Integrating the cooling systems of power electronics and electric machines (PEEMs) with other existing vehicle thermal management systems is an innovative technology for the next-generation hybrid electric vehicles (HEVs). As such, the reliability of PEEM must be assured under different dynamic duty cycles. Accumulation of excessive heat within the multilayered packages of PEEMs, due to the thermal contact resistance between the layers and variable temperature of the coolant, is the main challenge that needs to be addressed over a transient thermal duty cycle. Accordingly, a new analytical model is developed to predict transient heat diffusion inside multilayered composite packages. It is assumed that the composite exchanges heat via convection and radiation mechanisms with the surrounding fluid whose temperature varies arbitrarily over time (thermal duty cycle). As such, a time-dependent conjugate convection and radiation heat transfer is considered for the outer-surface. Moreover, arbitrary heat generation inside the layers and thermal contact resistances between the layers are taken into account. New closed-form relationships are developed to calculate the temperature distribution inside multilayered media. The present model is used to find an optimum value for the angular frequency of the surrounding fluid temperature to maximize the interfacial heat flux of composite media; up to 10% higher interfacial heat dissipation rate compared to constant fluid-temperature case. An independent numerical simulation is also performed using Comsol Multiphysics; the maximum relative difference between the obtained numerical data and the analytical model is less than 6%.

References

1.
O'Keefe
,
M.
, and
Bennion
,
K.
,
2007
, “
A Comparison of Hybrid Electric Vehicle Power Electronics Cooling Options
,”
IEEE Vehicle Power and Propulsion Conference
, Arlington, TX, Sept. 9–12, pp.
116
123
.
2.
Bennion
,
K.
, and
Thornton
,
M.
,
2010
, “
Integrated Vehicle Thermal Management for Advanced Vehicle Propulsion Technologies
,” SAE Paper No. 2010-01-0836.
3.
Bennion
,
K.
, and
Kelly
,
K.
,
2009
, “
Rapid Modeling of Power Electronics Thermal Management Technologies
,”
Vehicle Power and Propulsion Conference
, Dearborn, MI, Sept. 7–10, pp.
622
629
.
4.
Bennion
,
K.
, and
Thornton
,
M.
,
2010
, “
Integrated Vehicle Thermal Management for Advanced Vehicle Propulsion Technologies
,” SAE Paper No. NREL/CP-540-47416.
5.
Panão
,
M. R. O.
,
Correia
,
A. M.
, and
Moreira
,
A. L. N.
,
2012
, “
High-Power Electronics Thermal Management With Intermittent Multijet Sprays
,”
Appl. Therm. Eng.
,
37
, pp.
293
301
.10.1016/j.applthermaleng.2011.11.031
6.
Ghalambor
,
S.
,
Agonafer
,
D.
, and
Haji-Sheikh
,
A.
,
2013
, “
Analytical Thermal Solution to a Nonuniformly Powered Stack Package With Contact Resistance
,”
ASME J. Heat Transfer
,
135
(
11
), p.
111015
.10.1115/1.4024623
7.
McGlen
,
R. J.
,
Jachuck
,
R.
, and
Lin
,
S.
,
2004
, “
Integrated Thermal Management Techniques for High Power Electronic Devices
,”
Appl. Therm. Eng.
,
24
(
8–9
), pp.
1143
1156
.10.1016/j.applthermaleng.2003.12.029
8.
Brooks
,
D.
, and
Martonosi
,
M.
,
2001
, “
Dynamic Thermal Management for High-Performance Microprocessors
,”
7th International Symposium on High-Performance Computer Architucture (HPCA-7)
, Monterey, CA, Jan. 19–24, pp.
171
182
.
9.
Yuan
,
T.-D.
,
Hong
,
B. Z.
,
Chen
,
H. H.
, and
Wang
,
L.-K.
,
2001
, “
Thermal Management for High Performance Integrated Circuits With Non-Uniform Chip Power Considerations
,”
17th Annual IEEE Semiconductor Thermal Measurement and Management Symposium (Cat. No.01CH37189)
, San Jose, CA, pp.
