Design with Constructal Theory

ADRIAN BEJAN, PhD, is the J. A. Jones Distinguished Professor of Mechanical Engineering at Duke University. SYLVIE LORENTE, PhD, is Full Professor of Civil Engineering at the University of Toulouse, INSA, The Laboratory of Materials and Durability of Constructions.

"This book represents the outcome of over 12 years of research and teaching by the authors on constructal theory and its application. It provides comprehensive and elegant discussion of a revolutionary new approach for understanding and predicting the designs that arise in both nature and engineering, from the  tree and the forest to the cooling of electronics, urban design, decontamination, and vascular smart materials. This book is highly recommended for everyone, especially students and professionals in mechanical, civil, environmental, energy and power, chemical, aerospace, and biomedical engineering, as well in geophysics and biology." (International Journal of Energy Research, 2010) "The constructal law provides a broad coverage of "designedness" everywhere, from engineering to geophysics and biology….it provides the student with strategy for how to pursue and discover design-the configurations or patterns-in both space and time. Constructal theory pushes design thinking closer to science and away from art. It tears down the walls between engineering and natural sciences." (Mechanical Engineering, September 2009)"A balance between individual and institutional approaches is the best idea, according to a new theory by a Duke University engineer Adrian Bejan, who thinks institutions benefit most from the co-existence of large groups that self-organize naturally and lone scientists coming up with brilliant new ideas…. big thinkers didn't disappear. Bejan argues they continued to thrive. He thinks his "constructal theory," which he began describing in 1996, might explain why. The theory states that so-called flow systems evolve to balance and minimize imperfections, reducing friction or other forms of resistance, so that the least amount of useful energy is lost. Examples in nature include rivers and streams that make up a delta or the intricate airways of the lungs. In research done by humans, Bejan sees two main flows: those of ideas in the form of scientific findings, and those of support, measured by tangible factors such as funding and lab space." (Robert Roy Brit, LiveScience.com, Yahoo.news.com, December 2008)"Design with Constructal Theory offers a revolutionary new approach to design based on physics for understanding and predicting the designs that arise in nature and engineering…This book shows how you can use the method of constructal theory to design human-made systems in order to reduce trial and error and increase the system performance. It is beautifully illustrated, in color and black & white. This book is highly recommended to professors, students and professionals in mechanical, civil, environmental, chemical, aerospace and biomedical engineering. It is recommended to all the readers interested in design in nature, and in design as science, strategy, and novel and effective designs." (International Journal of Heat and Mass Transfer, 11/12/08)

