DARCY FRICTION COEFFICIENT CALCULATED USING AN ELLIPSOIDAL STATISTICAL MODEL.

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Bibliographic Details
Title:	DARCY FRICTION COEFFICIENT CALCULATED USING AN ELLIPSOIDAL STATISTICAL MODEL.
Authors:	Germider, O. V.¹ (AUTHOR) o.germider@narfu.ru, Popov, V. N.¹ (AUTHOR)
Source:	Journal of Applied Mechanics & Technical Physics. Aug2023, Vol. 64 Issue 4, p647-655. 9p.
Subjects:	Polynomial approximation, Chebyshev systems, Chebyshev polynomials, Statistical models, Algebraic equations, Partial sums (Series), Isothermal flows
Abstract:	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. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	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. [ABSTRACT FROM AUTHOR]
ISSN:	00218944
DOI:	10.1134/S0021894423040107