A novel formulation to explain heat propagation

February 11, 2020

Researchers at EPFL and MARVEL have developed a novel formulation that describes how heat spreads within crystalline materials. This can explain why and under which conditions heat propagation becomes fluid-like rather than diffusive. Their equations will make it easier to design next-generation electronic devices at the nanoscale, in which these phenomena can become prevalent.

Fourier's well-known heat equation describes how temperatures change over space and time when heat flows in a solid material. The formulation was developed in 1822 by Joseph Fourier, a French mathematician and physicist hired by Napoleon to increase a cannon's rate of fire, which was limited by overheating.

Fourier's equation works well to describe conduction in macroscopic objects (several millimeters in size or larger) and at high temperatures. However, it does not describe hydrodynamic heat propagation, which can appear in electronic devices containing materials such as graphite and graphene.

One of these heat-propagation phenomena is known as Poiseuille heat flow. This is where heat propagates within a material as a viscous-fluid flow. Another phenomenon, called "second sound," takes place when heat propagates in a crystal like a wave, similar to the way in which sound spreads through the air.

Since these phenomena are not described by Fourier's equation, until now researchers have analyzed them using explicit microscopic models, such as the Boltzmann transport equation. However, the complexity of these models means that they cannot be used to design complex electronic devices.

This problem has now been solved by Michele Simoncelli, a PhD student at EPFL, together with Andrea Cepellotti, a former EPFL PhD student now at Harvard, and Nicola Marzari, the chair of Theory and Simulation of Materials in the Institute of Materials at EPFL's School of Engineering and the director of NCCR MARVEL. They showed how heat originating from the atomic vibrations in a solid can be described rigorously by two novel "viscous heat equations", which extend Fourier's law to cover any heat propagation that is not diffusive.

"These viscous heat equations explain why and under which conditions heat propagation becomes fluid-like rather than diffusive. They show that heat conduction is governed not just by thermal conductivity, as described by Fourier's law, but also by a second parameter, thermal viscosity," says Simoncelli.

This breakthrough, published in Physical Review X, will help engineers design next-generation devices, particularly those that feature materials such as graphite or diamond in which hydrodynamic phenomena are prevalent. Overheating is the main limiting factor for the miniaturization and efficiency of electronic devices, and in order to maximize efficiency and predict whether a device will work - or simply melt - it is crucial to have the right model.

The results obtained by EPFL's team are timely. From the 1960s until recently, hydrodynamic heat phenomena had only been observed at cryogenic temperatures (around -260oC) and were therefore thought to be irrelevant for everyday applications. Already in 2015 Marzari and his colleagues predicted that this would be very different in two-dimensional and layered materials - a prediction that was confirmed with the publication in Science of pioneering experiments that found second-sound (or wavelike heat propagation) in graphite at temperatures around -170oC.

The formulation presented by the EPFL researchers yields results that line up closely with those experiments. Most important, they also predict that hydrodynamic heat propagation can also happen at room temperature, depending on the size and type of material.

Through their work, the EPFL researchers are providing new and original insight into heat transport, but also laying the groundwork for an understanding of shape and size effects - not only in next-generation electronic devices but also in "phononic" devices that control cooling and heating through engineered superstructures. Finally, the novel formulation can also be adapted to describe viscous phenomena involving electrons discovered in 2016 by Philip Moll, now a professor at EPFL's Institute of Materials.
For the mathematically inclined, these viscous heat equations were also immediately included in the documentation accompanying Wolfram Mathematica software (link).

Ecole Polytechnique Fédérale de Lausanne

Related Graphite Articles from Brightsurf:

Next-gen smartphones to keep their cool
Multilayered carbon material could be the perfect fit for heat management in electronic devices.

Ways to improve petroleum coke combustibility studied with presence of metal catalysts
The fixed fluidized bed technology is already widely used overseas, but is relatively new for the Russian oil industry.

Solvation rearrangement brings stable zinc/graphite batteries closer to commercial grid storage
A research team led by Prof. CUI Guanglei and ZHAO Jingwen from Qingdao Institute of Bioenergy and Bioprocess Technology (QIBEBT), Chinese Academy of Sciences (CAS) proposed an approach of solvation rearrangement that brings stable zinc/graphite batteries closer to commercial grid storage.

New advance in superconductors with 'twist' in rhombohedral graphite
An international research team led by The University of Manchester has revealed a nanomaterial that mirrors the 'magic angle' effect originally found in a complex man-made structure known as twisted bilayer graphene -- a key area of study in physics in recent years.

Serendipity broadens the scope for making graphite
Curtin University researchers have unexpectedly discovered a new way to make crystalline graphite, an essential material used in the making of lithium ion batteries.

Russian scientists identified energy storage mechanism of sodium-ion battery anode
Scientists unveiled pseudocapacitive behavior of hard carbon anode materials for sodium-ion batteries (SIB), a new promising class of electrochemical power sources.

Mysterious mechanism of graphene oxide formation explained
Natural graphite, used as the precursor for graphene oxide production, is a highly ordered crystalline inorganic material, which is believed to be formed by decay of organic matter.

Using Jenga to explain lithium-ion batteries
Tower block games such as Jenga can be used to explain to schoolchildren how lithium-ion batteries work, meeting an educational need to better understand a power source that has become vital to everyday life.

Skoltech scientists get a sneak peek of a key process in battery 'life'
Researchers from the Skoltech Center for Energy Science and Technology (CEST) visualized the formation of a solid electrolyte interphase on battery-grade carbonaceous electrode materials using in situ atomic force microscopy (AFM).

Ultrasonic technique discloses the identity of graphite
A group of researchers, led by Osaka University, created a high-quality defect-free monocrystalline graphite, and measured the elastic constant, demonstrating that the determined value of monocrystalline graphite was above 45 gigapascal (GPa), which was higher than conventionally believed.

Read More: Graphite News and Graphite Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.