Constructal Design for Heat Conduction

Constructal law was firstly found by Professor Bejan of Duke University in 1996, inspired by the evolutionary nature of various natural systems and organizations (including life and non-life systems). The core of constructal theory is the constructal law, which states that for a finite-size flow system to persist in time (to live), its configuration must change in time such that it provides easier and easier access to its currents. Or more simply stated as: the structures of matters come from their optimal performances. Since the establishment of constructal theory, the theory has been applied to extensive subjects, including heat and mass transfer, fluid flow, electricity, magnetism, transport, piping network, weathering dry, economic decision-making, weather forecasting, geophysical problem and so on.

Constructal theory was initially applied to the heat conduction design, which mainly serves to illustrate how the constructal theory works in a specific application. However, this theory has opened up a new direction for theoretical researches on heat conduction problems. With the prosperity of electrical industries in recent decades, constructal design for heat conduction, which now plays a key role in the design of electrical devices, has attracted more and more attentions. Thus there is a need for a comprehensive book on constructal design for heat conduction. The authors were inspired to write this book and are hopeful that it will be very useful for the research, design and advancement of constructal design for heat conduction.

This book is mainly based on the research works performed by the authors ranging from the original, basic and approximate version to more accurate, complicated, but also most advanced ones, including different types of elements, kinds of heat conduction channels, with or without the optimized last-order construct premise and nonuniform heat generation. However, the relevant works were also included for the completeness of the book.

The content of this book is divided into 14 chapters. The first chapter presents the fundamental concepts of constructal theory and related theories, and reviews the development of constructal theory in almost all subjects. Chapters 2 introduces the original approximate constructal design for heat conduction and compared and analyzed the deviation between the approximate solution and the exact solution. Chapters 3 and 4 improve the constructal tree-like heat conduction network by releasing the premise of optimal last-order construct based on the rectangular and triangular elements, respectively. Chapter 5 studies the constructal design with variable cross-section conducting path, and chapter 6 extendes to the emitter grid resistance minimization for solar cell. Chapter 7 also optimizes the tree-like network based on variable cross-section conducting path, but without the premise of optimal last-order construct. Chapter 8 further introduces a discrete variable cross-section conducting path. Chapter 9 studies the “disc-to-point” heat conduction problem without the premise of optimal last-order construct. Chapters 10 to 14 study the constructal designs for heat conduction under the circumstance of nonuniform heat generation. Chapter 10 studies the constructal design based on rectangular element, while chapters 11 and 12 study those based on triangular element, and chapter 12 minimizes the entropy generation. Chapters 13 and 14 study the constructal designs for radial-pattern disc and tree-shaped disc, respectively.