Unsteady MHD Couette Flows in an Annuli: The Riemann-Sum Approximation Approach

TLDR: In this paper, the MHD Couette flow of a viscous incompressible electrically conducting fluid between two concentric horizontal cylinders of infinite length has been analyzed when the outer cylinder has been set into uniform accelerated motion.

Abstract: The unsteady MHD Couette flow of a viscous incompressible electrically conducting fluid between two concentric horizontal cylinders of infinite length have been analysed when the outer cylinder has been set into uniform accelerated motion. A unified closed form expressions are derived corresponding to the cases of the magnetic field fixed relative to the fluid or to the accelerated outer cylinder. The well known Laplace transform technique is applied to solve the time-dependent governing equations, while the method of Riemann-sum approximation is employed to invert the Laplace domain to the time domain in order to obtain the velocity and the skin friction. The variations of the velocity and the skin friction with respect to the Hartmann number and time have been discussed.