Macroscopic Transport Equations for Rarefied Gas Flows

The well known transport laws of macroscopic physics, i.e. the laws of Navier-Stokes and Fourier, fail for the simulation of processes on lengthscales in the order of the mean free path of a particle. Thus, the proper simulation of flow in microdevices requires a more detailed description. This introductory textbook presents the development of continuum models for microscale effects in a concise form - mathematically sound, but as simple as possible. Based on the Boltzmann equation main approaches to develop microscale continuum models are presented such as the Chapman-Enskog method, the Grad's moment method, as well as combinations of the both. These methods can be used to study a wide number of problems, including applications to rarefied gas flow, the reentry problem of space craft, electron transport in solids, heat transfer in crystals at low temperatures, and radiative transfer. This book aims particularly to open make this applied mathematics subject accessible for engineers, who seek not absolute mathematical precision but workable and useful models, which are derived here in a transparent manner. TOC:Introduction.

- Phase density and its moments.

- Boltzmann equation, conservation laws and H-Theorem.

- Kinetic equations.

- Chapman-Enskog expansion.

- Grad's moment method.

- Regularized Grad equations (R13).

- Other applications of kinetic theory.

- Appendix.