In this paper, we optimized the topology of a thin-film resistive heater as well as the electrical potential of the electrodes on the boundaries. The objective was to minimize the difference between the actual and prescribed temperature profiles. The thin-film thickness was represented by 100 design variables, and the electrical potential at each electrode were also design variables. The topology optimization problem (inverse problem) has been solved with two methods, i.e., with a genetic algorithm (GA) and with a conjugate gradient method using adjoint and sensitivity problems (CGA). The genetic algorithm used here was modified in order to prevent nonconvergence due to the nonuniqueness of topology representation. The conjugate gradient method used in inverse conduction was extended to cope with our electrothermal problem. The GA and CGA methods started with random topologies and random electrical potential values at electrodes. Both the CGA and GA succeeded in finding optimal thin-film thickness distributions and electrode potential values, even with 100 topology design variables. For most cases, the maximum discrepancy between the optimized and prescribed temperature profiles was under 0.5°C, relative to temperature profiles of the order of 70°C. The CGA method was faster to converge, but was more complex to implement and sometimes led to local minima. The GA was easier to implement and was more unlikely to lead to a local minimum, but was much slower to converge.

1.
Bejan
,
A.
, and
Lorente
,
S.
, 2006, “
Constructal Theory of Generation of Configuration in Nature and Engineering
,”
J. Appl. Phys.
0021-8979,
100
(
4
), p.
041301
.
2.
Steinvurzel
,
P.
,
MacHarrie
,
R. A.
,
Baldwin
,
K. W.
,
Van Hise
,
C. W.
,
Eggleton
,
B. J.
, and
Rogers
,
J. A.
, 2005, “
Optimization of Distributed Resistive Metal Film Heaters in Thermally Tunable Dispersion Compensators for High-Bit-Rate Communication Systems
,”
Appl. Opt.
0003-6935,
44
(
14
), pp.
2782
2791
.
3.
Kalli
,
K.
,
Dobb
,
H. L.
,
Webb
,
D. J.
,
Carroll
,
K.
,
Komodromos
,
M.
,
Themistos
,
C.
,
Peng
,
G. D.
,
Fang
,
Q.
, and
Boyd
,
I. W.
, 2007, “
Electrically Tunable Bragg Gratings in Single-Mode Polymer Optical Fiber
,”
Opt. Lett.
0146-9592,
32
(
3
), pp.
214
216
.
4.
Salamon
,
T. R.
,
Rogers
,
J. A.
, and
Eggleton
,
B. J.
, 2001, “
Analysis of Heat Flow in Optical Fiber Devices That Use Microfabricated Thin Film Heaters
,”
Sens. Actuators, A
0924-4247,
95
(
1
), pp.
8
16
.
5.
Rogers
,
J. A.
,
Eggleton
,
B. J.
,
Pedrazzani
,
J. R.
, and
Strasser
,
T. A.
, 1999, “
Distributed On-Fiber Thin Film Heaters for Bragg Gratings With Adjustable Chirp
,”
Appl. Phys. Lett.
0003-6951,
74
(
21
), pp.
3131
3133
.
6.
Baroncini
,
M.
,
Placidi
,
P.
,
Cardinali
,
G. C.
, and
Scorzoni
,
A.
, 2004, “
Thermal Characterization of a Microheater for Micromachined Gas Sensors
,”
Sens. Actuators, A
0924-4247,
115
(
1
), pp.
8
14
.
7.
Deng
,
P. G.
,
Lee
,
Y. K.
, and
Cheng
,
P.
, 2006, “
An Experimental Study of Heater Size Effect on Micro Bubble Generation
,”
Int. J. Heat Mass Transfer
0017-9310,
49
(
15–16
), pp.
2535
2544
.
8.
Zhang
,
K. L.
,
Chou
,
S. K.
, and
Ang
,
S. S.
, 2007, “
Fabrication, Modeling and Testing of a Thin Film Au/Ti Microheater
,”
Int. J. Therm. Sci.
1290-0729,
46
(
6
), pp.
580
588
.
9.
Kozlov
,
A. G.
, 2006, “
Analytical Modelling of Temperature Distribution in Resistive Thin-Film Thermal Sensors
,”
Int. J. Therm. Sci.
1290-0729,
45
(
1
), pp.
41
50
.
10.
Cheng
,
C. -H.
,
Lin
,
H. -H.
, and
Aung
,
W.
, 2003, “
Optimal Shape Design for Packaging Containing Heating Elements by Inverse Heat Transfer Method
,”
Heat Mass Transfer
0947-7411,
39
(
8–9
), pp.
687
692
.
11.
Park
,
C. W.
, and
Yoo
,
Y. M.
, 1988, “
Shape Design Sensitivity Analysis of a Two-Dimensional Heat Transfer System Using the Boundary Element Method
,”
Comput. Struct.
0045-7949,
28
(
4
), pp.
543
550
.
12.
Mathieu-Potvin
,
F.
, and
Gosselin
,
L.