95
101
.
10.
Choobineh
,
L.
, and
Jain
,
A.
,
2013
, “
Determination of Temperature Distribution in Three-Dimensional Integrated Circuits (3D ICs) With Unequally-Sized Die
,”
Appl. Therm. Eng.
,
56
(
1–2
), pp.
176
184
.10.1016/j.applthermaleng.2013.03.006
11.
Gurrum
,
S.
, and
Suman
,
S.
,
2004
, “
Thermal Issues in Next-Generation Integrated Circuits
,”
IEEE Trans. Device Mater. Reliab.
,
4
(
4
), pp.
709
714
.10.1109/TDMR.2004.840160
12.
Kelly
,
K.
,
Abraham
,
T.
, and
Bennion
,
K.
,
2007
, “
Assessment of Thermal Control Technologies for Cooling Electric Vehicle Power Electronics
,”
23rd International Electric Vehicle Symposium (EVS-23)
, Anaheim, CA, Dec. 2–5, Paper No. NREL/CP-540-42267.
13.
De Monte
,
F.
,
2000
, “
Transient Heat Conduction in One-Dimensional Composite Slab, A “Natural” Analytic Approach
,”
Int. J. Heat Mass Transfer
,
43
(
19
), pp.
3607
3619
.10.1016/S0017-9310(00)00008-9
14.
Carslaw
,
H. S.
, and
Jaeger
,
J. C.
,
1959
,
Conduction of Heat in Solids
,
Oxford University
,
London
.
15.
Feng
,
Z. G.
, and
Michaelides
,
E. E.
,
1997
, “
The Use of Modified Green's Functions in Unsteady Heat Transfer
,”
Int. J. Heat Mass Transfer
,
40
(
12
), pp.
2997
3002
.10.1016/S0017-9310(96)00319-5
16.
Yener
,
Y.
, and
Ozisik
,
M. N.
,
1974
, “
On the Solution of Unsteady Heat Conduction in Multi-Region Finite Media With Time-Dependent Heat Transfer Coefficient
,”
5th International Heat Transfer Conference
, Tokyo.10.1016/S0017-9310(96)00319-5
17.
Mayer
,
E.
,
1952
, “
Heat Flow in Composite Slabs
,”
ARS J.
,
22
(
3
), pp.
150
158
.10.2514/8.4451
18.
Tittle
,
C. W.
,
1965
, “
Boundary Value Problems in Composite Media: Quasi-Orthogonal Functions
,”
Appl. Phys.
,
36
(4)
, pp.
1487
1488
.10.1063/1.1714335
19.
Yeh
,
H. C.
,
1976
, “
Solving Boundary Value Problems in Composite Media by Seperation of Variables and Transient Temperature of a Reactor Vessel
,”
Nucl. Eng. Des.
,
36
(2)
, pp.
139
157
.10.1016/0029-5493(76)90001-7
20.
Olek
,
S.
,
Elias
,
E.
,
Wacholder
,
E.
, and
Kaizerman
,
S.
,
1991
, “
Unsteady Conjugated Heat Transfer in Laminar Pipe Flow
,”
Int. J. Heat Mass Transfer
,
34
(
6
), pp.
1443
1450
.10.1016/0017-9310(91)90287-O
21.
Olek
,
S.
,
1998
, “
Heat Transfer in Duct Flow of Non-Newtonian Fluid With Axial Conduction
,”
Int. Commun. Heat Mass Transfer
,
25
(
7
), pp.
929
938
.10.1016/S0735-1933(98)00084-0
22.
Olek
,
S.
,
1999
, “
Multiregion Conjugate Heat Transfer
,”
Hybrid Methods Eng.
,
1
, pp.
119
137
.10.1615/HybMethEng.v1.i2.30
23.
Fakoor-Pakdaman
,
M.
,
Ahmadi
,
M.
,
Bagheri
,
F.
, and
Bahrami
,
M.
,
2014
Dynamic Heat Transfer Inside Multilayered Packages with Arbitrary Heat Generations
,”
Journal of Thermo. and Heat Trans.
