Exact solution of dispersion equation corresponding to ellipsoidal statistical equation from Stokes' second problem

TL;DR

This paper derives an exact analytical solution for the zeros of the dispersion function related to Stokes' second problem, analyzing the behavior of a rarefied gas under oscillating boundary conditions using the ellipsoidal statistical model.

Contribution

It provides an explicit solution for the zeros of the dispersion function in the context of the ellipsoidal statistical equation for Stokes' second problem.

Findings

Explicit form of zeros of dispersion function obtained

Dependence of zeros on collision frequency and parameters analyzed

Factorization formula for dispersion function proved

Abstract

In the present work zero of dispersive function from Stokes' second problem are investigated. Stokes' second problem is a problem about behavior of the rarefied gas filling half-space. A plane, limiting half-space, makes harmonious oscillations in the plane. The linearization kinetic ellipsoidal the statistical equation with parameter is used. The factorization formula of dispersion function is proved. By means of the factorization formula zero of dispersion function in an explicit form and their research is carried out. Dependence on dimensionless quantity collision frequency of a plane limiting gas and on parameter equation are investigated.