Hydromagnetic stability of plane Poiseuille and Couette flow of viscoelastic fluid

Fluid Dynamics Research

Volumn 38, Issue 10, 2006, Pages 699-715

  Eldabe, Nabil T M ^a   El Sabbagh, M F ^b  

^a Ain Shams University   (Egypt)

^b Hajjaj) M A S   (Egypt)

Author keywords

Chebyshev collocation method; Couette flow; Hydromagnetic stability; Poiseuille flow; Viscoelastic fluid

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LAMINAR FLOW; MAGNETIC FIELDS; PRANDTL NUMBER; REYNOLDS NUMBER;

CHEBYSHEV COLLOCATION METHOD; COUETTE FLOW; HYDROMAGNETIC STABILITY; POISEUILLE FLOW;

VISCOELASTICITY;

EIGENVALUES AND EIGENFUNCTIONS; LAMINAR FLOW; MAGNETIC FIELDS; PRANDTL NUMBER; REYNOLDS NUMBER; VISCOELASTICITY;

EID: 33748061957     PISSN: 01695983     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fluiddyn.2006.05.002     Document Type: Article

References (33)

1. Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. Spectral Methods in Fluid Dynamics (1988), Springer, New York
2. Drazin P.G., and Reid W.H. Hydrodynamic Stability (1981), Cambridge University Press, Binghamton, NY
3. Eldabe, N.T.M., El-Sabbagh, M.F., El-Sayed(Hajjaj), M.A.-S., 2006a. Hydromagnetic stability of plane Poiseuille flow of an upper convected Maxwell fluid, under preparation.
4. Eldabe, N.T.M., El-Sabbagh, M.F., El-Sayed(Hajjaj), M.A.-S., 2006b. Hydromagnetic stability of plane Couette flow of an upper convected Maxwell fluid, IMA J. Appl. Math., accepted for publication.
5. Gorodtsov V.A., and Leonov A.I. On a linear instability of a plane parallel Couette flow of viscoelastic fluid. J. Appl. Math. Mech. 31 (1967) 310-1319
6. Ho, T.C., Denn, M.M., 1977/1978. Stability of plane Poiseuille flow of a highly elastic liquid. J. Non-Newtonian Fluid Mech. 21, 179-195.
7. Kakutani T. The hydrodynamic stability of the modified plane Couette flow in the presence of a transverse magnetic field. Phys. Soc. Jpn. 19 (1964) 1041-1057
8. Kundu P.K. Small disturbance stability of plane Poiseuille flow of Oldroyd fluid. Phys. Fluids 15 (1972) 1207-1212
9. Kupferman R. On the linear stability of plane Couette flow for an Oldroyd-B fluid and its numerical approximation. J. Non-Newtonian Fluid Mech. 127 (2005) 169-190
10. Larson R.G. Constitutive Equations for Polymer Melts and Solutions (1988), Butterworths, Boston
11. Larson R.G. Instabilities in viscoelastic flows. Rheol. Acta 31 (1992) 213-263
12. Leal, L.G., 1989. Structure of Turbulence and Drag Reduction (IUTAM Symposium), Part 2. Springer, Berlin, pp. 155-185.
13. Lee K.C., and Finlayson B.A. Stability of plane Poiseuille and Couette flow of a Maxwell fluid. J. Non-Newtonian Fluid Mech. 21 (1986) 65-78
14. Lim F.J., and Schowalter W.R. Pseudo-spectral analysis of the stability of pressure-driven flow of a Giesekus fluid between parallel planes. J. Non-Newtonian Fluid Mech. 26 (1987) 135-142
15. Lingwood R.G., and Alboussiere T. On the stability of the Hartmann layer. Phys. Fluids 11 (1999) 2058-2068
16. Lock R.C. The stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field. Proc. Roy. Soc. Lond. A 221 (1955) 105-125
17. Martinson L.K., Pavlov K.B., and Simkhovich S.L. Hydrodynamic stability of a gradient flow of a conducting fluid with a rheological power law in a transverse magnetic field. Magnetohydrodynamics 2 (1972) 169-173
18. Moler C.B., and Stewart G.W. An algorithm for generalized matrix eigenproblems. SIAM J. Numer. Anal. 10 (1973) 241-256
19. Muller U., and Buhler L. Magnetofluiddynamics in Channels and Containers (2001), Springer, Berlin, Heidelberg
20. Orszag S.A. Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50 (1971) 689-703
21. Potter M.C., and Kutchey J.A. Stability of plane Hartmann flow subject to a transverse magnetic field. Phys. Fluids 16 (1973) 1848-1851
22. Ray R.N., Samad A., and Chaudhury T.K. Hydromagnetic stability of plane Poiseuille flow of an Oldroyd fluid. Acta Mech. 143 (2000) 155-164
23. Renardy M., and Renardy Y. Linear stability of plane Couette flow of an upper convected Maxwell fluid. J. Non-Newtonian Fluid Mech. 22 (1986) 23-33
24. Simkhovich S.L. Stability of the gradient flow of a conducting Maxwellian liquid in a perpendicular magnetic field. Magnetohydrodynamics 2 (1980) 142-145
25. Squire H.B. On the stability for three-dimensional disturbances of viscous fluid between parallel walls. Proc. Roy. Soc. Lond. A 142 (1933) 621-628
26. Sureshkumar R., and Beris A.N. Linear stability analysis of viscoelastic Poiseuille flow using an Arnoldi-based orthogonalization algorithm. J. Non-Newtonian Fluid Mech. 56 (1995) 151-182
27. Tackels G., and Crochet M.J. Stability of plane Poiseuille flow of a finite linear viscoelastic fluid. Phys. Fluids 16 (1973) 790-795
28. Takashima M. The stability of natural convection in a vertical layer of viscoelastic liquid. Fluid Dyn. Res. 11 (1993) 139-152
29. Takashima M. The stability of modified plane Poiseuille flow in presence of a transverse magnetic field. Fluid Dyn. Res. 17 (1996) 293-310
30. Takashima M. The stability of the modified plane Couette flow in the presence of a transverse magnetic field. Fluid Dyn. Res. 22 (1998) 105-121
31. Tlapa G., and Bernstein B. Stability of a relaxation-type viscoelastic fluid with slight elasticity. Phys. Fluids 13 (1970) 565-568
32. Toms, B.A., 1948. Observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In: Proceedings of International Rheologigal Congress, Holand, vol. 2, pp. 135-141.
33. Wilson H.J., Renardy M., and Renardy Y. Structure of the spectrum in zero Reynolds number shear flow of the UCM and Oldroyd-B liquids. J. Non-Newtonian Fluid Mech. 80 (1999) 251-268