Constructal design associated with genetic algorithm (GA) is employed to optimize the geometry of an isothermal Y-shaped cavity embedded into a solid conducting wall. The structure has four degrees of freedom (DOF). The main purpose is to minimize the maximum excess of temperature between the solid and the cavity by means of GA and exhaustive search (simulating every geometry combinations). Results showed that GA was well succeeded to find the best shapes which minimize the maximal excess of temperature with a number of simulations strongly lower than that required with exhaustive search, allowing the optimization of cavity under new constraint conditions.

References

References
1.
Bejan
,
A.
,
1997
,
Advanced Engineering Thermodynamics
,
Wiley
,
New York
.
2.
Bejan
,
A.
,
2000
,
Shape and Structure, from Engineering to Nature
,
Cambridge University Press
,
Cambridge, UK
.
3.
Bejan
,
A.
, and
Lorente
,
S.
,
2008
,
Design With Constructal Theory
,
Wiley
,
Hoboken
, NJ.
4.
Bejan
,
A.
, and
Zane
,
P.
,
2012
,
Design in Nature
,
Doubleday
, New York.
5.
Bejan
,
A.
, and
Lorente
,
S.
,
2006
, “
Constructal Theory of Generation of Configuration in Nature and Engineering
,”
J. Appl. Phys.
,
100
(4), p.
041301
.10.1063/1.2221896
6.
Beyene
,
A.
, and
Peffley
,
J.
,
2009
, “
Constructal Theory, Adaptive Motion, and Their Theoretical Application to Low-Speed Turbine Design
,”
ASCE J. Energy Eng.
,
135
(
4
), pp.
112
118
.10.1061/(ASCE)0733-9402(2009)135:4(112)
7.
Kang
,
D.-H.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2010
, “
Constructal Dendritic Configuration for the Radiation Heating of a Solid Stream
,”
J. Appl. Phys.
,
107
(11), p.
114910
.10.1063/1.3429195
8.
Kim
,
Y.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2010
, “
Constructal Multi-Tube Configuration for Natural and Forced Convection in Cross-Flow
,”
Int. J. Heat Mass Transfer
,
53
(23-24), pp.
5121
5128
.10.1016/j.ijheatmasstransfer.2010.07.053
9.
Kim
,
Y.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2011
, “
Steam Generator Structure: Continuous Model and Constructal Design
,”
Int. J. Energy Res.
,
35
(4), pp.
336
345
.10.1002/er.1694
10.
Azad
,
A. V.
, and
Amidpour
,
M.
,
2011
, “
Economic Optimization of Shell and Tube Heat Exchanger Based on Constructal Theory
,”
Energy
,
36
(
2
), pp.
1087
1096
.10.1016/j.energy.2010.11.041
11.
Kraus
,
A. D.
,
1999
, “
Developments in the Analysis of Finned Arrays
,”
Int. J. Transp. Phenom.
,
1
(
3
), pp.
141
164
.
12.
Aziz
,
A.
,
1992
, “
Optimum Dimensions of Extended Surfaces Operating in a Convective Environment
,”
Appl. Mech. Rev.
,
45
(
5
), pp.
155
173
.10.1115/1.3119754
13.
Biserni
,
C.
,
Rocha
,
L. A. O.
, and
Bejan
,
A.
,
2004
, “
Inverted Fins: Geometric Optimization of the Intrusion Into a Conducting Wall
,”
Int. J. Heat Mass Transfer
,
47
(
12–13
), pp.
2577
2586
.10.1016/j.ijheatmasstransfer.2003.12.018
14.
Rocha
,
L. A. O.
,
Lorenzini
,
E.
, and
Biserni
,
C.
,
2005
, “
Geometric Optimization of Shapes on the Basis of Bejan's Constructal Theory
,”
Int. Commun. Heat Mass Transfer
,
32
(
10
), pp.
1281
1288
.10.1016/j.icheatmasstransfer.2005.07.010
15.
Xie
,
Z.
,
Chen
,
L.
, and
Sun
,
F.
,
2010
, “
Geometry Optimization of T-Shaped Cavities According to Constructal Theory
,”
Math. Comput. Model.
,
52
(
9–10
), pp.
1538
1546
.10.1016/j.mcm.2010.06.017
16.
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
.10.1016/j.ijheatmasstransfer.2006.11.006
17.
Lorenzini
,
G.
,
Biserni
,
C.
,
Isoldi
,
L. A.
,
dos Santos
,
E. D.
, and
Rocha
,
L. A. O.
,
2011
, “
Constructal Design Applied to the Geometric Optimization of Y-Shaped Cavities Embedded in a Conducting Medium
,”
ASME J. Electron. Packag.
,
133
(
40
), p.
041008
.10.1115/1.4005296
18.
da Silva
,
A. K.
, and
Gosselinb
,
L.
,
2008
, “
Evolutionary Placement of Discrete Heaters in Forced Convection
,”
Numer. Heat Transfer
, A,
54
(
1
), pp.
20
33
.10.1080/10407780802024864
19.
Xie
,
Z. H.
,
Chen
,
L. G.
, and
Sun
,
F. R.
,
2010
, “
Constructal Optimization of Twice Y-Shaped Assemblies of Fins by Taking Maximum Thermal Resistance Minimization as Objective
,”
Sci. China Technol. Sci.
,
53
(
10
), pp.
2756
2764
.10.1007/s11431-010-4037-x
20.
Lorenzini
,
G.
, and
Rocha
,
L. A. O.
,
2006
, “
Constructal Design of Y-Shaped Assembly of Fins
,”
Int. J. Heat Mass Transfer
,
49
(
23–24
), pp.
4552
4557
.10.1016/j.ijheatmasstransfer.2006.05.019
21.
matlab,
2000
,
MATLAB User's Guide—Version 6.0.088—Release 12
,
The Mathworks, Inc.
,
Natick, MA
.
22.
Holland
,
J. H.
,
1975
,
Adaptation in Natural and Artificial Systems
,
University of Michigan Press
,
Ann Arbor
, MI.
23.
Goldberg
,
D. E.
,
1989
,
Algorithms in Search, Optimization, and Machine Learning
,
Addison-Wesley Longman Publishing, Co.
,
Boston, MA
.
24.
Haupt
,
R. L.
, and
Haupt
,
S. E.
,
1989
,
Practical Genetic Algorithms
,
John Wiley & Sons
,
Hoboken, NJ
.
You do not currently have access to this content.