The sun’s warmth crosses millions of miles of empty space to create a summer day; a campfire roasts marshmallows from several feet away. Scientists have understood the mathematics behind this ghostly transfer of heat since the late 19th century. But that math breaks down at very close quarters — within, for example, nano-scale electronics and solar electricity cells (with components separated or spanning billionths of a meter) where heat transfer is critical.
In a recent study, a researcher at Princeton and colleagues at the Massachusetts Institute of Technology have come up with a formula that describes the maximum heat transfer in such tight scenarios. Surprisingly — and encouragingly — the formula suggests that a million times more heat transfer is possible between close objects than previously thought.
“We now have a ceiling for how much heat transfer we can expect,” said Alejandro Rodriguez, an assistant professor of electrical engineering at Princeton. “The fact that this ceiling is several orders of magnitude higher than has been previously demonstrated in existing material structures is extremely promising and will motivate further studies of this phenomenon and its many applications.”
The formula is the first major amendment to the math that describes radiative heating — the Stefan-Boltzmann law — since it was established in 1879. With this new formula, engineers will know how much more performance can be squeezed out of their structural and material designs. Potential uses could include trapping heat and converting it directly into electricity (in devices called thermophotovoltaics), as well as cooling off electronics components such as processors.
Rodriguez and his collaborators Owen Miller and Steven Johnson, both of MIT, described the work in a paper published in November in Physical Review Letters. (The work is further discussed in the journal Physics.) The work was funded by the National Science Foundation and the Air Force Office of Scientific Research.
“The paper presents very novel results that highlight the possibility of dramatically enhancing radiative heat transfer between bodies,” said Pramod Reddy, an associate professor of mechanical engineering and materials science and engineering at the University of Michigan who was not involved in the study. “These computational results are especially interesting and useful as they come at a time when long-desired experimental tools that are critical for testing these important predictions are becoming available.”