MIT mathematicians have identified the limits to heat flow at the nanoscale.
How much heat can two bodies exchange without touching? For over a century, scientists have been able to answer this question for virtually any pair of objects in the macroscopic world, from the rate at which a campfire can warm you up, to how much heat the Earth absorbs from the sun. But predicting such radiative heat transfer between extremely close objects has proven elusive for the past 50 years. Now, MIT mathematicians have derived a formula for determining the maximum amount of heat exchanged between two objects separated by distances shorter than the width of a single hair. For any two objects situated mere nanometers apart, the formula can be used to calculate the most heat one body may transmit to another, based on two parameters: what the objects are made of, and how far apart they are. The formula may help engineers identify optimal materials and designs for tuning small, intricately patterned devices, such as thermophotovoltaic surfaces that convert thermal energy into electrical energy, and cooling systems for computer chips. As a demonstration, the scientists used their formula to calculate the maximum heat transfer between two nanometer-spaced metal plates, and found that the structures may be able to transmit orders of magnitude more heat than they currently achieve. "This [formula] provides a target to say, 'this is what we should be looking for,' and compared to what we've seen so far in simple structures, there's orders of magnitude more room for improvement for this kind of heat transfer," says Owen Miller, a postdoc in the Department of Mathematics.
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