Hydromagnetic stability of plane Poiseuille and Couette flow of viscoelastic fluid

The effect of transverse magnetic field on the stability of plane Poiseuille and Couette flow 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 the Couette flow.