Design with Constructal Theory

548 Pages·2008·28.585 MB·English

by  Adrian Bejan, Sylvie Lorente(auth.)

Design with Constructal Theory
Design with Constructal Theory
Adrian Bejan
DukeUniversity,Durham,NorthCarolina
Sylvie Lorente
UniversityofToulouse,INSA,LMDCToulouse,France
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LibraryofCongressCataloging-in-PublicationData
Bejan,Adrian.
Designwithconstructaltheory/AdrianBejan,SylvieLorente.
p.cm.
Includesindex.
ISBN978-0-471-99816-7(cloth)
1.Design,Industrial.I.Lorente,Sylvie.II.Title.
TS171.4.B432008
745.2–dc22
2008003739
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
Contents
AbouttheAuthors xi
Preface xiii
ListofSymbols xvii
1. FlowSystems 1
1.1 ConstructalLaw,Vascularization,andSvelteness 1
1.2 FluidFlow 6
1.2.1 InternalFlow:DistributedFrictionLosses 7
1.2.2 InternalFlow:LocalLosses 11
1.2.3 ExternalFlow 18
1.3 HeatTransfer 20
1.3.1 Conduction 20
1.3.2 Convection 24
References 31
Problems 31
2. Imperfection 43
2.1 EvolutiontowardtheLeastImperfectPossible 43
2.2 Thermodynamics 44
2.3 ClosedSystems 46
2.4 OpenSystems 51
2.5 AnalysisofEngineeringComponents 52
2.6 HeatTransferImperfection 56
2.7 FluidFlowImperfection 57
2.8 OtherImperfections 59
2.9 OptimalSizeofHeatTransferSurface 61
References 62
Problems 63
3. SimpleFlowConfigurations 73
3.1 FlowBetweenTwoPoints 73
3.1.1 OptimalDistributionofImperfection 73
3.1.2 DuctCrossSections 75
3.2 RiverChannelCross-Sections 78
3.3 InternalSpacingsforNaturalConvection 81
3.3.1 LearnbyImaginingtheCompetingExtremes 81
3.3.2 SmallSpacings 84
3.3.3 LargeSpacings 85
v
vi Contents
3.3.4 OptimalSpacings 86
3.3.5 StaggeredPlatesandCylinders 87
3.4 InternalSpacingsforForcedConvection 89
3.4.1 SmallSpacings 90
3.4.2 LargeSpacings 90
3.4.3 OptimalSpacings 91
3.4.4 StaggeredPlates,Cylinders,andPinFins 92
3.5 MethodofIntersectingtheAsymptotes 94
3.6 FittingtheSolidtothe“Body”oftheFlow 96
3.7 EvolutionofTechnology:FromNaturaltoForcedConvection 98
References 99
Problems 101
4. TreeNetworksforFluidFlow 111
4.1 OptimalProportions:T-andY-ShapedConstructs 112
4.2 OptimalSizes,NotProportions 119
4.3 TreesBetweenaPointandaCircle 123
4.3.1 OnePairingLevel 124
4.3.2 FreeNumberofPairingLevels 127
4.4 PerformanceversusFreedomtoMorph 133
4.5 Minimal-LengthTrees 136
4.5.1 MinimalLengthsinaPlane 137
4.5.2 MinimalLengthsinThreeDimensions 139
4.5.3 MinimalLengthsonaDisc 139
4.6 StrategiesforFasterDesign 144
4.6.1 MiniaturizationRequiresConstruction 144
4.6.2 OptimalTreesversusMinimal-LengthTrees 145
4.6.3 75DegreeAngles 149
4.7 TreesBetweenOnePointandanArea 149
4.8 Asymmetry 156
4.9 Three-DimensionalTrees 158
4.10 Loops,JunctionLossesandFractal-LikeTrees 161
References 162
Problems 164
5. ConfigurationsforHeatConduction 171
5.1 TreesforCoolingaDisc-ShapedBody 171
5.1.1 ElementalVolume 173
5.1.2 OptimallyShapedInserts 177
5.1.3 OneBranchingLevel 178
5.2 ConductionTreeswithLoops 189
5.2.1 OneLoopSize,OneBranchingLevel 190
5.2.2 Radial,One-BifurcationandOne-LoopDesigns 195
5.2.3 TwoLoopSizes,TwoBranchingLevels 197
5.3 TreesatMicroandNanoscales 202
Contents vii
5.4 EvolutionofTechnology:FromForcedConvectiontoSolid-Body
Conduction 206
References 209
Problems 210
6. MultiscaleConfigurations 215
6.1 DistributionofHeatSourcesCooledbyNaturalConvection 216
6.2 DistributionofHeatSourcesCooledbyForcedConvection 224
6.3 MultiscalePlatesforForcedConvection 229
6.3.1 ForcingtheEntireFlowVolumetoWork 229
6.3.2 HeatTransfer 232
6.3.3 FluidFriction 233
6.3.4 HeatTransferRateDensity:TheSmallestScale 234
6.4 MultiscalePlatesandSpacingsforNaturalConvection 235
6.5 MultiscaleCylindersinCrossflow 238
