Abstract

The topological optimization of a conducting solid simultaneously cooled by (i) conduction to a stationary, radiatively nonparticipating fluid and (ii) surface-to-surface radiation exchange is performed to minimize the overall thermal resistance of the solid configuration. A novel dual solid method (DSM) that utilizes concurrent discrete and continuous descriptions of the solid-phase distribution is introduced. Corresponding discrete and continuous solid models are used to (i) quantify the conduction and radiation heat transfer and (ii) power a density-based topology optimization, respectively. The discrete and continuous models of the DSM are linked by sharing information pertaining to the radiation exchange process. The DSM is the first design method to incorporate the effects of surface-to-surface radiation exchange into the topological optimization of a conducting solid. The influence of the relative strengths of conduction and radiation is illustrated by performing parametric simulations involving various domain boundary temperatures and solid-phase thermal conductivities. In general, use of the DSM to account for radiation heat transfer leads to solid shapes with lower overall thermal resistances and reduced complexity, relative to shapes predicted when radiation is neglected. For the problem considered here, the DSM produces solid shapes that have overall thermal resistances up to 25% smaller relative to overall thermal resistances of shapes determined by topology optimization considering conduction processes only.

References

1.
Bar-Cohen
,
A.
,
Iyengar
,
M.
, and
Kraus
,
A. D.
,
2003
, “
Design of Optimum Plate-Fin Natural Convective Heat Sinks
,”
ASME J. Electron Packag.
,
125
(
2
), pp.
208
216
.10.1115/1.1568361
2.
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
.10.1016/0017-9310(96)00175-5
3.
Almogbel
,
M.
, and
Bejan
,
A.
,
2001
, “
Constructal Optimization of Nonuniformly Distributed Tree-Shaped Flow Structures for Conduction
,”
Int. J. Heat Mass Transfer
,
44
(
22
), pp.
4185
4194
.10.1016/S0017-9310(01)00080-1
4.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
2003
,
Topology Optimization: Theory, Methods, and Applications
,
Springer
,
Berlin
.
5.
Sigmund
,
O.
, and
Maute
,
K.
,
2013
, “
Topology Optimization Approaches
,”
Struct. Multidiscip. Optim.
,
48
(
6
), pp.
1031
1055
.10.1007/s00158-013-0978-6
6.
Li
,
Q.
,
Steven
,
G. P.
,
Xie
,
Y. M.
, and
Querin
,
O. M.
,
2004
, “
Evolutionary Topology Optimization for Temperature Reduction of Heat Conducting Fields
,”
Int. J. Heat Mass Transfer
,
47
(
23
), pp.
5071
5083
.10.1016/j.ijheatmasstransfer.2004.06.010
7.
Gersborg-Hansen
,
A.
,
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
2006
, “
Topology Optimization of Heat Conduction Problems Using the Finite Volume Method
,”
Struct. Multidiscip. Optim.
,
31
(
4
), pp.
251
259
.10.1007/s00158-005-0584-3
8.
Zhang
,
Y.
, and
Liu
,
S.
,
2008
, “
Design of Conducting Paths Based on Topology Optimization
,”
Heat Mass Transfer
,
44
(
10
), pp.
1217
1227
.10.1007/s00231-007-0365-1
9.
Gao
,
T.
,
Zhang
,
W. H.
,
Zhu
,
J. H.
,
Xu
,
Y. J.
, and
Bassir
,
D. H.
,
2008
, “
Topology Optimization of Heat Conduction Problem Involving Design-Dependent Heat Load Effect
,”
Finite Elem. Anal. Des.
,
44
(
14
), pp.
805
813
.10.1016/j.finel.2008.06.001
10.
Marck
,
G.
,
Nemer
,
M.
,
Harion
,
J. L.
,
Russeil
,
S.
, and
Bougeard
,
D.
,
2012
, “
Topology Optimization Using the SIMP Method for Multiobjective Problems
,”
Numer. Heat Transfer B
,
61
(
6
), pp.
439
470
.10.1080/10407790.2012.687979
11.
