Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions

TL;DR

This paper analytically solves the second Stokes problem for a rarefied gas using the BGK model and Cercignani boundary conditions, deriving velocity, force, and energy dissipation characteristics.

Contribution

It provides an analytical solution for the second Stokes problem with Cercignani boundary conditions using the BGK equation, including velocity distribution and force calculations.

Findings

Derived the velocity distribution function of the gas.

Calculated the gas velocity at the wall.

Determined the force resistance and energy dissipation capacity.

Abstract

Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions The second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane, limiting half-space, makes harmonious fluctuations in the plane. The kinetic BGK-equation (Bhatnagar, Gross, Krook) is used. The boundary accomodation conditions of Cercignani of reflexion gaseous molecules from a wall are considered. Distribution function of the gaseous molecules is constructed. The velocity of gas in half-space is found, also its value direct at a wall is found. The force resistance operating from gas on border is found. Besides, the capacity of dissipation of the energy falling to unit of area of the fluctuating plate limiting gas is obtained.