Instability of magnetohydrodynamic flow of Hartmann layers between parallel plates

Abstract

This study investigates the linear stability of the Hartmann layers of an electrically conductive fluid between parallel plates under the impact of a transverse magnetic field. The corresponding Orr-Sommerfeld equations are numerically solved using Chebyshev's pseudo-spectral method with Chebyshev polynomial expansion. The QZ algorithm is applied to find neutral linear instability curves. Details of the instability are evaluated by solving the generalized Orr-Sommerfeld system, allowing growth rates to be determined. The results confirm that a 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. Further, the critical Reynolds number increases rapidly when the Hartmann number is greater than 0.7. Finally, it is shown that a transverse magnetic field overcomes the instability in the flow.