Non-equilibrium Phonon Green’s Function Simulation and Its Application to Carbon Nanotubes - Nanoscale Energy Transport and Harvesting - page 59

Chapter 2

Non-equilibrium Phonon Green's
Function Simulation and Its Application
to Carbon Nanotubes

Takahiro Yamamoto, a,b Kenji Sasaoka, c,d
and Satoshi Watanabe c
a Department of Liberal Arts, Faculty of Engineering, Tokyo University of Science,
6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
b Department of Electrical Engineering, Graduate School of Engineering,
Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan
c Department of Materials Engineering, Graduate School of Engineering,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
d Organization of Advanced Science and Technology, Kobe University, 1-1 Rokkodai-cho,
Nada-ku, Kobe 657-8501, Japan
[e-mail]

2.1 Introduction: Thermal Transport at Nanoscale

Theoreticalanalysesofthermaltransportbeganfromthepioneering
work by Fourier in 1820s. According to his theory known as
Fourier's law, the thermal current density I is proportional to the
temperature gradient dT / dx , that is

dT
dx ,

I

=− λ

(2.1)