Instability of three dimensional electrically conducting fluid of magnetohydrodynamics Couette flow

In this work, we consider a disturbed electrically conductive fluid between two parallel planes and study the stability of the fluid after applying a uniform magnetic field on it. We obtain a modified form of Orr-Sommerfeld system of equation and then use QZ (Qualitat and Zuverlassigkeit) technique to obtain neutral curves. We investigate the critical Reynolds numbers for large domain of Hartmann Number. Next we show that for particular values of oblique angle, Couette flow destabilizes in some range of magnetic field. We also show that the area of stability changes with change oblique angle, Hartmann number, Reynolds number and wave number. We also find that the instability region for Couette flow has conic type shape. It is found that magnetic field provides a stabilizing impact to the flow, and the extent of this impact is demonstrated for a range of Reynolds numbers. From numerical simulations, it is observed that a magnetic field with a specific magnitude stabilizes the Hartmann flow.