Nanotechnology Now

Our NanoNews Digest Sponsors
Heifer International



Home > Press > MIT mathematicians identify limits to heat flow at the nanoscale: New formula identifies limits to nanoscale heat transfer, may help optimize devices that convert heat to electricity

MIT mathematicians have identified the limits to heat flow at the nanoscale.
MIT mathematicians have identified the limits to heat flow at the nanoscale.

Abstract:
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.

MIT mathematicians identify limits to heat flow at the nanoscale: New formula identifies limits to nanoscale heat transfer, may help optimize devices that convert heat to electricity

Cambridge, MA | Posted on November 25th, 2015

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. "If that's practically achievable, that could make a huge difference in, for example, thermophotovoltaics."

Miller and his colleagues Steven Johnson, professor of applied mathematics at MIT, and Alejandro Rodriguez, assistant professor of electrical engineering at Princeton University, have published their results in Physical Review Letters.

Small scale, big effect

Since the late 1800s, scientists have used the Stefan-Boltzmann law to calculate the maximum amount of heat one body can transmit to another. This maximum heat transfer depends only on the two bodies' temperatures and can be reached only when both bodies are extremely opaque, absorbing all the heat that is radiated on them -- a theoretical notion known as the blackbody limit.

However, for objects smaller than the wavelength of heat -- about 8 micrometers -- scientists' established theories of heat transfer no longer apply. In fact, it appears that at the nanoscale, the amount of heat transmitted between objects actually exceeds that predicted by the blackbody limit, hundreds of times over.

As it turns out, when objects are extremely close together, heat flows not just as electromagnetic waves, but as evanescent waves -- exponentially decaying waves that have little effect at the macroscale, as they typically die away before reaching another object. At the nanoscale, however, evanescent waves can play a large role in heat transfer, tunneling between objects and essentially releasing trapped energy in the form of extra heat. Only in the last few years have Johnson and others at MIT, including Homer Reid, an applied mathematics instructor; Gang Chen, the Carl Richard Soderberg Professor of Power Engineering and head of the Department of Mechanical Engineering; and Mehran Kardar, the Francis Friedman Professor of Physics; begun to predict and quantify heat transfer at the nanoscale.

A surprisingly generalizable equation

Miller and his colleagues derived a formula for determining the maximum heat transfer between two extremely close objects. To do so, they used an existing model that describes radiative heat transfer as electrical currents flowing within two objects. Such currents arise from each object's fluctuating electric dipoles, or, its distribution of negative and positive charges.

Using this model as a framework, the team added two additional constraints: energy conservation, in which there is a limit to the amount of energy one body can absorb; and reciprocity, where each body may be treated as a source or receiver of heat. With this approach, the researchers derived a simple equation to calculate the maximum, or upper bound, of heat that two bodies may exchange at nanoscale separations.

The equation is surprisingly generalizable and can be applied to any pair of objects regardless of their shape. Scientists simply input two parameters into the equation: separation distance, and certain material properties of each object -- namely, the maximum amount of electric current that can build up in a given material.

"Now we have a formula for the upper bound," Johnson says. "Given the material and the separation you want, you'd just plug it into the formula and boom, you're done -- it's very easy. Now you can go backwards and try to play with materials and optimize them."

Johnson says engineers can use the formula to identify the best possible combination and orientation of materials for optimizing heat transfer in nanodevices such as thermophotovoltaics, which involves etching surfaces with very fine, intricate patterns to improve their heat-absorbing properties.

The team has done some preliminary work in exploring heat transfer between various materials at the nanoscale. Taking about 20 different materials from the periodic table -- mostly metals -- Miller calculated the maximum heat transfer between pairs of them, at extremely small separations.

"This is still ongoing work, but aluminum looks like it has a lot of potential if it can be designed properly," Miller says. "It has to be designed properly in order to achieve the limit, which is why people haven't seen large enhancements with such materials before, but this really opens up a new class of materials that may be used."

####

For more information, please click here

Contacts:
Abby Abazorius

617-253-2709

Copyright © Massachusetts Institute of Technology

If you have a comment, please Contact us.

Issuers of news releases, not 7th Wave, Inc. or Nanotechnology Now, are solely responsible for the accuracy of the content.

