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DARCY FRICTION COEFFICIENT CALCULATED USING AN ELLIPSOIDAL STATISTICAL MODEL.

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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]
Copyright of Journal of Applied Mechanics & Technical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: DARCY FRICTION COEFFICIENT CALCULATED USING AN ELLIPSOIDAL STATISTICAL MODEL.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mechanics+%26+Technical+Physics%22">Journal of Applied Mechanics & Technical Physics</searchLink>. Aug2023, Vol. 64 Issue 4, p647-655. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Polynomial+approximation%22">Polynomial approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Chebyshev+systems%22">Chebyshev systems</searchLink><br /><searchLink fieldCode="DE" term="%22Chebyshev+polynomials%22">Chebyshev polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+equations%22">Algebraic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+sums+%28Series%29%22">Partial sums (Series)</searchLink><br /><searchLink fieldCode="DE" term="%22Isothermal+flows%22">Isothermal flows</searchLink>
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  Label: Abstract
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Applied Mechanics & Technical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1134/S0021894423040107
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      – Code: eng
        Text: English
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        StartPage: 647
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      – SubjectFull: Polynomial approximation
        Type: general
      – SubjectFull: Chebyshev systems
        Type: general
      – SubjectFull: Chebyshev polynomials
        Type: general
      – SubjectFull: Statistical models
        Type: general
      – SubjectFull: Algebraic equations
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      – SubjectFull: Partial sums (Series)
        Type: general
      – SubjectFull: Isothermal flows
        Type: general
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      – TitleFull: DARCY FRICTION COEFFICIENT CALCULATED USING AN ELLIPSOIDAL STATISTICAL MODEL.
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              M: 08
              Text: Aug2023
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              Y: 2023
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