Size effect on thermal conductivity of thin films. Guihua Tang , Yue Zhao, Guangxin Zhai, Zengyao Li, Wenquan Tao School of Energy & Power Engineering, Xi’an Jiaotong University, China. 1. Background. 2. Local mean free path method. 3.1. 3. 3.2. 4. 4. Outline.
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Guihua Tang, Yue Zhao, Guangxin Zhai, Zengyao Li, Wenquan Tao
School of Energy & Power Engineering,
Xi’an Jiaotong University, China
Local mean free path method
Results 1: Local thermal conductivity distribution
Results 2:Overall thermal conductivity
The Phonon Gas
is the lattice volumetric specific heat;
is the average speed of phonons;
is the phonon mean free path.
Harmonic oscillator model of an atom
Apply the Matthiessen’s rule
A thin film for paths originated from the boundary surface
Simple interpolation between the two expressions
A thin film for paths originated from the centre
A thin circular wire for paths originated from the centre
p is the probability of specular scattering on the boundary
2. Local mean free path method
The probability of a phonon gas having a free path between x and x+dx
Local thermal conductivity distribution in a semi-infinitefilm
Local thermal conductivity distribution in a thin film
Overall thermal conductivity in a thin film VS Kn