Solution of the Kramers' problem about isothermal sliding of moderately dense gas with accomodation boundary conditions

TL;DR

This paper presents a new method for solving Kramers' boundary problem related to isothermal sliding of moderately dense gases, using a boundary condition representation as a source and Fourier integrals to derive a Fredholm integral equation.

Contribution

It introduces a novel approach to boundary problems in kinetic theory, enabling solutions with arbitrary accuracy for dense gases.

Findings

Solution expressed in terms of Neumann's number

Method applicable to arbitrary accuracy levels

Provides analytical framework for dense gas boundary problems

Abstract

Half-space boundary Kramers' problem about isothermal sliding of moderate dense gas with accomodation boundary conditions along a flat firm surface is solving. The new method of the solution of boundary problems of the kinetic theory is applied (see JVMMF, 2012, 52:3, 539-552). The method allows to receive the solution with arbitrary degree of accuracy. The idea of representation of boundary condition on distribution function in the form of source in the kinetic equation serves as the basis for the method mentioned above. By means of Fourier integrals the kinetic equation with a source comes to the Fredholm integral equation of the second kind. The solution has been received in the form of Neumann's number.