The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

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Numerical Heat Transfer And Fluid Flow

Self-healing polymeric materials: A review of recent developments

Self-healing polymers and fiber-reinforced polymer composites possess the ability to heal in response to damage wherever and whenever it occurs in the material. This phenomenal material behavior is...

Self-Healing Polymers and Composites

Inspired by the unique and efficient wound healing processes in biological systems, several approaches to develop synthetic polymers that can repair themselves with complete, or nearly complete, autonomy have recently been developed. This review aims to survey the rapidly expanding field of self-healing polymers by reviewing the major successful autonomic repairing mechanisms developed over the last decade. Additionally, we discuss several issues related to transferring these self-healing technologies from the laboratory to real applications, such as virgin polymer property changes as a result of the added healing functionality, healing in thin films v. bulk polymers, and healing in the presence of structural reinforcements.

Self-healing polymers and composites

Constructal theory is the view that the generation of “designedness” in nature is a universal (physics) phenomenon that can be based on principle (the constructal law): “For a finite-size flow system to persist in time (to live) its configuration must change in time so that it provides greater and greater access to its currents”. This principle predicts natural form across the board, from river basins to animal design, engineering and social dynamics. In this introduction to the theory we show examples of vascular designs at large and small scales and multi-objective flow configurations.

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Design with constructal theory

Constructal theory is the view that the generation of flow configuration is a physics phenomenon that can be based on a physics principle (the constructal law): “For a finite-size flow system to persist in time (to survive) its configuration must evolve in such a way that it provides an easier access to the currents that flow through it” [A. Bejan, Advanced Engineering Thermodynamics, 2nd ed. (Wiley, New York, 1997); Int. J. Heat Mass Transfer, 40, 799 (1997)]. This principle predicts natural configuration across the board: river basins, turbulence, animal design (allometry, vascularization, locomotion), cracks in solids, dendritic solidification, Earth climate, droplet impact configuration, etc. The same principle yields new designs for electronics, fuel cells, and tree networks for transport of people, goods, and information. This review describes a paradigm that is universally applicable in natural sciences, engineering and social sciences.

Constructal theory of generation of configuration in nature and engineering

Contents Preface 1 Porous Media Fundamentals 1.1 Structure 1.1.1 Microporous Media 1.1.2 Mesoporous Media 1.1.3 Macroporous Media 1.2 Mass Conservation 1.3 Darcy Flow and More Advanced Models 1.4 Energy Conservation 1.5 Heat and Mass Transfer 1.5.1 Fluid Flow 1.5.2 Heat Flow 2 Flows in Porous Media 2.1 Use Simple Methods First 2.2 Scale Analysis of Forced Convection Boundary Layers 2.3 Sphere and Cylinder with Forced Convection 2.4 Channels with Porous Media and Forced Convection 2.5 Scale Analysis of Natural Convection Boundary Layers 2.6 Thermal Stratification and Vertical Partitions 2.7 Horizontal Walls with Natural Convection 2.8 Sphere and Horizontal Cylinder with Natural Convection 2.9 Enclosures Heated from the Side 2.10 Enclosures Heated from Below 2.11 The Method of Intersecting the Asymptotes 2.11.1 The Many Counterflows Regime 2.11.2 The Few Plumes Regime 2.11.3 The Intersection of Asymptotes 3 Energy Engineering 3.1 Thermodynamics Fundamentals: Entropy Generation or Exergy Destruction 3.2 Exergy Analysis 3.3 Thermal Energy Storage 3.4 Sensible Heat Storage 3.5 Aquifer Thermal Energy Storage 3.6 Latent Heat Storage 3.7 Cold Thermal Energy Storage 3.8 Porous Medium Model of a Storage System with Phase-Change Material 3.9 Fuel Cell Principles and Operation 3.10 Fuel Cell Structure and Performance 3.11 The Concept of Exergy-Cost-Energy-Mass (EXCEM) Analysis 3.12 Exergy, Environment, and Sustainable Development 4 Environmental and Civil Engineering 4.1 The Energy-Environment Interface 4.2 Wakes: Concentrated Heat Sources in Forced Convection 4.3 Plumes: Concentrated Heat Sources in Natural Convection 4.4 Penetrative Convection 4.5 Aerosol Transport and Collection in Filters 4.6 Filter Efficiency and Filtration Theories 4.7 Pressure Drop, Permeability,and Filter Performance 4.8 Ionic Transport 4.9 Reactive Porous Media 4.10 Electrodiffusion 4.11 Tree-Shaped Flow Networks 4.12 Optimal Size of Flow Element 4.13 Hot Water Distribution Networks 4.14 Minimal Resistance Versus Minimal Flow Length 5 Compact Heat Transfer Flow Structures 5.1 Heat Exchangers as Porous Media 5.2 Optimal Spacings in Natural Convection 5.3 Optimal Spacings in Forced Convection 5.4 Pulsating Flow 5.5 Optimal Packing of Fibrous Insulation 5.6 Optimal Maldistribution: Tree-Shaped Flows 5.7 Dendritic Heat Exchangers 5.7.1 Elemental Volume 5.7.2 First Construct 5.7.3 Second Construct 5.8 Constructal Multiscale Structure for Maximal Heat Transfer Density 5.8.1 Heat Transfer 5.8.2 Fluid Friction 5.8.3 Heat Transfer Rate Density: The Smallest Scale 5.9 Concluding Remarks 6 Living Structures 6.1 Respiratory System 6.1.1 Airflow Within the Bronchial Tree 6.1.2 Alveolar Gas Diffusion 6.1.3 Particle Deposition 6.2 Blood and the Circulatory System 6.3 Biomembranes: Structure and Transport Mechanisms 6.3.1 Cell Membrane 6.3.2 Capillary Wall 6.4 Transport of Neutral Solutes Across Membranes 6.5 Transport of Charged Solutes Across Membranes 6.5.1 Membrane Potential 6.5.2 Electrical Equivalent Circuit 6.6 The Kidney and the Regulation of Blood Composition 6.6.1 Kidney Failure and Dialysis 6.6.2 Pumping Blood Through Semipermeable Membranes 7 Drying of Porous Materials 7.1 Introduction 7.2 Drying Equipment 7.3 Drying Periods 7.4 Basic Heat and Moisture Transfer Analysis 7.5 Wet Material 7.6 Types of Moisture Diffusion 7.7 Shrinkage 7.8 Modeling of Packed-Bed Drying 7.9 Diffusion in Porous Media with Low Moisture Content 7.10 Modeling of Heterogeneous Diffusion in Wet Solids 7.10.1 Mass Transfer 7.10.2 Heat Transfer 7.10.3 Boundary Cond

Porous and Complex Flow Structures in Modern Technologies

The constructal law and the evolution of design in nature.

This is a review of the theoretical and applied progress made based on the Constructal law of design and evolution in nature, with emphasis on the last decade. The Constructal law is the law of physics that accounts for the natural tendency of all flow systems (animate and inanimate) to change into configurations that offer progressively greater flow access over time. The progress made with the Constructal law covers the broadest range of science, from heat and fluid flow and geophysics, to animal design, technology evolution, and social organization (economics, government). This review presents the state of this fast growing field, and draws attention to newly opened directions for original research. The Constructal law places the concepts of life, design, and evolution in physics.

Sylvie Lorente

Papers

Design with constructal theory

Constructal theory of generation of configuration in nature and engineering

Porous and Complex Flow Structures in Modern Technologies

The constructal law and the evolution of design in nature.

Constructal law of design and evolution: Physics, biology, technology, and society