Elementary Kinetic Theory of Gases

Abstract

It is convenient to introduce the notion of collisional invariants (or summational invariants) (e.g., [55], p. 460; [90], p. 150). The validity of (2.211) is commonly justified by the following arguments: Due to the symmetry properties of the collision term expression, interchanging variables gives the following equalities:These symmetry properties can be combined to give the following relationship:The linearity of the J operator allows the latter result to be manipulated as:In conclusion, a function ψ(c) is a summation invariant if:

Thermodynamic and kinetic investigation of the influence of external centrifugal field and the heat transfer on a confined neutral gas

“…In a frame co-moving with the fluid [9,[21][22][23], the system consisting of four nonlinear partial differential equations is solved analytically. The moment method [28][29][30] with suitable boundary conditions is applied. The manner of the macroscopic properties of the neutral gas such as temperature and concentration is investigated.…”

“…2. For the steady motion, a centrifugal force F C can be expressed in terms of the Boltzmann equation [28][29][30] in the BGK model as:…”