United States. Predicting heat transfer by radiation between extremely close objects has been difficult to achieve over the past 50 years. Now, mathematicians at the Massachusetts Institute of Technology (MIT) have derived a formula to determine the maximum amount of heat exchanged between two objects separated by distances shorter than the width of a hair.
For any pair of objects located at a mere distance in nanometers, the formula can be used to calculate most of the heat that one body can transmit to another, based on two parameters: what the objects are made of, and how far away they are.
The formula can help engineers identify optimal materials and designs for small, intricately stamped fine-tuned devices, such as thermophotovoltaic surfaces that convert thermal energy into electrical energy and cooling systems for computer chips.
As a sample, the scientists used the formula to calculate the maximum heat transfer between two metal plates of nanometer space, and found that the structures may be able to transmit orders of magnitude with more heat than they currently reach.
The researchers obtained a formula for determining the maximum heat transfer between two very close objects. To do this, they used an existing model that describes heat transfer by radiation as the electric currents that flow within the two objects. Such currents arise from fluctuating electric dipoles of each object, or, its distribution of negative and positive charges.
Using this model as a frame of reference, the team added two additional constraints: energy conservation, in which there is a limit between the amount of energy a body can absorb; and reciprocity, where each body can be treated as a source or receiver of heat. With this approach, the researchers obtained an equation to calculate the maximum amount of heat that two bodies can exchange in nanoscale separations.
The equation is generalizable and can be applied to any pair of objects, regardless of their shape. Scientists simply enter two parameters into the equation: separation distances, and certain material properties of each object – that is, the maximum amount of electric current that can accumulate in a given material.
