Abstract

An enabling advantage of carbon-based conductors is their low density and high thermal conductivity. To put this in the perspective of applications, current rating of carbon-based and copper nanocomposite conductors of different lengths are modeled. For comparison, the current and current density required to raise the maximum temperature of studied conductors to 150°C are calculated with a joule heating model. The model is validated with an experimental setup equipped with a thermal camera. It is shown that while doped carbon nanotube (CNT) conductors may potentially result in improved performance compared with copper on a weight basis, ultra-conductive copper (UCC) can outperform copper on both volume and weight bases. Additionally, a hypothetical copper-matrix composite conductor with different volume fractions of high thermal conductivity and lightweight graphene fibers (Cu–C composite) is included in the analysis. The properties of the Cu–C composite are evaluated based on the Lewis–Nielson and rule of mixture models, as inputs for the joule heating model. The results show that while the improved thermal conductivity of the composite is beneficial for improving the current rating in micro-electronics applications, the tradeoff for the decreased electrical conductivity results in lower current carrying capacity in applications that use longer conductors.

References

1.
Nieto, A., Agarwal, A., Lahiri, D., Bisht, A., and Bakshi, S. R., 2021
,
Carbon Nanotubes: Reinforced Metal Matrix Composites
,
CRC Press
, Baco Raton, FL.
2.
Kinloch
,
I. A.
,
Suhr
,
J.
,
Lou
,
J.
,
Young
,
R. J.
, and
Ajayan
,
P. M.
,
2018
, “
Composites With Carbon Nanotubes and Graphene: An Outlook
,”
Science
,
362
(
6414
), pp.
547
553
.10.1126/science.aat7439
3.
Sidhu
,
S. S.
,
Kumar
,
S.
, and
Batish
,
A.
,
2016
, “
Metal Matrix Composites for Thermal Management: A Review
,”
Crit. Rev. Solid State Mater. Sci.
,
41
(
2
), pp.
132
157
.10.1080/10408436.2015.1076717
4.
Saboori
,
A.
,
Dadkhah
,
M.
,
Fino
,
P.
, and
Pavese
,
M.
,
2018
, “
An Overview of Metal Matrix Nanocomposites Reinforced With Graphene Nanoplatelets; Mechanical, Electrical and Thermophysical Properties
,”
Metals
,
8
(
6
), p.
423
.10.3390/met8060423
5.
Shirvanimoghaddam
,
K.
,
Hamim
,
S. U.
,
Karbalaei Akbari
,
M.
,
Fakhrhoseini
,
S. M.
,
Khayyam
,
H.
,
Pakseresht
,
A. H.
,
Ghasali
,
E.
, et al.,
2017
, “
Carbon Fiber Reinforced Metal Matrix Composites: Fabrication Processes and Properties
,”
Compos. Part A Appl. Sci. Manuf.
,
92
, pp.
70
96
.10.1016/j.compositesa.2016.10.032
6.
Cao
,
M.
,
Xiong
,
D.-B.
,
Yang
,
L.
,
Li
,
S.
,
Xie
,
Y.
,
Guo
,
Q.
,
Li
,
Z.
, et al.,
2019
, “
Ultrahigh Electrical Conductivity of Graphene Embedded in Metals
,”
Adv. Funct. Mater.
,
29
(
17
), p.
1806792
.10.1002/adfm.201806792
7.
Schwartz
,
A.
, and
James
,
W. H. N.
,
1905
, “
Low Tension Thermal Cut-Outs
,”
J. Inst. Electr. Eng.
,
35
(
174
), pp.
364
417
.10.1049/jiee-1.1905.0059
8.
Onderdonk
,
I. M.
,
1944
, “Short-Time Current Required to Melt Copper Conductors,”
Electr. World
, 121(26), p.
98
.
9.
Mertol
,
A.
,
1995
, “
Estimation of Aluminum and Gold Bond Wire Fusing Current and Fusing Time
,”
IEEE Trans. Compon. Packag. Manuf. Technol. Part B
,
18
(
1
), pp.
