In this paper, we show how a heat-generating domain can be cooled with embedded cooling channels and high-conductivity inserts. The volume of cooling channels and high-conductivity inserts is fixed, so is the volume of the heat-generating domain. The maximum temperature in the domain decreases with high-conductivity inserts even though the coolant volume decreases. The locations and the shapes of high-conductivity inserts corresponding to the smallest peak temperatures for different number of inserts are documented, x = 0.6L and D/B = 0.11 with two rectangular inserts. We also document how the length scales of the inserts should be changed as the volume fraction of the coolant volume over the high-conductivity material volume varies. The high-conductivity inserts should be placed nonequidistantly in order to provide the smallest peak temperature in the heat-generating domain. In addition, increasing the number of the inserts after a limit increases the peak temperature, i.e., this limit is eight number of inserts for the given conditions and assumptions. This paper shows that the overall thermal conductance of a heat-generating domain can be increased by embedding high-conductivity material in the solid domain (inverted fins) when the domain is cooled with forced convection, and the summation of high-conductivity material volume and coolant volume is fixed.

References

1.
Pop
,
E.
,
Sinha
,
S.
, and
Goodson
,
K. E.
,
2006
, “
Heat Generation and Transport in Nanometer-Scale Transistors
,”
Proc. IEEE
,
94
(
3
), pp.
1587
1601
.
2.
Cetkin
,
E.
,
2015
, “
Inverted Fins for Cooling of a Non-Uniformly Heated Domain
,”
J. Therm. Eng.
,
1
(
1
), pp.
1
9
.
3.
Bejan
,
A.
, and
Ledezma
,
G. A.
,
1996
, “
Thermodynamic Optimization of Cooling Techniques for Electronic Packages
,”
Int. J. Heat Mass Transfer
,
39
(
6
), pp.
1213
1221
.
4.
Said
,
S. A. M.
,
1996
, “
Investigation of Natural Convection in Convergent Vertical Channels
,”
Int. J. Energy Res.
,
20
(
7
), pp.
559
567
.
5.
Jang
,
D.
,
Yook
,
S.-J.
, and
Lee
,
K.-S.
,
2014
, “
Optimum Design of a Radial Heat Sink With a Fin-Height Profile for High-Power Led Lighting Applications
,”
Appl. Energy
,
116
, pp.
260
268
.
6.
Ho
,
T.
,
Mao
,
S. S.
, and
Greif
,
R.
,
2010
, “
Improving Efficiency of High-Concentrator Photovoltaics by Cooling With Two-Phase Forced Convection
,”
Int. J. Energy Res.
,
34
(
14
), pp.
1257
1271
.
7.
Kakac
,
S.
, and
Pramuanjaroenkij
,
A.
,
2009
, “
Review of Convective Heat Transfer Enhancement With Nanofluids
,”
Int. J. Heat Mass Transfer
,
52
(
13–14
), pp.
3187
3196
.
8.
Eastman
,
J. A.
,
Choi
,
S. U. S.
,
Li
,
S.
,
Yu
,
W.
, and
Thompson
,
L. J.
,
2001
, “
Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles
,”
Appl. Phys. Lett.
,
78
(6), pp.
718
720
.
9.
Lorenzini
,
G.
,
Correa
,
R. L.
,
dos Santos
,
E. D.
, and
Rocha
,
L. A. O.
,
2011
, “
Constructal Design of Complex Assembly of Fins
,”
ASME J. Heat Transfer
,
133
(
8
), p.
081902
.
10.
Bejan
,
A.
, and
Morega
,
A. M.
,
1993
, “
Optimal Arrays of Pin Fins and Plate Fins in Laminar Forced-Convection
,”
ASME J. Heat Transfer
,
115
(
1
), pp.
75
81
.
11.
Lorenzini
,
G.
, and
Moretti
,
S.
,
2011
, “
Bejan's Constructal Theory Analysis of Gas–Liquid Cooled Finned Modules
,”
ASME J. Heat Transfer
,
133
(
7
), p.
071801
.
12.
Bejan
,
A.
,
Fowler
,
A. J.
, and
Stanescu
,
G.
,
1995
, “
The Optimal Spacing Between Horizontal Cylinders in a Fixed Volume Cooled by Natural Convection
,”
Int. J. Heat Mass Transfer
,
38
(
11
), pp.
2047
2055
.
13.
da Silva
,
A. K.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2004
, “
Optimal Distribution of Discrete Heat Sources on a Wall With Natural Convection
,”
Int. J. Heat Mass Transfer
,
47
(
2
), pp.
203
214
.
14.
da Silva
,
A. K.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2004
, “
Optimal Distribution of Discrete Heat Sources on a Plate With Laminar Forced Convection
,”
Int. J. Heat Mass Transfer
,
47
(
10–11
), pp.
2139
2148
.
15.
Bejan
,
A.
, and
Fautrelle
,
Y.
,
2003
, “
Constructal Multi-Scale Structure for Maximal Heat Transfer Density
,”
Acta Mech.
,
163
(
1–2
), pp.
39
49
.
16.
Bejan
,
A.
,
2000
,
Shape and Structure, From Engineering to Nature
,
Cambridge University
,
Cambridge, UK
.
17.
Bejan
,
A.
, and
Lorente
,
S.
,
2008
,
Design With Constructal Theory
,
Wiley
,
Hoboken, NJ
.
18.
Barrau
,
J.
,
Omri
,
M.
,
Chemisana
,
D.
,
Rosell
,
J.
,
Ibañez
,
M.
, and
Tadrist
,
L.
,
2012
, “
Numerical Study of a Hybrid Jet Impingement/Micro-Channel Cooling Scheme
,”
Appl. Therm. Eng.
,
33–34
, pp.
237
245
.
19.