Bruns
,
T. E.
,
2007
, “
Topology Optimization of Convection-Dominated, Steady-State Heat Transfer Problems
,”
Int. J. Heat Mass Transfer
,
50
(
15–16
), pp.
2859
2873
.10.1016/j.ijheatmasstransfer.2007.01.039
12.
Iga
,
A.
,
Nishiwaki
,
S.
,
Izui
,
K.
, and
Yoshimura
,
M.
,
2009
, “
Topology Optimization for Thermal Conductors Considering Design-Dependent Effects, Including Heat Conduction and Convection
,”
Int. J. Heat Mass Transfer
,
52
(
11–12
), pp.
2721
2732
.10.1016/j.ijheatmasstransfer.2008.12.013
13.
Yoon
,
G. H.
,
2010
, “
Topological Design of Heat Dissipating Structure With Forced Convective Heat Transfer
,”
J. Mech. Sci. Technol.
,
24
(
6
), pp.
1225
1233
.10.1007/s12206-010-0328-1
14.
Marck
,
G.
,
Nemer
,
M.
, and
Harion
,
J. L.
,
2013
, “
Topology Optimization of Heat and Mass Transfer Problems: Laminar Flow
,”
Numer. Heat Transfer B
,
63
(
6
), pp.
508
539
.10.1080/10407790.2013.772001
15.
Yan
,
S. N.
,
Wang
,
F. W.
,
Hong
,
J.
, and
Sigmund
,
O.
,
2019
, “
Topology Optimization of Microchannel Heat Sinks Using a Two-Layer Model
,”
Int. J. Heat Mass Transfer
,
143
, p.
118462
.10.1016/j.ijheatmasstransfer.2019.118462
16.
Zhang
,
B.
,
Zhu
,
J.
,
Xiang
,
G.
, and
Gao
,
L.
,
2021
, “
Design of Nanofluid-Cooled Heat Sink Using Topology Optimization
,”
Chin. J. Aeronaut.
,
34
(
2
), pp.
301
317
.10.1016/j.cja.2020.05.023
17.
Alexandersen
,
J.
,
Aage
,
N.
,
Andreasen
,
C. S.
, and
Sigmund
,
O.
,
2014
, “
Topology Optimisation for Natural Convection Problems
,”
Int. J. Numer. Methods Fluids
,
76
(
10
), pp.
699
721
.10.1002/fld.3954
18.
Alexandersen
,
J.
,
Sigmund
,
O.
, and
Aage
,
N.
,
2016
, “
Large Scale Three-Dimensional Topology Optimisation of Heat Sinks Cooled by Natural Convection
,”
Int. J. Heat Mass Transfer
,
100
, pp.
876
891
.10.1016/j.ijheatmasstransfer.2016.05.013
19.
Alexandersen
,
J.
,
Sigmund
,
O.
,
Meyer
,
K. E.
, and
Lazarov
,
B. S.
,
2018
, “
Design of Passive Coolers for Light-Emitting Diode Lamps Using Topology Optimisation
,”
Int. J. Heat Mass Transfer
,
122
, pp.
138
149
.10.1016/j.ijheatmasstransfer.2018.01.103
20.
Lazarov
,
B. S.
,
Sigmund
,
O.
,
Meyer
,
K. E.
, and
Alexandersen
,
J.
,
2018
, “
Experimental Validation of Additively Manufactured Optimized Shapes for Passive Cooling
,”
Appl. Energy
,
226
, pp.
330
339
.10.1016/j.apenergy.2018.05.106
21.
Audunson
,
T.
, and
Gebhart
,
B.
,
1972
, “
An Experimental and Analytical Study of Natural Convection With Appreciable Thermal Radiation Effects
,”
J. Fluid Mech.
,
52
(
1
), pp.
57
95
.10.1017/S0022112072002976
22.
Carpenter
,
J. R.
,
Briggs
,
D. G.
, and
Sernas
,
V.
,
1976
, “
Combined Radiation and Developing Laminar Free Convection Between Vertical Flat Plates With Asymmetric Heating
,”
ASME J. Heat Transfer
,
98
(
1
), pp.