• About the Authors xiPreface xiiiList of Symbols xvii1. Flow Systems 11.1 Constructal Law, Vascularization, and Svelteness 11.2 Fluid Flow 61.2.1 Internal Flow: Distributed Friction Losses 71.2.2 Internal Flow: Local Losses 111.2.3 External Flow 181.3 Heat Transfer 201.3.1 Conduction 201.3.2 Convection 24References 31Problems 312. Imperfection 432.1 Evolution toward the Least Imperfect Possible 432.2 Thermodynamics 442.3 Closed Systems 462.4 Open Systems 512.5 Analysis of Engineering Components 522.6 Heat Transfer Imperfection 562.7 Fluid Flow Imperfection 572.8 Other Imperfections 592.9 Optimal Size of Heat Transfer Surface 61References 62Problems 633. Simple Flow Configurations 733.1 Flow Between Two Points 733.1.1 Optimal Distribution of Imperfection 733.1.2 Duct Cross Sections 753.2 River Channel Cross-Sections 783.3 Internal Spacings for Natural Convection 813.3.1 Learn by Imagining the Competing Extremes 813.3.2 Small Spacings 843.3.3 Large Spacings 853.3.4 Optimal Spacings 863.3.5 Staggered Plates and Cylinders 873.4 Internal Spacings for Forced Convection 893.4.1 Small Spacings 903.4.2 Large Spacings 903.4.3 Optimal Spacings 913.4.4 Staggered Plates, Cylinders, and Pin Fins 923.5 Method of Intersecting the Asymptotes 943.6 Fitting the Solid to the “Body” of the Flow 963.7 Evolution of Technology: From Natural to Forced Convection 98References 99Problems 1014. Tree Networks for Fluid Flow 1114.1 Optimal Proportions: T –and Y -Shaped Constructs 1124.2 Optimal Sizes, Not Proportions 1194.3 Trees Between a Point and a Circle 1234.3.1 One Pairing Level 1244.3.2 Free Number of Pairing Levels 1274.4 Performance versus Freedom to Morph 1334.5 Minimal-Length Trees 1364.5.1 Minimal Lengths in a Plane 1374.5.2 Minimal Lengths in Three Dimensions 1394.5.3 Minimal Lengths on a Disc 1394.6 Strategies for Faster Design 1444.6.1 Miniaturization Requires Construction 1444.6.2 Optimal Trees versus Minimal-Length Trees 1454.6.3 75 Degree Angles 1494.7 Trees Between One Point and an Area 1494.8 Asymmetry 1564.9 Three-Dimensional Trees 1584.10 Loops, Junction Losses and Fractal-Like Trees 161References 162Problems 1645. Configurations for Heat Conduction 1715.1 Trees for Cooling a Disc-Shaped Body 1715.1.1 Elemental Volume 1735.1.2 Optimally Shaped Inserts 1775.1.3 One Branching Level 1785.2 Conduction Trees with Loops 1895.2.1 One Loop Size, One Branching Level 1905.2.2 Radial, One-Bifurcation and One-Loop Designs 1955.2.3 Two Loop Sizes, Two Branching Levels 1975.3 Trees at Micro and Nanoscales 2025.4 Evolution of Technology: From Forced Convection to Solid-Body Conduction 206References 209Problems 2106. Multiscale Configurations 2156.1 Distribution of Heat Sources Cooled by Natural Convection 2166.2 Distribution of Heat Sources Cooled by Forced Convection 2246.3 Multiscale Plates for Forced Convection 2296.3.1 Forcing the Entire Flow Volume to Work 2296.3.2 Heat Transfer 2326.3.3 Fluid Friction 2336.3.4 Heat Transfer Rate Density: The Smallest Scale 2346.4 Multiscale Plates and Spacings for Natural Convection 2356.5 Multiscale Cylinders in Crossflow 2386.6 Multiscale Droplets for Maximum Mass Transfer Density 241References 245Problems 2477. Multiobjective Configurations 2497.1 Thermal Resistance versus Pumping Power 2497.2 Elemental Volume with Convection 2507.3 Dendritic Heat Convection on a Disc 2577.3.1 Radial Flow Pattern 2587.3.2 One Level of Pairing 2657.3.3 Two Levels of Pairing 2677.4 Dendritic Heat Exchangers 2747.4.1 Geometry 2757.4.2 Fluid Flow 2777.4.3 Heat Transfer 2787.4.4 Radial Sheet Counterflow 2847.4.5 Tree Counterflow on a Disk 2867.4.6 Tree Counterflow on a Square 2897.4.7 Two-Objective Performance 2917.5 Constructal Heat Exchanger Technology 2947.6 Tree-Shaped Insulated Designs for Distribution of Hot Water 2957.6.1 Elemental String of Users 2957.6.2 Distribution of Pipe Radius 2977.6.3 Distribution of Insulation 2987.6.4 Users Distributed Uniformly over an Area 3017.6.5 Tree Network Generated by Repetitive Pairing 3077.6.6 One-by-One Tree Growth 3137.6.7 Complex Flow Structures Are Robust 318References 325Problems 3288. Vascularized Materials 3298.1 The Future Belongs to the Vascularized: Natural Design Rediscovered 3298.2 Line-to-Line Trees 3308.3 Counterflow of Line-to-Line Trees 3348.4 Self-Healing Materials 3438.4.1 Grids of Channels 3448.4.2 Multiple Scales, Loop Shapes, and Body Shapes 3528.4.3 Trees Matched Canopy to Canopy 3558.4.4 Diagonal and Orthogonal Channels 3628.5 Vascularization Fighting against Heating 3648.6 Vascularization Will Continue to Spread 369References 371Problems 3739. Configurations for Electrokinetic Mass Transfer 3819.1 Scale Analysis of Transfer of Species through a Porous System 3819.2 Model 3859.3 Migration through a Finite Porous Medium 3879.4 Ionic Extraction 3939.5 Constructal View of Electrokinetic Transfer 3969.5.1 Reactive Porous Media 4009.5.2 Optimization in Time 4019.5.3 Optimization in Space 403References 40510. Mechanical and Flow Structures Combined 40910.1 Optimal Flow of Stresses 40910.2 Cantilever Beams 41110.3 Insulating Wall with Air Cavities and Prescribed Strength 41610.4 Mechanical Structures Resistant to Thermal Attack 42410.4.1 Beam in Bending 42510.4.2 Maximization of Resistance to Sudden Heating 42710.4.3 Steel-Reinforced Concrete 43110.5 Vegetation 44210.5.1 Root Shape 44310.5.2 Trunk and Canopy Shapes 44610.5.3 Conical Trunks, Branches and Canopies 44910.5.4 Forest 453References 458Problems 45911. Quo Vadis Constructal Theory? 46711.1 The Thermodynamics of Systems with Configuration 46711.2 Two Ways to Flow Are Better than One 47011.3 Distributed Energy Systems 47311.4 Scaling Up 48211.5 Survival via Greater Performance, Svelteness and Territory 48311.6 Science as a Consructal Flow Architecture 486References 488Problems 490Appendix 491A. The Method of Scale Analysis 491B. Method of Undetermined Coefficients (Lagrange Multipliers) 493C. Variational Calculus 494D. Constants 495E. Conversion Factors 496F. Dimensionless Groups 499G. Nonmetallic Solids 499H. Metallic Solids 503I. Porous Materials 507J. Liquids 508K. Gases 513References 516Author Index 519Subject Index 523