Author(s)

Ibrahima Kama^1*, Mamadou Lamine Sow¹, Kodjo Kpode², Cheikh Mbow¹

¹Department of Physics, University Cheikh Anta DIOP-UCAD, Dakar, Senegal.
²Department of Physics, University of Kara, Kara, Togo.

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 10⁷ 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.

Viscoelastic Fluids, Oldroyd-B Model, Linear Stability, Petrov-Galerkin, Generalized Eigenvalue Problem

Kama, I. , Sow, M. , Kpode, K. and Mbow, C. (2018) Effects of the Reynolds and Weissenberg’s Numbers on the Stability of Linear Pipe Flow of Viscous Fluid. Modern Mechanical Engineering, 8, 264-277. doi: 10.4236/mme.2018.84018.