DARCY FRICTION COEFFICIENT CALCULATED USING AN ELLIPSOIDAL STATISTICAL MODEL

This study describes a method for calculating the Darcy friction coefficient in a flat channel formed by two infinite parallel plates as a function of the Reynolds numbers and the gas rarefaction parameter in the channel. Maxwell’s diffuse reflection model is used as a model for the reflection of gas molecules from the channel walls. The isothermal gas flow is due to the presence of a pressure gradient that is small in absolute magnitude and directed along the channel walls. The method proposed in this paper is based on solving a linearized ellipsoidal-statistical Boltzmann kinetic equation with homogeneous boundary conditions using the Chebyshev polynomial approximation. An unknown function that interpolates the solution to this equation is represented as a partial sum of a series in Chebyshev polynomials of the first kind. The properties of finite sums for an orthonormal system of Chebyshev polynomials are used to reduce the problem to a system of linear algebraic equations with respect to the values of the sought function at interpolation nodes. The results obtained in this study are analyzed.