, 2006, “
Optimal Conduction Pathways for Cooling a Heat Generating Body: A Comparison Exercise
,”
Int. J. Heat Mass Transfer
0017-9310,
50
(
15–16
), pp.
2996
3006
.
13.
Li
,
Q.
,
Steven
,
G. P.
,
Querin
,
O. M.
, and
Xie
,
Y. M.
, 1999, “
Shape and Topology Design for Heat Conduction by Evolutionary Structural Optimization
,”
Int. J. Heat Mass Transfer
0017-9310,
42
(
17
), pp.
3361
3371
.
14.
Steven
,
G. P.
,
Li
,
Q.
, and
Xie
,
Y. M.
, 2000, “
Evolutionary Topology and Shape Design for General Physical Field Problem
,”
Comput. Mech.
0178-7675,
26
(
2
), pp.
129
139
.
15.
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
0017-9310,
47
(
23
), pp.
5071
5083
.
16.
Novotny
,
A. A.
,
Feijóo
,
R. A.
,
Taroco
,
E.
, and
Padra
,
C.
, 2003, “
Topological Sensitivity Analysis
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
192
(
7–8
), pp.
803
829
.
17.
Gersborg-Hansen
,
A.
,
Bendsøe
,
M. P.
, and
Sigmund
,
O.
, 2006, “
Topology Optimization of Heat Conduction Problems Using the Finite Volume Method
,”
Struct. Multidiscip. Optim.
1615-147X,
31
(
4
), pp.
251
259
.
18.
Wang
,
A. -H.
,
Liang
,
X. -G.
, and
Ren
,
J. -X.
, 2006, “
Constructal Enhancement of Heat Conduction With Phase Change
,”
Int. J. Thermophys.
0195-928X,
27
(
1
), pp.
126
138
.
19.
Yin
,
L.
, and
Ananthasuresh
,
G. K.
, 2002, “
A Novel Topology Design Scheme for the Multi-Physics Problems of Electro-Thermally Actuated Compliant Micromechanisms
,”
Sens. Actuators, A
0924-4247,
97–98
(
1
), pp.
599
609
.
20.
Nelli Silva
,
E. C.
,
Nishiwaki
,
S.
,
Ono Fonseca
,
J. S.
, and
Kikuchi
,
N.
, 1999, “
Optimization Methods Applied to Material and Flextensional Actuator Design Using the Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
172
(
1–4
), pp.
241
271
.
21.
Li
,
Y.
,
Saitou
,
K.
, and
Kikuchi
,
N.
, 2004, “
Topology Optimization of Thermally Actuated Compliant Mechanisms Considering Time-Transient Effect
,”
Finite Elem. Anal. Design
0168-874X,
40
(
11
), pp.
1317
1331
.
22.
Ozisik
,
M. N.
, and
Orlande
,
H. R. B.
, 2000,
Inverse Heat Transfer
,
Taylor & Francis
,
New York
.
23.
Gosselin
,
L.
,
Tye-Gingras
,
M.
, and
Mathieu-Potvin
,
F.
, 2009, “
Review of Genetic Algorithms Utilization in Heat Transfer Problems
,”
Int. J. Heat Mass Transfer
0017-9310,
52
(
9–10
), pp.
2169
2188
.
24.
1998, FLUENT User’s Guide, www.fluent.comwww.fluent.com
25.
Mathieu-Potvin
,
F.
, and
Gosselin
,
L.
, 2009, “
Bilinearization Approach for Diffusion Problems Involving the Calculation of Second-Law Fields
,”
Numer. Heat Transfer, Part B
1040-7790,
55
(
6
), pp.
457
479
.
26.
Reddy
,
J. N.
, 2006,
An Introduction to the Finite Element Method
,
3rd ed.
,
McGraw-Hill
,
New York
, Chap. 8.
27.
Colaço
,
M. J.
,
Dulikravich
,
G. S.
, and
Martin
,
T. J.
, 2004, “
Optimization of Wall Electrodes for Electro-Hydrodynamic Control of Natural Convection During Solidification
,”
Mater. Manuf. Processes
1042-6914,
19
(
4
), pp.
719
736
.
28.
Tye-Gingras
,
M.
, and
Gosselin
,
L.
, 2008, “
Thermal Resistance Minimization of a Fin-and-Porous Medium Heat Sink With Evolutionary Algorithms
,”
Numer. Heat Transfer
0149-5720,
54
(
4
), pp.
349
366
.
29.
Leblond
,
G.
, and
Gosselin
,
L.
, 2008, “
Effect of Non-Local Equilibrium on Minimal Thermal Resistance Porous Layered Systems
,”
Int. J. Heat Fluid Flow
0142-727X,
29
(
1
), pp.
281
291
.
30.
Wildi-Tremblay
,
P.
, and
Gosselin
,
L.
, 2007, “
Layered Porous Media Architecture for Maximal Cooling
,”
Int. J. Heat Mass Transfer
0017-9310,
50
(
3–4
), pp.
464
478
.
You do not currently have access to this content.