Derivation of equations of motion of a slightly rarefied gas around highly heated bodies from boltzmann's equation

Abstract

The motion of a slightly rarefied gas (K ≪ 1, where K is the Knudsen number) around highly heated bodies is examined. On the assumption that the characteristic macroscopic velocity of gas motion generated during contact with a highly heated body is on the order of or much greater than the velocity of the impinging stream, the corresponding hydrodynamic equations are derived from Boltzmann's equation by Hubert's method [1]. A qualitative study is made of the region of applicability of the equations obtained. A class of flows of a continuous medium in which the characteristic change in enthalpy is much larger than the characteristic kinetic energy was studied in [2]. The Navier-Stokes equations with boundary conditions of adhesion proved to be inadequate for a description of these flows since it was already necessary in the first basic approximation to take into account part of the Barnett terms and slippage. The authors of [2] suggest using simplified Barnett equations with the condition of creep, with the Barnett terms being on the same order as the inertial and Navier-Stokes terms. On the other hand, it is known that the Barnett equations are derived on the assumption that the additional terms are small in comparison with the Navier-Stokes and Eulerian terms. This makes it desirable to obtain equations describing this class of flows directly from Boltzmann's equation.