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March 28th, 2012

‘Transformation thermodynamics’ shows potential of thermal invisibility cloaking

Published on March 28th, 2012 | By: Eileen De Guire
The object in the center of the thermal cloak (letters OSA) stays cold, while the heat diffuses elsewhere. The source of the heat is on the left-hand side and held constant at 100°C, and the material inside the invisibility region remains cold. Credit: Sebastien Guenneau; Institut Fresnel, CNRS/AMU.

Managing heat is no small issue, but so far it’s been done mostly by more-or-less brute force methods: keep it away, diffuse it away or blow it away. Truthfully, they work pretty well, but it’s easy to imagine situations where a more subtle approach would be desirable. For example, as devices shrink into the micro- and nano-range, applying traditional methods of heat management may be tricky. What kind of fan does one use to cool an array of nanodevices?

What if heat could be guided, though, similar to the way light is guided? With the development of metamaterials, there is the opportunity to custom design new materials with specific, tuned properties. Might it be possible to make a waveguide-type device of metamaterials for heat?

Such thinking is familiar territory for optics scientists. The idea of optical cloaking is based on the physics of transformation optics, where metamaterials are used to bend and propagate light around a space rather than through it.

A French group wondered whether a similar approach could be used to guide heat around an object. Sebastien Guenneau and colleagues have just published a paper (pdf) in the Optical Society’s open access journal, Optics Express, where they go through the mathematics and show that the concept is feasible. In a news release, Guenneau said, “Our key goal with this research was to control the way heat diffuses in a manner similar to those that have already been achieved for waves, such as light waves, by using the tools of transformation optics.”

But, there are some important differences in the way the mathematics is applied. Transformation optics is based on elliptic wave equations. Transformation thermodynamics, however, is governed by the parabolic heat equation. Guenneau puts it, “Heat isn’t a wave — it simply diffuses from hot to cold regions. The mathematics and physics at play are much different. For instance, a wave can travel long distances with little attenuation, whereas temperature usually diffuses over smaller distances.”

In the paper, the team focuses on the two-dimensional case. Heat flows from a hot region to a cool object. The heat flux in a given region is represented by the distance between isotherms, which they define as concentric rings of diffusivity. The geometry of the isotherms is altered to force them to go around, rather than through, the cool object, effectively shielding the object from the flow of heat. They make the important assumption that material properties are not temperature dependent, however, they say temperature dependence can be accommodated in their approach.

The paper outlines an approach to constructing a thermal invisibility cloak device based on a multilayer metamaterials coating “consisting of 20 homogeneous concentric layers with a piecewise constant isotropic diffusivity.” Basically, it is a precisely tuned, custom-designed functionally gradient coating. And, while the authors imagine devices made of metamaterials, they note in the paper that the material properties are not too far afield from real materials. For example, if the cool object is polyvinyl chloride, silver would be a suitable innermost layer of the cloak.

It is also interesting, that like a prism that can split light or focus it, the same mathematical approach can be used to create a device that concentrates heat rather than channel it.

It might not be much of a leap to imagine nanoscale photovoltaic devices with nanoscale concentrators. Cyrus Wadia, the White House OSTP’s Materials Genome shepherd, did his PhD work on nanostructured photovoltaic solar cells. In this paper (pdf), he and his coauthors synthesized nanostructured Cu2S and demonstrated the feasibility of a functioning nanocrystal photovoltaic cells made of Cu2S-CdS deposited on ITO-coated plastic. If the substrate had heat concentration materials built in, a fully integrated PV device might be achievable.

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