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The Thermodynamics of Roof Design: A Study by Adrian Bejan

During his tenure as a visiting professor in Benevento, a town located just outside Naples, Italy, Adrian Bejan made an intriguing observation about the region’s architecture: the roofs of the buildings shared a striking similarity in design. Featuring peaks that appeared too shallow, especially on the older structures, Bejan contemplated whether this uniformity was simply a stylistic choice of the era or if it had a deeper, practical foundation.

As an accomplished expert in thermodynamics, especially in the realms of heat movement and transfer, Bejan, who is the J.A. Jones Distinguished Professor of Mechanical Engineering at Duke University, set out to investigate the matter further. His analytical approach involved meticulous calculations pertinent to the behavior of heat flow in relation to roof designs.

Alongside Pezhman Mardanpour, an assistant professor of mechanical and materials engineering at Florida International University, Bejan published findings on March 28, 2023, in the journal International Communications of Heat and Mass Transfer. Their research revealed specific roof shapes that optimize heat retention, suggesting that these historical Italian architects were indeed privy to essential principles of thermodynamics.

“Pockets of air function as effective insulators, and attics can be viewed as uniquely shaped air pockets,” Bejan explained. “While the concept of energy conservation is often discussed today, it was once essential for the survival of past generations.”

In understanding how the shape and height of a roof influences the behavior of air trapped within, the study drew interesting conclusions. For an A-frame or conical roof, if the peak stands less than three feet tall, the airflow behaves fluidly, akin to water flowing smoothly down a sink. Conversely, should the peak exceed three feet, the air moves more unpredictably, akin to smoke being swept by the wind.

The research indicated that a roof with a peak lower than approximately three feet should ideally be three to four times wider than it is tall to minimize heat loss. In contrast, if the peak exceeds three feet, the optimal design appears as an equilateral triangle, where the height and width share a ratio of one to one.

Intriguingly, these ratios resonate with those observed in numerous older, modest homes globally, mirroring the architectural styles Bejan noted during his visit to Italy.

“This kind of insight is straightforward to understand, yet often overlooked despite its prevalence,” Bejan remarked. “It’s essential for us, including students and educators, to think deeply and question the rationale behind design choices.”

While Bejan speculates that ancient architects may not have directly applied thermodynamic principles to their designs, he believes that their choices were not merely coincidental. Over generations, homeowners likely observed their neighbors’ homes and adapted their designs to optimize warmth and comfort.

He emphasizes that contemporary architects should also reflect on these findings. “Buildings today are crafted with energy efficiency in mind, yet it seems that the physical architecture itself is rarely considered as a factor in enhancing efficiency. This is an area we should certainly explore further,” Bejan concluded.

This research received backing from the U.S. Air Force Office of Scientific Research.

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