Constructal Theory of Design in Nature Hits the Classroom

A novel design course offers undergraduates and graduate students at Duke’s Pratt School of Engineering an opportunity to apply “constructal theory” -- a fundamental principle describing natural patterns of flow -- to their own designs and to their understanding of design in nature.

Taught by the theory’s developer Adrian Bejan, a mechanical engineer at the Pratt School, and his collaborator Sylvie Lorente, a civil engineer from the Institut National des Sciences Appliques in France, the course ME166: Constructal Theory and Design, has been under development for four years with support from the National Science Foundation, and was recently approved as a permanent offering at Duke.

“By understanding how networks form naturally with constructal theory, students learn how to get to a design solution faster,” Bejan said.

“The classroom is the place where teaching meets research,” Lorente added. “We bring the latest research into the classroom and ideas sparked in the classroom through teaching later become research. It goes both ways.”

Bejan and Lorente describe the new course in a special issue of the International Journal of Engineering Education ( on the emergence of biological engineering. Bejan and Lorente have also begun a new book project based on the course. The textbook, “Design with Constructal Theory,” will be published by Wiley.

First conceived by Bejan in 1996, the constructal theory arises from the basic principle that flow systems evolve so as to minimize imperfections -- energy wasted to friction or other forms of resistance -- such that the least amount of useful energy is lost. The theory applies to virtually everything that moves, according to Bejan. For example, his earlier work has examined how the law explains traffic flows, the cooling of small-scale electronics, animal locomotion and global climate. Lorente said she has applied the theory to such practical applications as the study of water distribution in urban planning and the most efficient method of connecting buildings in Paris to a city-wide heating network.

The constructal theory’s general relevance has led to the view that it represents a fundamental law of nature. The theory also offers a new approach to engineering, Bejan said.

“What is new about this approach is the focus on the principle and method of generating geometry for energy systems with flows of fluid, heat, electricity and mass. The course is about design discovery–— the maximization of global performance subject to global constraints–— in engineered systems and natural systems as well,” Bejan and Lorente wrote.

“We believe this course offers the ideal mechanism for teaching the connection between engineering and nature, and for demonstrating to students the real-life importance of core courses – fluid mechanics, heat transfer and thermodynamics – in design.”

The course at Duke begins with the simplest examples and progresses to more complex, multi-disciplinary problems including multiple objectives, Bejan said. Each class includes examples, which are then extended by original problems proposed as homework.

Every student in the class is asked to develop an original topic in a term paper, and to defend it orally at the end of the course, the instructors said. For example, past Duke students have presented papers on topics including the universal shape of Egyptian pyramids, leaf venation, the branching of coral and hot-water networks for preventing the icing of bridges, Bejan said.

“This part of the course has been a source of real intellectual growth for all those enrolled in the course, and a source of new directions for inquiry in constructal theory and design,” he said.

This semester, students from departments including civil engineering, mechanical engineering and the masters of engineering management program have proposed projects applying constructal theory to the evolution in time of the Chinese alphabet, water flow through trees and the flow of goods and money through a city, among others.

The course has also been offered in shorter format to faculty and researchers in locations around the world, including the University of Evora, Portugal; the University of Lausanne, Switzerland; Yildiz University, Istanbul; and Memorial University, St. John’s, in Canada.