210
214
.10.1109/96.365510
10.
Chen
,
K. C.-Y.
,
Warne
,
L. K.
,
Lin
,
Y. T.
,
Kinzel
,
R. L.
,
Huff
,
J. D.
,
McLean
,
M. B.
,
Jenkins
,
M. W.
, and
Rutherford
,
B. M.
,
2013
, “
Conductor Fusing and Gapping for Bond Wires
,”
Prog. Electromagn. Res. M
,
31
, pp.
199
214
.10.2528/PIERM13051311
11.
Neher
,
J. H.
, and
McGrath
,
M. H.
,
1994
, “
The Calculation or the Temperature Rise and Load Capability of Cable Systems
,”
Trans. Am. Inst. Electr. Eng. Part III: Power Appar. Syst.
, 76(3), pp. 752–764.10.1109/AIEEPAS.1957.4499653
12.
Sedaghat
,
A.
, and
De Leon
,
F.
,
2014
, “
Thermal Analysis of Power Cables in Free Air: Evaluation and Improvement of the IEC Standard Ampacity Calculations
,”
IEEE Trans. Power Deliv.
,
29
(
5
), pp.
2306
2314
.10.1109/TPWRD.2013.2296912
13.
Pollak
,
P.
,
1985
, “
Neher-McGrath Calculations for Insulated Power Cables
,”
IEEE Trans. Ind. Appl.
,
IA-21
(
5
), pp.
1319
1323
.10.1109/TIA.1985.349561
14.
Khanbolouki
,
P.
, and
Tehrani
,
M.
,
2021
, “
Numerical Simulation of Ampacity in Advanced Electrical Conductors
,”
ASME
Paper No. IMECE2020-23698.10.1115/IMECE2020-23698
15.
Abu-Eishah
,
S. I.
,
2001
, “
Correlations for the Thermal Conductivity of Metals as a Function of Temperature
,”
Int. J. Thermophys.
,
22
(
6
), pp.
1855
1868
.10.1023/A:1013155404019
16.
Pietrak
,
K.
, and
Wiśniewski
,
T. S.
,
2014
, “
A Review of Models for Effective Thermal Conductivity of Composite Materials
,”
J. Power Technol.
,
95
(
1
), pp.
14
24
.https://papers.itc.pw.edu.pl/index.php/JPT/article/view/463
17.
Xin
,
G.
,
Zhu
,
W.
,
Deng
,
Y.
,
Cheng
,
J.
,
Zhang
,
L. T.
,
Chung
,
A. J.
,
De
,
S.
, and
Lian
,
J.
,
2019
, “
Microfluidics-Enabled Orientation and Microstructure Control of Macroscopic Graphene Fibres
,”
Nat. Nanotechnol.
,
14
(
2
), pp.
168
175
.10.1038/s41565-018-0330-9
18.
Fang
,
B.
,
Chang
,
D.
,
Xu
,
Z.
, and
Gao
,
C.
,
2020
, “
A Review on Graphene Fibers: Expectations, Advances, and Prospects
,”
Adv. Mater.
,
32
(
5
), p.
1902664
.10.1002/adma.201902664
19.
Pal
,
R.
,
2008
, “
On the Lewis–Nielsen Model for Thermal/Electrical Conductivity of Composites
,”
Compos. Part A Appl. Sci. Manuf.
,
39
(
5
), pp.
718
726
.10.1016/j.compositesa.2008.02.008
20.
Moreira
,
D. C.
,
Junior
,
N. B.
,
Benevides
,
R. O.
,
Sphaier
,
L. A.
, and
Nunes
,
L. C. S.
,
2015
, “
Temperature-Dependent Thermal Conductivity of Silicone-Al2O3 Nanocomposites
,”
Appl. Phys. A
,
121
(
3
), pp.
1227
1234
.10.1007/s00339-015-9494-4
21.
