This work relies on constructal design to perform the geometric optimization of the V-shaped pathways of highly conductive materials (inserts) that remove a constant heat generation rate from a body and deliver it to isothermal heat sinks. It is shown numerically that the global thermal resistance of the V-shaped pathway can be minimized by geometric optimization subject to total volume and V-shaped pathways material constraints. Constructal design and genetic algorithm (GA) optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly of pathways and optimal geometry features for the V-shaped pathway. Parametric study was performed to show the behavior of the minimized global thermal resistance as function of the volume fraction of the V-shaped pathways. First achieved results for ϕ = 0.3 indicated that when freedom is given to the geometry, the thermal performance is improved. Afterward, the employment of GA with constructal design allowed the achievement of the optimal shapes of V-shaped pathways for different volume fractions (0.2 ≤ ϕ ≤ 0.4). It was not realized the occurrence of one universal optimal shape for the several values of ϕ investigated, i.e., the optimal design was dependent on the degrees of freedom and the parameter ϕ and it is reached according to constructal principle of optimal distribution of imperfections.
Issue Section:
Research Papers
References
1.
Bejan
, A.
, and Lorente
, S.
, 2011
, “The Constructal Law and the Evolution of Design in Nature
,” Phys. Life Rev.
, 8
(3), pp. 209
–240
.10.1016/j.plrev.2011.05.0102.
Bejan
, A.
, and Zane
, J. P.
, 2012
, Design in Nature, Doubleday
, New York
.3.
Bejan
, A.
, and Lorente
, S.
, 2008
, Design With Constructal Theory
, Wiley
, Hoboken, NJ
.10.1002/97804704327094.
Bejan
, A.
, 2000
, Shape and Structure, From Engineering to Nature
, Cambridge University Press
, Cambridge, UK
.10.3390/e30502935.
Bejan
, A.
, Lorente
, S.
, and Lee
, J.
, 2008
, “Unifying Constructal Theory of Tree Roots, Canopies and Forests
,” J. Theor. Biol.
, 254
(3
), pp. 529
–540
.10.1016/j.jtbi.2008.06.0266.
Reis
, A. H.
, and Bejan
, A.
, 2006
, “Constructal Theory of Global Circulation and Climate
,” Int. J. Heat Mass Transfer
, 49
(11–12
), pp. 1857
–1875
.10.1016/j.ijheatmasstransfer.2005.10.0377.
Miguel
, A. F.
, 2013
, “The Emergence of Design in Pedestrian Dynamics: Locomotion, Self-Organization, Walking Paths and Constructal Law
,” Phys. Life Rev.
, 10
(2
), pp. 168
–190
.10.1016/j.plrev.2013.03.0078.
Bejan
, A.
, and Merkx
, G. W.
, 2007
, Constructal Theory of Social Dynamics
, Springer
, New York
.9.
Beyene
, A.
, and Peffley
, J.
, 2009
, “Constructal Theory, Adaptive Motion, and Their Theoretical Application to Low-Speed Turbine Design
,” J. Energy Eng
, 135
(4
), pp. 112
–118
.10.1061/(ASCE)0733-9402(2009)135:4(112)10.
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.169411.
Chen
, L.
, 2012
, “Progress in Study on Constructal Theory and Its Applications
,” Sci. China Technol. Sci.
, 55
(3
), pp. 802
–820
.10.1007/s11431-011-4701-912.
Rocha
, L. A. O.
, Lorente
, S.
, and Bejan
, A.
, 2013
, Constructal Law and the Unifying Principle of Design
, Springer
, New York
.10.1007/978-1-4614-5049-813.
Lorenzini
, G.
, Biserni
, C.
, and Rocha
, L. A. O.
, 2013
, “Constructal Design of Non-Uniform X-Shaped Conductive Pathways for Cooling
,” Int. J. Thermal Sci.
, 71
, pp. 140
–147
.10.1016/j.ijthermalsci.2013.04.02114.
Kraus
, A. D.
, 1999
, “Developments in the Analysis of Finned Arrays
,” Int. J. Transp. Phenom.
, 1
(3
), pp. 141
–164
.15.
Aziz
, A.
, 1992
, “Optimum Dimensions of Extended Surfaces Operating in a Convective Environment
,” ASME Appl. Mech. Rev.
, 45
(5
), pp. 155
–173
.10.1115/1.311975416.
Bonjour
, J.
, Rocha
, L. A. O.
, Bejan
, A.
, and Meunier
, F.
, 2004
, “Dendritic Fins Optimization for a Coaxial Two-Stream Heat Exchanger
,” Int. J. Heat Mass Transfer
, 47
(1
), pp. 111
–124
.10.1016/S0017-9310(03)00406-X17.
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.2003.12.01818.
Xie
, Z.
, Chen
, L.
, and Sun
, F.
, 2010
, “Geometry Optimization of T-Shaped Cavities According to Constructal Theory
,” Math. Comput. Modell.
, 52
(9–10
), pp. 1538
–1546
.10.1016/j.mcm.2010.06.01719.
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.2005.07.01020.
Lorenzini
, G.
