Eldabe, Nabil T. M.; El-Sabbagh, M. F.; El-Sayed (Hajjaj), M. A.-S. Hydromagnetic stability of plane Poiseuille and Couette flow of viscoelastic fluid. (English) Zbl 1135.76025 Fluid Dyn. Res. 38, No. 10, 699-715 (2006). Summary: The effect of transverse magnetic field on the stability of plane Poiseuille and Couette flows between two parallel flat plates is investigated for Oldroyd-B fluid. The classical Orr-Sommerfeld analysis is extended to electrically conducting fluid for Oldroyd-B model, assuming that the magnetic Prandtl number is sufficiently small. The Chebyshev collocation method with the QZ-algorithm is used for solving the stability equations to find the eigenvalues. The critical values of Reynolds number, wave number, and wave speed are computed. It is found that the magnetic field has a stabilizing effect on Poiseuille flow, while it has both destabilizing and stabilizing effects on Couette flow. Cited in 4 Documents MSC: 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 76E05 Parallel shear flows in hydrodynamic stability 76A10 Viscoelastic fluids Keywords:Chebyshev collocation method; Orr-Sommerfeld analysis; QZ-algorithm PDFBibTeX XMLCite \textit{N. T. M. Eldabe} et al., Fluid Dyn. Res. 38, No. 10, 699--715 (2006; Zbl 1135.76025) Full Text: DOI