,
28
(
4
), pp.
687
699
.10.2514/1.T4328
24.
Antonopoulos
,
K. A.
, and
Tzivanidis
,
C.
,
1996
, “
Analytical Solution of Boundary Value Problems of Heat Conduction in Composite Regions With Arbitrary Convection Boundary Conditions
,”
Acta Mech.
,
118
(
1–4
), pp.
65
78
.10.1007/BF01410508
25.
De Monte
,
F.
,
2004
, “
Transverse Eigenproblem of Steady-State Heat Conduction for Multi-Dimensional Two-Layered Slabs With Automatic Computation of Eigenvalues
,”
Int. J. Heat Mass Transfer
,
47
(
2
), pp.
191
201
.10.1016/j.ijheatmasstransfer.2003.07.002
26.
Jain
,
P. K.
, and
Singh
,
S.
,
2010
, “
An Exact Analytical Solution for Two-Dimensional, Unsteady, Multilayer Heat Conduction in Spherical Coordinates
,”
Int. J. Heat Mass Transfer
,
53
(
9–10
), pp.
2133
2142
.10.1016/j.ijheatmasstransfer.2009.12.035
27.
Jain
,
P. K.
, and
Singh
,
S.
,
2009
, “
Analytical Solution to Transient Asymmetric Heat Conduction in a Multilayer Annulus
,”
ASME J. Heat Transfer
,
131
(
1
), p.
011304
.10.1115/1.2977553
28.
Miller
,
J. R.
, and
Weaver
,
P. M.
,
2003
, “
Temperature Profiles in Composite Plates Subject to Time-Dependent Complex Boundary Conditions
,”
Compos. Struct.
,
59
(
2
), pp.
267
278
.10.1016/S0263-8223(02)00054-5
29.
Lu
,
X.
,
Tervola
,
P.
, and
Viljanen
,
M.
,
2006
, “
Transient Analytical Solution to Heat Conduction in Composite Circular Cylinder
,”
Int. J. Heat Mass Transfer
,
49
(
1–2
), pp.
341
348
.10.1016/j.ijheatmasstransfer.2005.06.019
30.
Kreyszig
,
E.
,
Kreyzig
,
H.
, and
Norminton
,
E. J.
,
2012
,
Advanced Engineering Mathematics
,
Wiley
,
New York
.
31.
Chapman
,
A. J.
,
1960
,
Heat Transfer
,
Macmillan
,
New York
.
32.
Jakob
,
M.
,
1949
,
Heat Transfer
,
Wiley
,
New York
.
33.
Zerkle
,
R. D.
, and
Sunderland
,
J. E.
,
1965
, “
The Transint Temperature Distribution in a Slab Subject to Thermal Radiation
,”
ASME J.Heat Transfer
,
87
(
1
), pp.
117
132
.10.1115/1.3689025
34.
Narumanchi
,
S.
,
Mihalic
,
M.
, and
Kelly
,
K.
,
2008
, “
Thermal Interface Materials for Power Electronics Applications
,” Itherm’08, Orlando, FL, May 28–31, Paper No. NREL/CP–540–42972.
35.
Iyengar
,
M.
, and
Schmidt
,
R.
,
2006
, “
Analytical Modeling for Prediction of Hot Spot Chip Junction Temperature for Electronics Cooling Applications
,” ITHERM’06, San Diego, CA, May 30–Jun. 2, pp.
87
95
.
36.
Mudawar
,
I.
,
Bharathan
,
D.
,
Kelly
,
K.
, and
Narumanchi
,
S.
,
2009
, “
Two-Phase Spray Cooling of Hybrid Vehicle Electronics
,”
IEEE Trans. Compon. Packag. Technol.
,
32
(
2
), pp.
501
512
.10.1109/TCAPT.2008.2006907
37.
Incropera
,
F. P.
,
Dewitt
,
D. P.
,
Bergman
,
T. L.
, and
Lavine
,
A. S.
,
2007
,
Introduction to Heat Transfer
,
Wiley
,
New York
.
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