Stability of MHD Wall driven Flow through a Tube

In this work, wall driven incompressible viscous fluid flow through a tube in the presence of magnetic field is considered. The mathematical model of the problem is formulated and solved using series solution method and Hermite-Padé approximation method. Flow becomes unstable due to movement of wall and existence of magnetic field where critical Reynolds number and critical Hartmann number indicate the point of flow instability. This critical point for instability in terms of Reynolds number and Hartmann number are determined and described using bifurcation diagrams. The effect of these two dimensionless numbers on flow velocity and their interaction on flow stability are discussed.