Bejan
,
A.
, and
Kraus
,
A. D.
,
2003
,
Heat Transfer Handbook
,
John Wiley & Sons, Hoboken, NJ
.
22.
Guan
,
N.
,
Liu
,
Z.
,
Zhang
,
C.
, and
Jiang
,
G.
,
2014
, “
Natural Convection Heat Transfer on Surfaces of Copper Micro-Wires
,”
Heat Mass Transfer
,
50
(
2
), pp.
275
284
.10.1007/s00231-013-1240-x
23.
Kakac
,
S.
,
Shah
,
R. K.
, and
Aung
,
W.
,
1987
, “
Handbook of Single-Phase Convective Heat Transfer
,” Wiley-Interscience, New York.
24.
Behabtu
,
N.
,
Young
,
C. C.
,
Tsentalovich
,
D. E.
,
Kleinerman
,
O.
,
Wang
,
X.
,
Ma
,
A. W. K.
,
Bengio
,
E. A.
, et al.,
2013
, “
Strong, Light, Multifunctional Fibers of Carbon Nanotubes With Ultrahigh Conductivity
,”
Science
,
339
(
6116
), pp.
182
186
.10.1126/science.1228061
25.
Tsentalovich
,
D. E.
,
Headrick
,
R. J.
,
Mirri
,
F.
,
Hao
,
J.
,
Behabtu
,
N.
,
Young
,
C. C.
, and
Pasquali
,
M.
,
2017
, “
Influence of Carbon Nanotube Characteristics on Macroscopic Fiber Properties
,”
ACS Appl. Mater. Interfaces
,
9
(
41
), pp.
36189
36198
.10.1021/acsami.7b10968
26.
Headrick
,
R. J.
,
Tsentalovich
,
D. E.
,
Berdegué
,
J.
,
Bengio
,
E. A.
,
Liberman
,
L.
,
Kleinerman
,
O.
,
Lucas
,
M. S.
,
Talmon
,
Y.
, and
Pasquali
,
M.
,
2018
, “
Structure–Property Relations in Carbon Nanotube Fibers by Downscaling Solution Processing
,”
Adv. Mater.
,
30
(
9
), p.
1704482
.10.1002/adma.201704482
27.
Zeller
,
C.
,
Pendrys
,
L. A.
, and
Vogel
,
F. L.
,
1979
, “
Electrical Transport Properties of Low-Stage AsF5-Intercalated Graphite
,”
J. Mater. Sci.
,
14
(
9
), pp.
2241
2248
.10.1007/BF00688431
28.
Xin
,
G.
,
Yao
,
T.
,
Sun
,
H.
,
Scott
,
S. M.
,
Shao
,
D.
,
Wang
,
G.
, and
Lian
,
J.
,
2015
, “
Highly Thermally Conductive and Mechanically Strong Graphene Fibers
,”
Science
,
349
(
6252
), pp.
1083
1087
.10.1126/science.aaa6502
29.
Issi
,
J.-P.
,
Nysten
,
B.
, and
Piraux
,
L.
,
1987
, “
Electrons and Phonons as Tools to Characterise Carbon Fibres
,”
J. Phys. D Appl. Phys.
,
20
(
3
), pp.
257
260
.10.1088/0022-3727/20/3/003
30.
Tehrani
,
M.
,
2021
, “
Advanced Electrical Conductors: An Overview and Prospects of Metal Nanocomposite and Nanocarbon Based Conductors
,”
Phys. Status Solidi (a)
,
218
(
8
), p.
2000704
.10.1002/pssa.202000704
31.
Oshima
,
H.
,
Woollam
,
J. A.
,
Yavrouian
,
A.
, and
Dowell
,
M. B.
,
1983
, “
Electrical and Mechanical Properties of Copper Chloride-Intercalated Pitch-Based Carbon Fibers
,”
Syn. Met.
,
5
(
2
), pp.
113
123
.10.1016/0379-6779(83)90125-X
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