6.6 MultiscaleDropletsforMaximumMassTransferDensity 241
References 245
Problems 247
7. MultiobjectiveConfigurations 249
7.1 ThermalResistanceversusPumpingPower 249
7.2 ElementalVolumewithConvection 250
7.3 DendriticHeatConvectiononaDisc 257
7.3.1 RadialFlowPattern 258
7.3.2 OneLevelofPairing 265
7.3.3 TwoLevelsofPairing 267
7.4 DendriticHeatExchangers 274
7.4.1 Geometry 275
7.4.2 FluidFlow 277
7.4.3 HeatTransfer 278
7.4.4 RadialSheetCounterflow 284
7.4.5 TreeCounterflowonaDisk 286
7.4.6 TreeCounterflowonaSquare 289
7.4.7 Two-ObjectivePerformance 291
7.5 ConstructalHeatExchangerTechnology 294
7.6 Tree-ShapedInsulatedDesignsforDistributionofHotWater 295
7.6.1 ElementalStringofUsers 295
7.6.2 DistributionofPipeRadius 297
7.6.3 DistributionofInsulation 298
7.6.4 UsersDistributedUniformlyoveranArea 301
7.6.5 TreeNetworkGeneratedbyRepetitivePairing 307
7.6.6 One-by-OneTreeGrowth 313
7.6.7 ComplexFlowStructuresAreRobust 318
References 325
Problems 328
viii Contents
8. VascularizedMaterials 329
8.1 TheFutureBelongstotheVascularized:NaturalDesign
Rediscovered 329
8.2 Line-to-LineTrees 330
8.3 CounterflowofLine-to-LineTrees 334
8.4 Self-HealingMaterials 343
8.4.1 GridsofChannels 344
8.4.2 MultipleScales,LoopShapes,andBodyShapes 352
8.4.3 TreesMatchedCanopytoCanopy 355
8.4.4 DiagonalandOrthogonalChannels 362
8.5 VascularizationFightingagainstHeating 364
8.6 VascularizationWillContinuetoSpread 369
References 371
Problems 373
9. ConfigurationsforElectrokineticMassTransfer 381
9.1 ScaleAnalysisofTransferofSpeciesthroughaPorousSystem 381
9.2 Model 385
9.3 MigrationthroughaFinitePorousMedium 387
9.4 IonicExtraction 393
9.5 ConstructalViewofElectrokineticTransfer 396
9.5.1 ReactivePorousMedia 400
9.5.2 OptimizationinTime 401
9.5.3 OptimizationinSpace 403
References 405
10. MechanicalandFlowStructuresCombined 409
10.1 OptimalFlowofStresses 409
10.2 CantileverBeams 411
10.3 InsulatingWallwithAirCavitiesandPrescribedStrength 416
10.4 MechanicalStructuresResistanttoThermalAttack 424
10.4.1 BeaminBending 425
10.4.2 MaximizationofResistancetoSuddenHeating 427
10.4.3 Steel-ReinforcedConcrete 431
10.5 Vegetation 442
10.5.1 RootShape 443
10.5.2 TrunkandCanopyShapes 446
10.5.3 ConicalTrunks,BranchesandCanopies 449
10.5.4 Forest 453
References 458
Problems 459
11. QuoVadisConstructalTheory? 467
11.1 TheThermodynamicsofSystemswithConfiguration 467
11.2 TwoWaystoFlowAreBetterthanOne 470
Contents ix
11.3 DistributedEnergySystems 473
11.4 ScalingUp 482
11.5 SurvivalviaGreaterPerformance,SveltenessandTerritory 483
11.6 ScienceasaConsructalFlowArchitecture 486
References 488
Problems 490
Appendix 491
A. TheMethodofScaleAnalysis 491
B. MethodofUndeterminedCoefficients(Lagrange
Multipliers) 493
C. VariationalCalculus 494
D. Constants 495
E. ConversionFactors 496
F. DimensionlessGroups 499
G. NonmetallicSolids 499
H. MetallicSolids 503
I. PorousMaterials 507
J. Liquids 508
K. Gases 513
References 516
AuthorIndex 519
SubjectIndex 523
About the Authors
AdrianBejanreceivedallofhisdegrees(BS,1971;MS,1972;PhD,1975)inme-
chanicalengineeringfromtheMassachusettsInstituteofTechnology.Hehasheld
the J. A. Jones distinguished professorship at Duke University since 1989. His
work covers thermodynamics, convective heat transfer, porous media, and con-
structal theory of design in nature. He developed the methods of entropy genera-
tion minimization, scale analysis, heatlines and masslines, intersection of asymp-
totes,andtheconstructallaw.ProfessorBejanisrankedamongthe100mostcited
authors in engineering, all disciplines all countries. He received the Max Jakob
MemorialAwardand15honorarydoctoratesfromuniversitiesintencountries.