Sharma
,
C. S.
,
Tiwari
,
M. K.
,
Zimmermann
,
S.
,
Brunschwiler
,
T.
,
Schlottig
,
G.
,
Michel
,
B.
, and
Poulikakos
,
D.
,
2015
, “
Energy Efficient Hotspot-Targeted Embedded Liquid Cooling of Electronics
,”
Appl. Energy
,
138
, pp.
414
422
.
20.
Spread Your Wings, It's Time to Fly
,” Last accessed July 26,
2006
, www.nasa.gov
21.
Bejan
,
A.
,
1998
, “
Constructal Theory: From Thermodynamics and Geometric Optimization to Predicting the Shape in Nature
,”
Energy Convers. Manage.
,
39
(16–18), pp.
1705
1718
.
22.
Bejan
,
A.
, and
Lorente
,
S.
,
2010
, “
The Constructal Law and the Design of the Biosphere: Nature and Globalization
,”
ASME J. Heat Transfer
,
133
(
1
), p.
011001
.
23.
Reis
,
A. H.
,
2006
, “
Constructal View of Scaling Laws of River Basins
,”
Geomorphology
,
78
(3–4), pp.
201
206
.
24.
Miguel
,
A. F.
,
2006
, “
Constructal Pattern Formation in Stony Corals, Bacterial Colonies and Plant Roots Under Different Hydrodynamics Conditions
,”
J. Theor. Biol.
,
242
(
4
), pp.
954
961
.
25.
Wechsatol
,
W.
,
Ordonez
,
J. C.
, and
Kosaraju
,
S.
,
2006
, “
Constructal Dendritic Geometry and the Existence of Asymmetric Bifurcation
,”
J. Appl. Phys.
,
100
(
11
), p.
113514
.
26.
Wang
,
X.-Q.
,
Mujumdar
,
A. S.
, and
Yap
,
C.
,
2005
, “
Numerical Analysis of Blockage and Optimization of Heat Transfer Performance of Fractal-Like Microchannel Nets
,”
ASME J. Electron. Packag.
,
128
(
1
), pp.
38
45
.
27.
Azoumah
,
Y.
,
Neveu
,
P.
, and
Mazet
,
N.
,
2007
, “
Optimal Design of Thermochemical Reactors Based on Constructal Approach
,”
AIChe J.
,
53
(
5
), pp.
1257
1266
.
28.
Biserni
,
C.
,
Rocha
,
L. A. O.
,
Stanescu
,
G.
, and
Lorenzini
,
E.
,
2007
, “
Constructal H-Shaped Cavities According to Bejan's Theory
,”
Int. J. Heat Mass Transfer
,
50
(
11–12
), pp.
2132
2138
.
29.
Lorenzini
,
G.
,
Biserni
,
C.
,
Garcia
,
F. L.
, and
Rocha
,
L. A. O.
,
2012
, “
Geometric Optimization of a Convective T-Shaped Cavity on the Basis of Constructal Theory
,”
Int. J. Heat Mass Transfer
,
55
(
23–24
), pp.
6951
6958
.
30.
Lorenzini
,
G.
,
Rocha
,
L. A. O.
,
Biserni
,
C.
,
dos Santos
,
E. D.
, and
Isoldi
,
L. A.
,
2012
, “
Constructal Design of Cavities Inserted Into a Cylindrical Solid Body
,”
ASME J. Heat Transfer
,
134
(
7
), p.
071301
.
31.
Bejan
,
A.
, and
Zane
,
J. P.
,
2012
,
Design in Nature
,
Doubleday
,
New York
.
32.
Almogbel
,
M.
, and
Bejan
,
A.
,
1999
, “
Conduction Trees With Spacings at the Tips
,”
Int. J. Heat Mass Transfer
,
42
(
20
), pp.
3739
3756
.
33.
Cetkin
,
E.
,
2014
, “
Three-Dimensional High Conductivity Trees for Volumetric Cooling
,”
Int. J. Energy Res.
,
38
(
12
), pp.
1571
1577
.
34.
Bejan
,
A.
,
2003
, “
Constructal Tree-Shaped Paths for Conduction and Convection
,”
Int. J. Energy Res.
,
27
(
4
), pp.
283
299
.
35.
Bejan
,
A.
,
1997
, “
Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume
,”
Int. J. Heat Mass Transfer
,
40
(
4
), pp.
799
816
.
36.
Rocha
,
L. A. O.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2006
, “
Conduction Tree Networks With Loops for Cooling a Heat Generating Volume
,”
Int. J. Heat Mass Transfer
,
49
(
15–16
), pp.
2626
2635
.
37.
Ledezma
,
G. A.
,
Bejan
,
A.
, and
Errera
,
M. R.
,
1997
, “
Constructal Tree Networks for Heat Transfer
,”
J. Appl. Phys.
,
82
(1), pp.
89
100
.
38.
Ledezma
,
G. A.
, and
Bejan
,
A.
,
1998
, “
Constructal Three-Dimensional Trees for Conduction Between a Volume and One Point
,”
ASME J. Heat Transfer
,
120
(
4
), pp.
977
984
.
39.
Bhattacharjee
,
S.
, and
Grosshandler
,
W. L.
,
1988
, “
The Formation of Wall Jet Near a High Temperature Wall Under Microgravity Environment
,”
ASME National Heat Transfer Conference
, Houston, TX, July 24–27, American Society of Mechanical Engineers, New York, Vol.
96
, pp.
711
716
.
40.
Petrescu
,
S.
,
1994
, “
Comments on ‘the Optimal Spacing of Parallel Plates Cooled by Forced Convection’
,”
Int. J. Heat Mass Transfer
,
37
(
8
), p.
1283
.
41.
Comsol Multiphysics
,” www.comsol.com
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