interface Materials With Carbon Nanotube Arrays
,”
Int. J. Heat Mass Transfer
,
49
(
9–10
), pp.
1658
1666
.10.1016/j.ijheatmasstransfer.2005.09.039
6.
Hao
,
M.
,
Saviers
,
K. R.
, and
Fisher
,
T. S.
,
2016
, “
Design and Validation of a High-Temperature Thermal Interface Resistance Measurement System
,”
ASME J. Therm. Sci. Eng. Appl.
,
8
(
3
), p.
031008
.10.1115/1.4033011
7.
Angström
,
A.
,
1863
, “
XVII—New Method of Determining the Thermal Conductibility of Bodies
,”
Philos. Mag.
,
25
(
166
), pp.
130
142
.10.1080/14786446308643429
8.
Zhu
,
Y.
,
2016
, “
Heat-Loss Modified Angstrom Method for Simultaneous Measurements of Thermal Diffusivity and Conductivity of Graphite Sheets: The Origins of Heat Loss in Angstrom Method
,”
Int. J. Heat Mass Transfer
,
92
, pp.
784
791
.10.1016/j.ijheatmasstransfer.2015.09.032
9.
Prasad
,
A.
, and
Ambirajan
,
A.
,
2018
, “
Criteria for Accurate Measurement of Thermal Diffusivity of Solids Using the Angstrom Method
,”
Int. J. Therm. Sci.
,
134
, pp.
216
223
.10.1016/j.ijthermalsci.2018.08.007
10.
Muscio
,
A.
,
Bison
,
P. G.
,
Marinetti
,
S.
, and
Grinzato
,
E.
,
2004
, “
Thermal Diffusivity Measurement in Slabs Using Harmonic and One-Dimensional Propagation of Thermal Waves
,”
Int. J. Therm. Sci.
,
43
(
5
), pp.
453
463
.10.1016/j.ijthermalsci.2003.10.005
11.
Lopez-Baeza
,
E.
,
Rubia
,
J. D. H.
, and
Goldsmid
,
H. J.
,
1987
, “
Angstrom's Thermal Diffusivity Method for Short Samples
,”
J. Phys. D
,
20
(
9
), pp.
1156
1158
.10.1088/0022-3727/20/9/011
12.
SobolIlya
,
M.
,
2001
, “
Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates
,”
Math. Comput. Simul.
,
55
(
1–3
), pp.
271
280
.10.1016/S0378-4754(00)00270-6
13.
Ostrach
,
S.
,
1952
, “
An Analysis of Laminar Free-Convection Flow and Heat Transfer about a Flat Plate Parallel to the Direction of the Generating Body Force
,” National Aeronautics and Space Administration Cleveland Oh Lewis Research Center, Report No. NACA-TN-2635.
14.
Howarth
,
L.
, and
Bairstow
,
L.
,
1938
, “
On the Solution of the Laminar Boundary Layer Equations
,”
Proc. R. Soc. A
,
164
(
919
), pp.
547
579
.10.1098/rspa.1938.0037
15.
Butterworth
,
S.
,
1930
, “
On the Theory of Filter Amplifiers
,”
Wireless Eng.
,
7
(
6
), pp.
536
541
.https://www.changpuak.ch/electronics/downloads/On_the_Theory_of_Filter_Amplifiers.pdf
16.
Hu
,
Y.
,
Brahim
,
S.
,
Maat
,
S.
,
Davies
,
P.
,
Kundu
,
A.
, and
Fisher
,
T.
,
2020
, “
Rapid Analytical Instrumentation for Electrochemical Impedance Spectroscopy Measurements
,”
J. Electrochem. Soc.
,
167
(
2
), p.
027545
.10.1149/1945-7111/ab6ee8
17.
Hahn
,
J.
,
Reid
,
T.
, and
Marconnet
,
A.
,
2019
, “
Infrared Microscopy Enhanced Angstrom's Method for Thermal Diffusivity of Polymer Monofilaments and Films
,”
ASME J. Heat Transfer
,
141
(
8
), p.
081601
.10.1115/1.4043619
18.
Visser
,
E.
,
Versteegen
,
E.
, and
van Enckevort
,
W.
,
1992
, “
Measurement of Thermal Diffusion in Thin Films Using a Modulated Laser Technique: Application to Chemical-Vapor-Deposited Diamond Films
,”
J. Appl. Phys.
,
71
(
7
), pp.
3238
3248
.10.1063/1.350970
19.
Dunson
,
D.
,
2001
, “
Commentary: Practical Advantages of Bayesian Analysis of Epidemiologic Data
,”
Am. J. Epidemiol.
,
153
(
12
), pp.
1222
1226
.10.1093/aje/153.12.1222
20.
Wang
,
J.
, and
Zabaras
,
N.
,
2004
, “
A Bayesian Inference Approach to the Inverse Heat Conduction Problem
,”
Int. J. Heat Mass Transfer
,
47
(
17–18
), pp.
