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Design with Constructal Theory

ISBN: 978-0-471-99816-7
552 pages
September 2008
Design with Constructal Theory (0471998168) cover image
Design course on the universal principle of configurations in nature and engineering-the constructal law

Design with Constructal Theory offers a revolutionary new approach based on physics for understanding and predicting the designs that arise in nature and engineering, from the tree and the forest to the cooling of electronics, urban design, decontamination, and vascular smart materials. 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.

First developed in the late 1990s, constructal theory holds that flow architecture arises from the natural evolutionary tendency to generate greater flow access in time and in flow configurations that are free to morph. It unites flow systems with solid mechanical structures, which are viewed as systems for the flow of stresses. Constructal theory unites nature with engineering, and helps us generate novel designs across the board, from high-density packages to vascular materials with new functionalities (self-healing, self-cooling), and from tree-shaped heat exchangers to svelte fluid-flow and solid structures.

Design with Constructal Theory starts with basic principles and then shows how these principles are applied to understanding and designing increasingly complex systems. Problems and exercises at the end of each chapter give you an opportunity to use constructal theory to solve actual design problems.

This book is based on a design course developed by the two authors for upper-level undergraduates and graduate students at Duke University and other universities all over the world. With the authors' expert guidance, students and professionals in mechanical, civil, environmental, chemical, aerospace, and biomedical engineering will understand natural systems, and then practice design as science, by relying on constructal strategies to pursue and discover novel and effective designs.

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About the Authors.


List of Symbols.

1. Flow Systems.

1.1 Constructal Law, Vascularization, and Svelteness.

1.2 Fluid Flow.

1.3 Heat Transfer.

1.3.1 Conduction.

1.3.2 Convection.



2. Imperfection.

2.1 Evolution toward the Least Imperfect Possible.

2.2 Thermodynamics.

2.3 Closed Systems.

2.4 Open Systems.

2.5 Analysis of Engineering Components.

2.6 Heat Transfer Imperfection.

2.7 Fluid Flow Imperfection.

2.8 Other Imperfections.

2.9 Optimal Size of Heat Transfer Surface.



3. Simple Flow Configurations.

3.1 Flow Between Two Points.

3.2 River Channel Cross-Sections.

3.3 Internal Spacings for Natural Convection.

3.4 Internal Spacings for Forced Convection.

3.5 Method of Intersecting the Asymptotes.

3.6 Fitting the Solid to the “Body” of the Flow.

3.7 Evolution of Technology: From Natural to Forced Convection.



4. Tree Networks for Fluid Flow.

4.1 Optimal Proportions: T- and Y -Shaped Constructs.

4.2 Optimal Sizes, Not Proportions.

4.3 Trees Between a Point and a Circle.

4.4 Performance versus Freedom to Morph.

4.5 Minimal-Length Trees.

4.6 Strategies for Faster Design.

4.7 Trees Between One Point and an Area.

4.8 Asymmetry.

4.9 Three-Dimensional Trees.

4.10 Loops, Junction Losses and Fractal-Like Trees.



5. Configurations for Heat Conduction.

5.1 Trees for Cooling a Disc-Shaped Body.

5.2 Conduction Trees with Loops.

5.3 Trees at Micro and Nanoscales.

5.4 Evolution of Technology: From Forced Convection to Solid-Body Conduction.



6. Multiscale Configurations.

6.1 Distribution of Heat Sources Cooled by Natural Convection.

6.2 Distribution of Heat Sources Cooled by Forced Convection.

6.3 Multiscale Plates for Forced Convection.

6.4 Multiscale Plates and Spacings for Natural Convection.

6.5 Multiscale Cylinders in Crossflow.

6.6 Multiscale Droplets for Maximum Mass Transfer Density.



7. Multiobjective Configurations.

7.1 Thermal Resistance versus Pumping Power.

7.2 Elemental Volume with Convection.

7.3 Dendritic Heat Convection on a Disc.

7.4 Dendritic Heat Exchangers.

7.5 Constructal Heat Exchanger Technology.

7.6 Tree-Shaped Insulated Designs for Distribution of Hot Water.



8. Vascularized Materials.

8.1 The Future Belongs to the Vascularized: Natural Design Rediscovered.

8.2 Line-to-Line Trees.

8.3 Counterflow of Line-to-Line Trees.

8.4 Self-Healing Materials.

8.5 Vascularization Fighting against Heating.

8.6 Vascularization Will Continue to Spread.



9. Configurations for Electrokinetic Mass Transfer.

9.1 Scale Analysis of Transfer of Species through a Porous System.

9.2 Model.

9.3 Migration through a Finite Porous Medium.

9.4 Ionic Extraction.

9.5 Constructal View of Electrokinetic Transfer.


10. Mechanical and Flow Structures Combined.

10.1 Optimal Flow of Stresses.

10.2 Cantilever Beams.

10.3 Insulating Wall with Air Cavities and Prescribed Strength.

10.4 Mechanical Structures Resistant to Thermal Attack.

10.5 Vegetation.



11. Quo Vadis Constructal Theory?

11.1 The Thermodynamics of Systems with Configuration.

11.2 Two Ways to Flow Are Better than One.

11.3 Distributed Energy Systems.

11.4 Scaling Up.

11.5 Survival via Greater Performance, Svelteness and Territory.

11.6 Science as a Consructal Flow Architecture.




A. The Method of Scale Analysis.

B. Method of Undetermined Coefficients (Lagrange Multipliers).

C. Variational Calculus.

D. Constants.

E. Conversion Factors.

F. Dimensionless Groups.

G. Nonmetallic Solids.

H. Metallic Solids.

I. Porous Materials.

J. Liquids.

K. Gases.


Author Index.

Subject Index.

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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.

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"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)

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Constructal Theory Web PortalHome page of Adrian Bejan's website devoted to the 'Constructal Theory' also a portal and clearinghouse for information on this theory.
http://www.duke.edu/today/archive/oncamera.php?id=11138 Adrian Bejan talks about his 'Constructal Theory' in an informative interview
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Instructors Resources
Wiley Instructor Companion Site
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