MHD Run-up Flow between Parallel Plates in the Presence of a Transverse Magnetic Field with Dynamic Wall Slip

Abstract

In this study, we investigate the impact of a uniform transverse magnetic field on the flow between parallel plates. We analyze both impulsive and uniformly accelerated motion of the lower plate in an open circuit system. The magnetic lines of force are assumed to be fixed either relative to the fluid (MFFRF) or fixed relative to the moving lower plate (MFFRP). The Laplace transform technique is employed to obtain the velocity field and skin friction. The obtained solutions are then inverted back into the time domain using a numerical inversion technique based on the Riemann-sum approximation. The results reveal that slip relaxation time affects velocity differently for impulsive versus accelerated motion. This research contributes to our understanding of magnetohydrodynamic (MHD) flow dynamics, with potential applications in aerospace engineering and material processing.