3927
3941
.10.1016/j.ijheatmasstransfer.2004.02.028
21.
Xu
,
X.
,
Zhang
,
Q.
,
Hao
,
M.
,
Hu
,
Y.
,
Lin
,
Z.
,
Peng
,
L.
,
Wang
,
T.
,
Ren
,
X.
,
Wang
,
C.
,
Zhao
,
Z.
,
Wan
,
C.
,
Fei
,
H.
,
Wang
,
L.
,
Zhu
,
J.
,
Sun
,
H.
,
Chen
,
W.
,
Du
,
T.
,
Deng
,
B.
,
Cheng
,
G. J.
,
Shakir
,
I.
,
Dames
,
C.
,
Fisher
,
T. S.
,
Zhang
,
X.
,
Li
,
H.
,
Huang
,
Y.
, and
Duan
,
X.
,
2019
, “
Double-Negative-Index Ceramic Aerogels for Thermal Superinsulation
,”
Science
,
363
(
6428
), pp.
723
727
.10.1126/science.aav7304
22.
Fisher
,
R. A.
,
1915
, “
Frequency Distribution of the Values of the Correlation Coefficient in Samples From an Indefinitely Large Population
,”
Biometrika
,
10
(
4
), pp.
507
521
.10.2307/2331838
23.
Metropolis
,
N.
,
Rosenbluth
,
A. W.
,
Rosenbluth
,
M. N.
,
Teller
,
A. H.
, and
Teller
,
E.
,
1953
, “
Equation of State Calculations by Fast Computing Machines
,”
J. Chem. Phys.
,
21
(
6
), pp.
1087
1092
.10.1063/1.1699114
24.
Robert
,
C.
, and
Casella
,
G.
,
2004
,
Monte Carlo Statistical Methods
,
Springer Science and Business Media
,
New York
.
25.
Misumi USA
,
2020
, “
Air Colliding Force Property Table (AFTC7)
,” ,
Misumi USA, Inc
.,
Schaumburg, IL
, accessed May 20, 2020, https://us.misumi-ec.com/pdf/fa/2019/2019_US_3552_001.pdf
26.
ESPI Metal
,
2018
, “
ESPI Metal Data Sheet for Copper 110
,”
ESPI Metals
,
Ashland, OR
, accessed May 20, 2020, https://espimetals.com/shop/elements/copper
27.
Sidles
,
P. H.
, and
Danielson
,
G. C.
,
1954
, “
Thermal Diffusivity of Metals at High Temperatures
,”
J. Appl. Phys.
,
25
(
1
), pp.
58
66
.10.1063/1.1721521
28.
Min
,
S.
,
Blumm
,
J.
, and
Lindemann
,
A.
,
2007
, “
A New Laser Flash System for Measurement of the Thermophysical Properties
,”
Thermochim. Acta
,
455
(
1–2
), pp.
46
49
.10.1016/j.tca.2006.11.026
29.
Gustafsson
,
S.
,
Karawacki
,
E.
, and
Khan
,
M.
,
1979
, “
Transient Hot-Strip Method for Simultaneously Measuring Thermal Conductivity and Thermal Diffusivity of Solids and Fluids
,”
J. Phys. D Appl. Phys
,
12
(
9
), pp.
1411
1421
.10.1088/0022-3727/12/9/003
30.
Gustavsson
,
M.
,
Karawacki
,
E.
, and
Gustafsson
,
S.
,
1994
, “
Thermal Conductivity, Thermal Diffusivity, and Specific Heat of Thin Samples From Transient Measurements With Hot Disk Sensors
,”
Rev. Sci. Instrum.
,
65
(
12
), pp.
3856
3859
.10.1063/1.1145178
31.
Spiegelhalter
,
D. J.
,
Best
,
N. G.
,
Carlin
,
B. P.
, and
Van der Linde
,
A.
,
1998
, “
Bayesian Deviance, the Effective Number of Parameters, and the Comparison of Arbitrarily Complex Models
,”,
Division of Biostatistics
,
University of Minnesota
,
Minneapolis, MN
, Report No.
98
009
.
32.
Lau
,
W.
, and
Tan
,
C.
,
1973
, “
Errors in One-Dimensional Heat Transfer Analysis in Straight and Annular Fins
,”
ASME J. Heat Transfer
,
95
(
4
), pp.
723
727
.
33.
Liu
,
J.
, and
Yang
,
R.
,
2010
, “
Tuning the Thermal Conductivity of Polymers With Mechanical Strains
,”
Phys. Rev. B
,
81
(
17
), p.
174122
.10.1103/PhysRevB.81.174122
34.
Abuseada
,
M.
,
Ophoff
,
C.
, and
Ozalp
,
N.
,
2019
, “
Characterization of a New 10 kWe High Flux Solar Simulator Via Indirect Radiation Mapping Technique
,”
ASME J. Sol. Energy Eng.
,
141
(
2
), p.
021005
.10.1115/1.4042246
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