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In an attempt to better regulate temperature in a variety of synthetic structures and gain a deeper understanding of biological systems, a newly published paper by researchers from the Cullen College of Engineering’s Civil and Environmental Engineering Department finds some surprising conclusions about using fluids to control temperature.

“Configuration-independent thermal invariants under flow reversal in thin vascular systems” was published recently in PNAS Nexus. Its lead author is Kalyana Nakshatrala, associate professor and associate chairman of the Civil and Environmental Engineering Department. Additional authors include Kripa Adhikari, a doctoral student of Nakshatrala at UH; Jason Patrick, an assistant professor in the Department of Civil, Construction, and Environmental Engineering at North Carolina State University; and Sandeep Rajendra Kumar, a student of Patrick.

Describing the initial stages of their research as curiosity-based, Nakshatrala said it was inspired by how living organisms control their internal temperature.

“Much like how mammals and birds regulate their body temperature through the circulation of blood in their vascular systems, we aim to mimic a similar mechanism in the synthetic world,” he said. “We want to modulate temperature by flowing a fluid through a network of vesicles embedded within the body. Surprisingly, we found several symmetries or invariances – Swapping the locations of the fluid’s inlet and outlet does not alter thermal efficiency.”

“What is remarkable is that the whole work started from mathematical scribbles on a yellow pad. Initially, we could not believe the 'surprising invariants' that the mathematical derivations revealed,” he said. “This is partly because the results are counterintuitive. Second, a minor mistake in the derivation, say a sign mistake, could give rise to a completely different outcome.”

Worried there could be an alternative but a simpler explanation to the surprising results, like a silly sign mistake in the derivation, Nakshatrala shared his findings with Gemunu Gunaratne, Moores Professor and the former chairman of the University of Houston's Department of Physics.

Gunaratne, who works on symmetries and invariances, also acknowledged the results were counterintuitive. He encouraged publishing the results and suggested the phrase “configuration-independent invariants,” which the authors used in the paper’s title.

“Whether ‘configuration-independent’ features have a function is a question that is not often addressed,” Gunaratne said. “In an impressive study, Professor Nakshatrala’s group demonstrates that in the case of thermal regulation, they do. This observation may have far-reaching consequences and may be useful in the optimal design of cooling in computers, robotics, and implantable devices, all of which critically need transport of heat away from a central device.”

Nakshatrala’s initial uneasiness disappeared eventually.

He added, “After multiple derivations, numerical simulations, and finally experimental evidence made us comfortable with the result.”

He also noted that the work is synoptic, multi-disciplinary and inter-institutional. While the team at UH developed those “mathematical scribbles” and “computer games,” the researchers at N.C. State ran the experiments to validate the results.

Adhikari was glad to be able to contribute to the research with Nakshatrala.

“I am deeply privileged and fortunate to have had the chance to contribute to this pioneering study,” she said. “Throughout the process of creating the paper, I had a great opportunity to acquire a wealth of knowledge, not just in terms of the research itself, but also with regard to the art of scientific writing, thanks to my advisor, Dr. Nakshatrala. The insights and expertise I have gained from this experience will undoubtedly prove invaluable in my current and future research endeavors.”

Nakshatrala and Adhikari said, “Several related research initiatives are currently underway utilizing and extending the findings presented in the paper. These endeavors span mathematical analysis, design optimization, and additive manufacturing with an overarching goal of mimicking nature and bringing various thermal regulation and active-cooling strategies to the synthetic world. Stay cool!”