Abstract
A ballistic-diffusive heat conduction model is derived from the Boltzmann transport equation by a coarse-graining approach developed in the present study. By taking into account of the lagging effect, this model avoids the infinite heat propagation speed implied by the classical Fourier law. By expressing the heat conductivity as a function of the Knudsen number, it accounts for the size effect of the nanoscale heat conduction. The variation of the obtained effective heat conductivity with respect to the characteristic length shows an agreement with the experimental results for thin silicon films and nanowires in the nanoscale regime.
| Original language | English |
|---|---|
| Pages (from-to) | 1851-1864 |
| Number of pages | 14 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 467 |
| Issue number | 2131 |
| DOIs | |
| Publication status | Published - 8 Jul 2011 |
Keywords
- Boltzmann transport equation
- Heat conduction
- Silicon film
- Silicon nanowire
- Size effect