SylvieLorentereceivedallherdegreesincivilengineering(BS,1992;MS,1992;
PhD,1996)fromtheNationalInstituteofAppliedSciences(INSA),Toulouse.She
is Professor of Civil Engineering at the University of Toulouse, INSA, and is af-
filiated with the Laboratory of Durability and Construction of Materials, LMDC.
Herworkcoversseveralfields,includingheattransferinbuildingstructures,fluid
mechanics,andtransportmechanismsincementbasedmaterials.Sheistheauthor
of70peer-referredarticlesandthreebooks.SylvieLorentereceivedthe2004Ed-
wardF.ObertAwardandthe2005Bergles-RohsenowYoungInvestigatorAwardin
HeatTransferfromtheAmericanSocietyofMechanicalEngineers,andthe2007
JamesP.HartnettAwardfromtheInternationalCenterofHeatandMassTransfer.
Constructaltheoryadvancesarepostedatwww.constructal.org.
xi
Preface
This book is the new design course that we have developed on several campuses
during the past five years. The approach is new because it is based on constructal
theory—the view that flow configuration (geometry, design) can be reasoned on
the basis of a principle of configuration generation and evolution in time toward
greaterglobalflowaccessinsystemsthatarefreetomorph.Thegenerationofflow
configuration is viewed as a physics phenomenon, and the principle that sums up
itsuniversaloccurrenceinnature(theconstructallaw,p.2)isdeterministic.
Constructal theory provides a broad coverage of “designedness” everywhere,
from engineering to geophysics and biology. To see the generality of the method,
considerthefollowingmetaphor,whichweuseintheintroductorysegmentofthe
course. Imagine the formation of a river drainage basin, which has the function
of providing flow access from an area (the plain) to one point (the river mouth).
Theconstructallawcallsforconfigurationswithsuccessivelysmallerglobalflow
resistancesintime.Theinvocationofthislawleadstoabalancingofalltheinternal
flow resistance, from the seepage along the hill slopes to the flow along all the
channels. Resistances (imperfection) cannot be eliminated. They can be matched
neighbortoneighbor,anddistributedsothattheirglobaleffectisminimal,andthe
wholebasinistheleastimperfectthatitcanbe.Theriverbasinmorphsandtends
towardanequilibriumflow-accessconfiguration.
The visible and valuable product of this way of thinking is the configuration:
the river basin, the lung, the tree of cooling channels in an electronics package,
and so on. The configuration is the big unknown in design: the constructal law
draws attention to it as the unknown and guides our thoughts in the direction of
discoveringit.
In the river basin example, the configuration that the constructal law uncovers
is a tree-shaped flow, with balances between highly dissimilar flow resistances
such as seepage (Darcy flow) and river channel flow. The tree-shaped flow is the
theoreticalwayofprovidingeffectiveflowaccessbetweenonepoint(source,sink)
andaninfinityofpoints(area,volume).Thetreeisacomplexflowstructure,which
hasmultiple-lengthscalesthataredistributednonuniformlyovertheavailablearea
orvolume.
Allthesefeatures,thetreeshapeandthemultiplescales,arefoundinanyother
flowsystemwhosepurposeistoprovideaccessbetweenonepointandanareaor
volume.Thinkofthetreesofelectronics,vascularizedtissues,andcitytraffic,and
you will get a sense of the universality of the principle that was used to generate
andtodiscoverthetreeconfiguration.
xiii