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Effects of the Reynolds and Weissenberg’s Numbers on the Stability of Linear Pipe Flow of Viscous Fluid
Department of Physics, University Cheikh Anta DIOP-UCAD, Dakar, Senegal
Department of Physics, University Cheikh Anta DIOP-UCAD, Dakar, Senegal
Department of Physics, University of Kara, Kara, Togo
Department of Physics, University Cheikh Anta DIOP-UCAD, Dakar, Senegal
- 1 Department of Physics, University Cheikh Anta DIOP-UCAD, Dakar, Senegal
- 2 Department of Physics, University Cheikh Anta DIOP-UCAD, Dakar, Senegal
- 3 Department of Physics, University of Kara, Kara, Togo
- 4 Department of Physics, University Cheikh Anta DIOP-UCAD, Dakar, Senegal
Modern Mechanical Engineering·Volume 08 (2018)·Pages 264–277·Published 18 October 2018·DOI10.4236/mme.2018.84018
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Abstract
A Fourier-Chebyshev Petrov-Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables and is written in FORTRAN. Systematic studies are presented of the dependence of eigenval-ues and other quantities on the axial and azimuthal wave numbers; the Reyn-olds’ number of up to 10 7 and the Weissenberg’s number that is considered lower here. The flow will be considered stable if all the real parts of the ei-genvalues obtained are negative and unstable if only one of these values is positive.
KeywordsViscoelastic FluidsOldroyd-B ModelLinear StabilityPetrov-GalerkinGeneralized Eigenvalue Problem
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