, and Rocha
, L. A. O.
, 2009
, “Geometric Optimization of T–Y-Shaped Cavity According to Constructal Design
,” Int. J. Heat Mass Transfer
, 52
(21–22
), pp. 4683
–4688
.10.1016/j.ijheatmasstransfer.2009.06.02021.
Lorenzini
, G.
, Garcia
, F. L.
, dos Santos
, E. D.
, Biserni
, C.
, and Rocha
, L. A. O.
, 2012
, “Constructal Design Applied to the Optimization of Complex Geometries: T–Y-Shaped Cavities With Two Additional Lateral Intrusions Cooled By Convection
,” Int. J. Heat Mass Transfer
, 55
(5–6
), pp. 1505
–1512
.10.1016/j.ijheatmasstransfer.2011.10.05722.
Hajmohammadi
, M. R.
, Poozesh
, S.
, Campo
, A.
, and Nourazar
, S. S.
, 2013
, “Valuable Reconsideration in the Constructal Design of Cavities
,” Energy Convers. Manage.
, 66
, pp. 33
–40
.10.1016/j.enconman.2012.09.03123.
Lorenzini
, G.
, Biserni
, C.
, dos Santos
, E. D.
, Isoldi
, L. A.
, and Rocha
, L. A. O.
, 2014
, “Constructal Design of Isothermal X-Shaped Cavities
,” Therm. Sci.
, 18
(2
), pp. 349
–356
.10.2298/TSCI120804005L24.
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
.10.1115/1.400610325.
Pouzesh
, A.
, Mohammad
, R. H.
, and Poozesh
, S.
, “Investigations on the Internal Shape of Constructal Cavities Intruding a Heat Generating Body
,” Therm. Sci.
(published online).10.2298/tsci120427164p26.
Bejan
, A.
, and Almogbel
, M.
, 2000
, “Constructal T-Shaped Fins
,” Int. J. Heat Mass Transfer
, 43
(12
), pp. 2101
–2115
.10.1016/S0017-9310(99)00283-527.
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.2006.05.01928.
Lorenzini
, G.
, and Rocha
, L. A. O.
, 2009
, “Constructal Design of T–Y Assembly of Fins for an Optimized Heat Removal
,” Int. J. Heat Mass Transfer
, 52
(5–6
), pp. 1458
–1463
.10.1016/j.ijheatmasstransfer.2008.09.00729.
Hajmohammadi
, M. R.
, Poozesh
, S.
, and Hosseini
, R.
, 2012
, “Radiation Effect on Constructal Design Analysis of a T–Y-Shaped Assembly of Fins
,” J. Therm. Sci. Technol.
, 7
(4
), pp. 677
–692
.10.1299/jtst.7.67730.
Hui
, X. Z.
, Gen
, C. L.
, and Rui
, S. F.
, 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-x31.
Lorenzini
, G.
, Corrêa
, 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
.10.1115/1.400371032.
Bhanja
, D.
, and Kundu
, B.
, 2011
, “Thermal Analysis of a Constructal T-Shaped Porous Fin With Radiation Effects
,” Int. J. Refrig.
, 34
(6
), pp. 1483
–1496
.10.1016/j.ijrefrig.2011.04.00333.
Bhanja
, D.
, and Kundu
, B.
, 2012
, “Radiation Effect on Optimum Design Analysis of a Constructal T-Shaped Fin With Variable Thermal Conductivity
,” Heat Mass Transfer
, 48
(1
), pp. 109
–122
.10.1007/s00231-011-0845-134.
Kundu
, B.
, and Bhanja
, D.
, 2010
, “Performance and Optimization Analysis of a Construtal T-Shaped Fin Subject to Variable Thermal Conductivity and Convective Heat Transfer Coefficient
,” Int. J. Heat Mass Transfer
, 53
(1–3
), pp. 254
–267
.10.1016/j.ijheatmasstransfer.2009.09.03435.
Bello-Ochende
, T.
, Meyer
, J. P.
, and Bejan
, A.
, 2010
, “Constructal Multi-Scale Pin–Fins
,” Int. J. Heat Mass Transfer
, 53
(13–14
), pp. 2773
–2779
.10.1016/j.ijheatmasstransfer.2010.02.02136.
Hajmohammadi
, M. R.
, Poozesh
, S.
, Nourazar
, S. S.
, and Manesh
, A. H.
, 2013
, “Optimal Architecture of Heat Generating Pieces in a Fin
,” J. Mech. Sci. Technol.
, 27
(4
), pp. 1143
–1149
.10.1007/s12206-013-0217-537.
Hajmohammadi
, M. R.
, Poozesh
, S.
, and Nourazar
, S. S.
, 2012
, “Constructal Design of Multiple Heat Sources in a Square-Shaped Fin
,” Proc. Inst. Mech. Eng., Part E
, 226
(4
), pp. 324
–336
.10.1177/095440891244772038.
Ghodoossi
, L.
, and Eǧrican
, N.
, 2004
, “Conductive Cooling of Triangular Shaped Electronics Using Constructal Theory
,” Energy Convers. Manage.
