Research Topic

Topic: Nanoscale Heat Transfer
Team: Amit Singh, Ellad Tadmor
Funding: AFOSR
Figure:
A schematic showing heat transfer in a nanoscale bar. A temperature gradient
is established by maintaining the two ends at different temperatures using
numerical thermostats. As a result, heat flows from the hot end to the cold
end. In nanoscale systems, heat propagates as wave with a finite velocity
(called second sound) and is therefore better described by a nonFourier
heat transfer model.

Description:
Fourier's law leads to a diffusive model of heat transfer in which a thermal signal propagates infinitely fast and the only material parameter is the thermal conductivity. In micro and nanoscale systems, nonFourier effects involving coupled diffusion and wavelike propagation of heat can become important. An extension of Fourier's law to account for such effects leads to a Jeffreystype model for heat transfer with two relaxation times. We propose a new Thermal Parameter Identification (TPI) method for obtaining the Jeffreystype thermal parameters from molecular dynamics simulations. The TPI method makes use of a nonlinear regressionbased approach for obtaining the coefficients in analytical expressions for cosine and sineweighted averages of temperature and heat flux over the length of the system. The method is applied to argon nanobeams over a range of temperature and system sizes. The results for thermal conductivity are found to be in good agreement with standard GreenKubo and direct method calculations. The TPI method is more efficient for systems with high diffusivity and has the advantage, that unlike the direct method, it is free from the influence of thermostats. In addition, the method provides the thermal relaxation times for argon. Using the determined parameters, the Jeffreystype model is able to reproduce the molecular dynamics results for a shortduration heat pulse where wavelike propagation of heat is observed thereby confirming the existence of second sound in argon.
Software:

Thermal Parameter Identification (TPI): TPI is a method for computing the thermal parameters associated with the nonFourier CattaneoVernotte and Jefreystype models for heat transfer (thermal conductivity and one or two relaxation times) from a series of predesigned nonequilibrium molecular dynamics (MD) simulations. The code and files necessary to carry out a TPI calculation are freely available. The TPI archive, which contains documentation for using the method, input files and extensions needed to use the LAMMPS MD program to perform the required MD simulations, and a MATLAB program for processing the LAMMPS output to obtain the thermal parameters, is available here (gzipped tar file). (To unpack the pacakge, use the following Linux/Unix command: "tar zxvf tpiv2.tgz". This will create the directory TPI_v2. To start, read the README file in this directory.)
Publications:

"Thermal parameter identification for nonFourier heat transfer from molecular dynamics",
A. Singh and E. B. Tadmor,
Journal of Computational Physics, 299, 667–686 (2015).
pdf  doi  bibtex

"Removing artificial Kapitza effects from bulk thermal conductivity calculations in direct molecular dynamics",
A. Singh and E. B. Tadmor,
Journal of Applied Physics, 117, 185101 (2015).
pdf  doi  bibtex