Bookmark:
Delicious Digg Newsvine Google Yahoo Reddit Magnoliacom Furl Facebook

Related News Press

News and information

Researchers develop artificial building blocks of life March 8th, 2024

How surface roughness influences the adhesion of soft materials: Research team discovers universal mechanism that leads to adhesion hysteresis in soft materials March 8th, 2024

Two-dimensional bimetallic selenium-containing metal-organic frameworks and their calcinated derivatives as electrocatalysts for overall water splitting March 8th, 2024

Curcumin nanoemulsion is tested for treatment of intestinal inflammation: A formulation developed by Brazilian researchers proved effective in tests involving mice March 8th, 2024

Physics

Nanoscale CL thermometry with lanthanide-doped heavy-metal oxide in TEM March 8th, 2024

Optically trapped quantum droplets of light can bind together to form macroscopic complexes March 8th, 2024

Scientists use heat to create transformations between skyrmions and antiskyrmions January 12th, 2024

Focused ion beam technology: A single tool for a wide range of applications January 12th, 2024

Discoveries

What heat can tell us about battery chemistry: using the Peltier effect to study lithium-ion cells March 8th, 2024

Researchers’ approach may protect quantum computers from attacks March 8th, 2024

High-tech 'paint' could spare patients repeated surgeries March 8th, 2024

Nanoscale CL thermometry with lanthanide-doped heavy-metal oxide in TEM March 8th, 2024

Materials/Metamaterials/Magnetoresistance

How surface roughness influences the adhesion of soft materials: Research team discovers universal mechanism that leads to adhesion hysteresis in soft materials March 8th, 2024

Nanoscale CL thermometry with lanthanide-doped heavy-metal oxide in TEM March 8th, 2024

Focused ion beam technology: A single tool for a wide range of applications January 12th, 2024

Catalytic combo converts CO2 to solid carbon nanofibers: Tandem electrocatalytic-thermocatalytic conversion could help offset emissions of potent greenhouse gas by locking carbon away in a useful material January 12th, 2024

Announcements

What heat can tell us about battery chemistry: using the Peltier effect to study lithium-ion cells March 8th, 2024

Curcumin nanoemulsion is tested for treatment of intestinal inflammation: A formulation developed by Brazilian researchers proved effective in tests involving mice March 8th, 2024

The Access to Advanced Health Institute receives up to $12.7 million to develop novel nanoalum adjuvant formulation for better protection against tuberculosis and pandemic influenza March 8th, 2024

Nanoscale CL thermometry with lanthanide-doped heavy-metal oxide in TEM March 8th, 2024

Interviews/Book Reviews/Essays/Reports/Podcasts/Journals/White papers/Posters

Researchers develop artificial building blocks of life March 8th, 2024

How surface roughness influences the adhesion of soft materials: Research team discovers universal mechanism that leads to adhesion hysteresis in soft materials March 8th, 2024

Curcumin nanoemulsion is tested for treatment of intestinal inflammation: A formulation developed by Brazilian researchers proved effective in tests involving mice March 8th, 2024

Nanoscale CL thermometry with lanthanide-doped heavy-metal oxide in TEM March 8th, 2024

Battery Technology/Capacitors/Generators/Piezoelectrics/Thermoelectrics/Energy storage

What heat can tell us about battery chemistry: using the Peltier effect to study lithium-ion cells March 8th, 2024

Two-dimensional bimetallic selenium-containing metal-organic frameworks and their calcinated derivatives as electrocatalysts for overall water splitting March 8th, 2024

Discovery of new Li ion conductor unlocks new direction for sustainable batteries: University of Liverpool researchers have discovered a new solid material that rapidly conducts lithium ions February 16th, 2024

A battery’s hopping ions remember where they’ve been: Seen in atomic detail, the seemingly smooth flow of ions through a battery’s electrolyte is surprisingly complicated February 16th, 2024

Research partnerships

Researchers’ approach may protect quantum computers from attacks March 8th, 2024

How surface roughness influences the adhesion of soft materials: Research team discovers universal mechanism that leads to adhesion hysteresis in soft materials March 8th, 2024

'Sudden death' of quantum fluctuations defies current theories of superconductivity: Study challenges the conventional wisdom of superconducting quantum transitions January 12th, 2024

Development of zinc oxide nanopagoda array photoelectrode: photoelectrochemical water-splitting hydrogen production January 12th, 2024

NanoNews-Digest
The latest news from around the world, FREE




  Premium Products
NanoNews-Custom
Only the news you want to read!
 Learn More
NanoStrategies
Full-service, expert consulting
 Learn More











ASP
Nanotechnology Now Featured Books




NNN

The Hunger Project