95
100
.10.1115/1.3450476
23.
Hall
,
D. A.
,
Vliet
,
G. C.
, and
Bergman
,
T. L.
,
1999
, “
Natural Convection Cooling of Vertical Rectangular Channels in Air Considering Radiation and Wall Conduction
,”
ASME J. Electron Packaging
,
121
(
2
), pp.
75
84
.10.1115/1.2792671
24.
Howell
,
J. R.
,
Daun
,
K. J.
,
Erturk
,
H.
,
Gamba
,
M.
, and
Sarvari
,
M. H.
,
2003
, “
The Use of Inverse Methods for the Design and Control of Radiant Sources
,”
JSME Int. J. Ser. B—Fluids Therm. Eng.
,
46
(
4
), pp.
470
478
.10.1299/jsmeb.46.470
25.
Daun
,
K. J.
,
Morton
,
D. P.
, and
Howell
,
J. R.
,
2003
, “
Geometric Optimization of Radiant Enclosures Containing Specular Surfaces
,”
ASME J. Heat Transfer
,
125
(
5
), pp.
845
851
.10.1115/1.1599369
26.
Tan
,
J. Y.
,
Zhao
,
J. M.
, and
Liu
,
L. H.
,
2011
, “
Geometric Optimization of a Radiation-Conduction Heating Device Using Meshless Method
,”
Int. J. Therm. Sci.
,
50
(
10
), pp.
1820
1831
.10.1016/j.ijthermalsci.2011.05.009
27.
Jang
,
D.
,
Yu
,
S. H.
, and
Lee
,
K. S.
,
2012
, “
Multidisciplinary Optimization of a Pin-Fin Radial Heat Sink for LED Lighting Applications
,”
Int. J. Heat Mass Transfer
,
55
(
4
), pp.
515
521
.10.1016/j.ijheatmasstransfer.2011.11.016
28.
Farahmand
,
A.
,
Payan
,
S.
, and
Hosseini Sarvari
,
S. M.
,
2012
, “
Geometric Optimization of Radiative Enclosures Using PSO Algorithm
,”
Int. J. Therm. Sci.
,
60
, pp.
61
69
.10.1016/j.ijthermalsci.2012.04.024
29.
Kwak
,
D. B.
,
Kwak
,
H. P.
,
Noh
,
J. H.
, and
Yook
,
S. J.
,
2018
, “
Optimization of the Radial Heat Sink With a Concentric Cylinder and Triangular Fins Installed on a Circular Base
,”
J. Mech. Sci. Technol.
,
32
(
1
), pp.
505
512
.10.1007/s12206-017-1252-4
30.
Huang
,
C. H.
, and
Wu
,
Y. T.
,
2021
, “
An Optimum Design for a Natural Convection Pin Fin Array With Orientation Consideration
,”
Appl. Therm. Eng.
,
188
, p.
116633
.10.1016/j.applthermaleng.2021.116633
31.
Czerwiński
,
G.
, and
Wołoszyn
,
J.
,
2021
, “
Optimization of Air Cooling System Using Adjoint Solver Technique
,”
Energies
,
14
(
13
), p.
3753
.10.3390/en14133753
32.
Mosavati
,
B.
,
Mosavati
,
M.
, and
Kowsary
,
F.
,
2013
, “
Solution of Radiative Inverse Boundary Design Problem in a Combined Radiating-Free Convecting Furnace
,”
Int. Commun. Heat Mass Transfer
,
45
, pp.
130
136
.10.1016/j.icheatmasstransfer.2013.04.011
33.
Mosavati
,
B.
,
Mosavati
,
M.
, and
Kowsary
,
F.
,
2016
, “
Inverse Boundary Design Solution in a Combined Radiating-Free Convection Furnace Filled With Participating Medium Containing Specularly Reflecting Walls
,”
Int. Commun. Heat Mass Transfer
,
76
, pp.
69
76
.10.1016/j.icheatmasstransfer.2016.04.029
34.
