Kinetic Theory Description of Rarefied Gas Flow

In an early paper with H. Bolza and Max Born, von Karman examined the relation between the "collision-dominated" and "collision-free" regimes in the simple case of steady flow or steady heat conduction through a porous medium. Von Karman also formulated the boundary condition at a gas-solid interface, and showed that the temperature "jump" arises quite naturally from the two-sidedness of the velocity distribution function, independently of any statements about the thermal accommodation coefficient. We reexamine this question of the transition between gas-kinetics and gasdynamics with the aid of the Maxwell moment method, utilizing a two-sided Maxwellian-type distribution as weighting function. The main features deduced from this approach are illustrated by considering two simple examples: (1) steady heat conduction between two concentric cylinders, and between two concentric spheres; (2) the "signaling problem" generated by the sudden motion and heating of an infinite flat plate.