Stability of MHD Taylor–Couette Flow in a Narrow Gap with Radial Throughflow

An analysis which considers the stability of dissipative, conducting, incompressible flow between two permeable circular cylinders in presence of an axially applied magnetic field is presented. The impact of radial inflow and outflow was investigated on the Taylor–Couette flow in a narrow gap via differential transform method combined with a shooting technique. The semi analytic computations made by differential transformation method are consistent with linear instability predictions. For impermeable cylinders the critical Taylor number at the onset of instability increases with increase in Hartmann number for both conducting and non-conducting walls that establishes the stabilizing influence of the magnetic field. Radial inflow has a stabilizing effect and the stabilization is more for perfectly conducting walls, while a radial outflow destabilizes the system. Also, the critical wave number is independent of radial flow through the cylinders. For non-conducting cylinders, the asymptotes as the Hartmann numbers approaches infinity are obtained for inflow as well as outflow and found that the asymptotes increases for radial inflow and decreases for outflow.