Mosavati
,
B.
, and
Mosavati
,
M.
,
2022
, “
A New Approach to Solve Inverse Boundary Design of a Radiative Enclosure With Specular-Diffuse Surfaces
,”
ASME J. Heat Transfer
,
144
(
1
), p.
012801
.10.1115/1.4052606
35.
Castro
,
D. A.
,
Kiyono
,
C. Y.
, and
Silva
,
E. C. N.
,
2015
, “
Design of Radiative Enclosures by Using Topology Optimization
,”
Int. J. Heat Mass Transfer
,
88
, pp.
880
890
.10.1016/j.ijheatmasstransfer.2015.04.077
36.
Shen
,
X.
,
Han
,
H.
,
Li
,
Y.
,
Yan
,
C.
, and
Mu
,
D.
,
2021
, “
A Topology Optimization Based Design of Space Radiator for Focal Plane Assemblies
,”
Energies
,
14
(
19
), p.
6252
.10.3390/en14196252
37.
Wang
,
C.
,
Yu
,
Z.
,
Zhou
,
M.
, and
Qian
,
X.
,
2022
, “
Topology Optimization of Thermophotonic Problem for Daytime Passive Radiative Cooling
,”
Int. J. Heat Mass Transfer
,
183
, p.
122097
.10.1016/j.ijheatmasstransfer.2021.122097
38.
Sevart
,
C. D.
, and
Bergman
,
T. L.
,
2021
, “
Evolutionary Design Method for a Conducting Solid Cooled by Combined Free Convection and Radiation
,”
ASME J. Heat Transfer
,
143
(
4
), p.
042103
.10.1115/1.4049841
39.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
McGraw-Hill
,
New York
.
40.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
1999
, “
Material Interpolation Schemes in Topology Optimization
,”
Arch. Appl. Mech.
,
69
(
9–10
), pp.
635
654
.10.1007/s004190050248
41.
Svanberg
,
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
Int. J. Numer. Methods Eng.
,
24
(
2
), pp.
359
373
.10.1002/nme.1620240207
42.
Kandis
,
M.
, and
Bergman
,
T. L.
,
2000
, “
A Simulation-Based Correlation of the Density and Thermal Conductivity of Objects Produced by Laser Sintering of Polymer Powders
,”
ASME J. Manuf. Sci. Eng.
,
122
(
3
), pp.
439
444
.10.1115/1.1286558
43.
Yang
,
P.
,
Deibler
,
L. A.
,
Bradley
,
D. R.
,
Stefan
,
D. K.
, and
Carrol
,
J. D.
,
2018
, “
Microstructure Evolution and Thermal Properties of an Additively Manufactured, Solution Treatable AlSi10 Mg Part
,”
J. Mater. Res.
,
33
(
23
), pp.
4040
4052
.10.1557/jmr.2018.405
44.
Wen
,
C. D.
, and
Mudawar
,
I.
,
2004
, “
Emissivity Characteristics of Roughened Aluminum Alloy Surfaces and Assessment of Multispectral Radiation Thermometry (MRT) Emissivity Models
,”
Int. J. Heat Mass Transfer
,
47
(
17–18
), pp.
3591
3605
.10.1016/j.ijheatmasstransfer.2004.04.025
45.
Wen
,
C. D.
, and
Mudawar
,
I.
,
2006
, “
Modeling the Effects of Surface Roughness on the Emissivity of Aluminum
,”
Int. J. Heat Mass Transfer
,
49
(
23–24
), pp.
4279
4289
.10.1016/j.ijheatmasstransfer.2006.04.037
46.
Bergman
,
T. L.
, and
Lavine
,
A. S.
,
2017
,
Fundamentals of Heat and Mass Transfer
, 8th ed.,
Wiley
, Hoboken,
NJ
.
47.
Hottel
,
H. C.
,
1954
, “
Radiant Heat Transmission
,”
Heat Transmission
,
W. H.
McAdams
, ed.,
McGraw-Hill
,
New York
.
You do not currently have access to this content.