"The Many and the Few", Feature Article, July 2007

the many
and the few

In a parade of machines, a young engineer saw the principle that everything flows one way, from high to low.

by Adrian Bejan

ME 101 is the number of the thermodynamics course in mechanical engineering at Duke University. I cannot think of a better course for "ME101." It was put on the books by the old professors, the ones who had the vision to build Duke many decades ago. Today, I am sure, thermodynamics would get a less memorable course number.

Times change. Generations replace generations, but the principles remain. Contrivances, gadgets, and fads are the opposite. They parade in front of our eyes, but their impact on the "thin book" of fundamentals is nil.

I was reminded of this recently. I had just finished teaching thermodynamics for the semester when I visited two colleagues in Paris. With them I use constructal theory to predict the global weather. They work in a historic university called The National Conservatory of Arts and Professions (CNAM), a few blocks north of the Pompidou Center. It is historic for many ideas that persist today: evening classes for co-op students, continuing education, and the first museum of technology in the world.

A statue of French physicist Denis Papin (1647-1712), one of the inventors of the steam engine.

CNAM has a 300-year-old edifice with towers, an inner court, statues, clocks, and history that is chiseled in stone. In the front court, there is the statue of Denis Papin and the first piston-and-cylinder machine that expanded steam to produce work (1690). This was before the engine builders of Britain, and 80 years before James Watt.

Around the buildings, and around the ceilings of the oldest and most decorated classrooms, are the names of professors and students who breathed at CNAM. One name is Sadi Carnot. Without his work there would be no thermodynamics, engineering, or standard of living as we know them today.

Early in the 19th century, Sadi Carnot was a young engineer, not unlike my students today. He had graduated from the École Polytechnique. Tradition holds that he came to CNAM to contemplate, to think in quiet about the army of contrivances that was invading France: the steam engines. The industrial revolution was on the march. Britain had industrialized itself in the 1700s. A century later, it was the turn of the Continent to do the same.

Freedom Through Steam

Why were the steam engines invading? Because their effect on people's lives was good. It was dramatic. Engines were empowering people. They were liberating serfs, slaves, and animals. They were facilitating the movement of humanity all over the globe.

Sadi Carnot came to CNAM to study the machines that were on display. They were built by many hands-on engineers in Britain. These "many" fed the imagination of one individual. In turn, today Sadi Carnot's mental viewing feeds the minds of enormous numbers of builders of all sorts of machines throughout the world.

The principle that Sadi Carnot saw in that parade of machines is that everything flows one way, from high to low. Water flows through a pipe from high pressure to low pressure. Heat flows from high temperature to low temperature. This principle is known today as the second law of thermodynamics, irreversibility, dissipation, inefficiency, one way, water under the bridge, etc. Today, this is thermodynamics, the science of everything that kicks and moves.

The new principle that Carnot's visit at CNAM illustrates today is that one individual sustains the crowd, and vice versa. The big river sustains the many tiny streams of the river basin.

The reverse is equally true: The numerous sustain the singular. The river basin, like the tree of the lung, connects an entire area or volume to one point—flow resistances allocated to areas and volumes, all over the world, so the whole world flows best. This principle is the "constructal law"; to read more, see www.constructal.org.

Both principles—the second law and the constructal law—are in action. Their footprints persist, like the river beds and the beaten tracks. The river and the caravan that do not follow their beds and beaten tracks do not get far.

No flow system is an island. No river exists without its wet plain. No human settlement thrives without its farmland and open spaces. Everything that flowed to this day to "survive" is in an optimal balance with the flows that surround it and sustain it. The airflow to the alveolus is optimally matched to the blood flow through the vascularized tissue, and vice versa.

"Vascularized" is a good name for the energy systems that thermodynamics covers. The tissues of energy flows, like the fabric of society and all the tissues of biology, are optimized architectures. The climbing to this high level of performance is the transdisciplinary effort: the balance between seemingly unrelated flows, territories, and disciplines. This balancing act—the optimal distribution of imperfection—generates the very design of the process, power plant, city, geography, and economics.

All things that flow follow certain principles, whether it is the constructal design for maximum flow access from the center to the edge of a circle, or the delta of the River Lena in northern Siberia. The flow goes from high to low, with hierarchy and multiple scales.

The need for considering the whole—the macroscopic system—is great and universal. No matter how successful we are in discovering and understanding small-scale phenomena and processes, we are forced to face the challenge to assemble the invisible elements into palpable devices. The invisible grains must be kept alive with flows, which connect them and serve them. The challenge is to construct—that is, to connect and optimize while assembling.

This challenge is becoming increasingly difficult. While the smallest scales are becoming smaller, the number of components and the complexity of the useful device (always macroscopic) become greater.

A good example is the rush to nanotechnology. Technology means more than the new physical phenomena that may appear on the frontiers of progressively smaller scales. A technology is truly new when it is made useful in the form of macroscopic devices that improve our lives. Usefulness means that we must discover principles of constructing, connecting, and packing multiscale flow systems into macroscopic spaces.

And so I return to the start of this article. The new gadgets are like the engines in the invasion contemplated by Carnot. It's certain they will all be forgotten, unless there is a Sadi Carnot watching, to see a pattern and immortalize it with a short page in the thin book of principles. This happens only rarely, and when it does, it illustrates again the constructal principle of "one sustains the crowd."

Adrian Bejan is the J.A. Jones Distinguished Professor of
Mechanical Engineering at Duke University in Durham, N.C. His research covers thermodynamics, natural convection, heat and mass transfer, convection in porous media, and the constructal theory of organization in nature.