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Computational Approach for Complete Lyapunov Functions Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Stokes Flow Through a Tube with Wavy Wall

Authors : Włodzimierz Bielski, Ryszard Wojnar

Published in: Dynamical Systems in Theoretical Perspective

Publisher: Springer International Publishing

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Abstract

We propose a study of the flow in a tube with wavy wall adopting Malevich - Mityushev - Adler’s method, and find a correction to Hagen-Poiseuille’s solution. The problem is to be solved by expanding the velocity and pressure fields in Fourier series involving an infinite set of unknown coefficients. The boundary surface is expanded in Taylor’s series. A perturbation expansion in terms of the powers of the small parameter \(\varepsilon \) of the full set of Stokes’ equations yields a cascade of boundary value problems which are solved at each step in closed form. Even in the first order approximation \(O(\varepsilon )\), new results are obtained.

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Metadata
Title
Stokes Flow Through a Tube with Wavy Wall
Authors
Włodzimierz Bielski
Ryszard Wojnar
Copyright Year
2018
Book
Dynamical Systems in Theoretical Perspective

Print ISBN: 978-3-319-96597-0

Electronic ISBN: 978-3-319-96598-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-96598-7_30

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