To Understand the Boltzmann Transport Equation

Here are some internet resources

1. The easiest and vivid explanation of BTE: http://homepage.univie.ac.at/Franz.Vesely/sp_english/sp/node7.html

2. Fundamental textbook: Microscale energy transport By Chang L. Tien, Arunava Majumdar, Frank M. Gerner

3. Explanation of phonon dispersion: http://www.chembio.uoguelph.ca/educmat/chm729/Phonons/intro.htm

Study notes:
Phonon
1)An ensemble of travelling waves having a certain frequency, n, a certain group velocity, Vg , and carrying with it energy equal to hn , where h is the Planck constant.
2)Just as light is a wave motion that is considered as composed of particles called photons, we can think of the normal modes of vibration in a solid as being particle-like. Quantum of lattice vibration is called the phonon.

Wave Vector k -- a vector which points in the direction of propagation of the wave.
Phonon Dispersion -- the relation between phonon frequency(energy) and wave vector