, 45
(6
), pp. 811
–828
.10.1016/S0196-8904(03)00190-039.
Hajmohammadi
, M. R.
, Alizadeh Abianeh
, V.
, Moezzinajafabadi
, M.
, and Daneshi
, M.
, 2013
, “Fork-Shaped Highly Conductive Pathways for Maximum Cooling in a Heat Generating Piece
,” Appl. Therm. Eng.
, 61
(2
), pp. 228
–235
.10.1016/j.applthermaleng.2013.08.00140.
Hajmohammadi
, M. R.
, and Shariatzadeh
, O. J.
, 2014
, “Phi and Psi Shaped Conductive Routes for Improved Cooling in a Heat Generating Piece
,” Int. J. Therm. Sci.
, 77
, pp. 66
–74
.10.1016/j.ijthermalsci.2013.10.01541.
Hajmohammadi
, M. R.
, Campo
, A.
, Nourazar
, S. S.
, and Masood Ostad
, A.
, 2013
, “Improvement of Forced Convection Cooling Due to the Attachment of Heat Sources to a Conducting Thick Plate
,” ASME J. Heat Transfer
, 135
(12
), p. 124504
.10.1115/1.402489742.
Hajmohammadi
, M. R.
, Moulod
, M.
, Shariatzadeh
, O. J.
, and Campo
, A.
, 2014
, “Effects of a Thick Plate on the Excess Temperature of Iso-Heat Flux Heat Sources Cooled by Laminar Forced Convection Flow: Conjugate Analysis
,” Numer. Heat Transfer, Part A
, 66
(2
), pp. 205
–216
.10.1080/10407782.2013.87324443.
Hajmohammadi
, M. R.
, Salimpour
, M. R.
, Saber
, M.
, and Campo
, A.
, 2013
, “Detailed Analysis for the Cooling Performance Enhancement of a Heat Source Under a Thick Plate
,” Energy Convers. Manage.
, 76
, pp. 691
–700
.10.1016/j.enconman.2013.08.01644.
Hajmohammadi
, M.
, Moulod
, M.
, Joneydi
, S.
, and Nourazar
, S.
, 2013
, “New Methods to Cope With Temperature Elevations in Heated Segments of Flat Plates Cooled by Boundary Layer Flow
,” Therm. Sci.
(published online).10.2298/TSCI130128159H45.
Hajmohammadi
, M. R.
, and Nourazar
, S. S.
, 2014
, “On the Insertion of a Thin Gas Layer in Micro Cylindrical Couette Flows Involving Power-Law Liquids
,” Int. J. Heat Mass Transfer
, 75
, pp. 97
–108
.10.1016/j.ijheatmasstransfer.2014.03.06546.
Hajmohammadi
, M. R.
, Rahmani
, M.
, Campo
, A.
, and Joneydi Shariatzadeh
, O.
, 2014
, “Optimal Design of Unequal Heat Flux Elements for Optimized Heat Transfer Inside a Rectangular Duct
,” Energy
, 68
, pp. 609
–616
.10.1016/j.energy.2014.02.01147.
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
.10.1016/j.ijheatmasstransfer.2003.12.00948.
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
.10.1016/j.ijheatmasstransfer.2003.07.00749.
Lorenzini
, G.
, Biserni
, C.
, Estrada
, E. D.
, Isoldi
, L. A.
, dos Santos
, E. D.
, and Rocha
, L. A. O.
, 2014
, “Constructal Design of Convective Y-Shaped Cavities by Means of Genetic Algorithm
,” ASME J. Heat Transfer
, 136
(7
), p. 071702
.10.1115/1.402719550.
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
(4
), p. 041008
.10.1115/1.400529651.
Cheng
, C.-H.
, and Chen
, Y.-F.
, 2014
, “Topology Optimization of Heat Conduction Paths by a Non-Constrained Volume-of-Solid Function Method
,” Int. J. Therm. Sci.
, 78
, pp. 16
–25
.10.1016/j.ijthermalsci.2013.11.01152.
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.2008.12.01353.
matlab
, 2000
, User's Guide, Version 6.0.088, Release 12
, The Mathworks, Inc.
, Natick, MA
.54.
Holland
, J. H.
, 1975
, Adaptation in Natural and Artificial Systems
, University of Michigan Press
, Ann Arbor, MI
.55.
Goldberg
, D. E.
, 1989
, Algorithms in Search, Optimization, and Machine Learning
, Addison-Wesley
, Boston, MA
.56.
Haupt
, R. L.
, and Haupt
, S. E.
, 1989
, Practical Genetic Algorithms
, Wiley
, Hoboken, NJ
.57.
Renner
, G.
, and Ekart
, A.
, 2003
, “Genetic Algorithms in Computer Aided Design
,” Comput.-Aided Des.
, 35
(8
), pp. 709
–726
.10.1016/S0010-4485(03)00003-458.
DeJong
, K. A.
, and Spears
, W. M.
, 1990
, “An Analysis of the Interacting Roles of Population Size and Crossover in Genetic Algorithms
,” First Workshop Parallel Problem Solving From Nature
, Springer, Berlin, Germany, pp. 38
–47
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