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Time dependent MHD Couette flow due to ramped motion of one of the boundaries

Jha B. K., Jibril H. M.

International Journal of Applied Mechanics and Engineering

2012

Vol. 17, no. 2

383-399

The effects of a transverse magnetic field on the Couette flow of an electrically conducting fluid between two infinite parallel plates have been discussed when one of the plates has been set into ramped motion. Under the assumption of a negligible induced magnetic field and applied magnetic field being fixed relative to the fluid or moving plate, the governing momentum equation has been solved exactly. The expressions for velocity field and skin-friction have been presented. The transient features of velocity and skin-friction have been discussed for different values of the Hartmann number. It is seen that the velocity field and skin-friction increases with an increase of the Hartman number when the magnetic field is fixed with respect to the moving plate while the result is just reverse when it is fixed with respect to the fluid.

Hydromagnetic flow due to ramped motion of the boundary

Jha B. K., Jibril H. M.

International Journal of Applied Mechanics and Engineering

2010

Vol. 15, no 4

1101-1109

The unsteady flow of a viscous, incompressible and electrically conducting fluid subject to a uniform transverse magnetic field near a horizontal plate having ramped motion is considered. A unified closed form analytical solutions have been obtained for the velocity field and the skin-friction corresponding to the cases of a magnetic field fixed relative to the fluid or the moving boundary. Under the assumption of a negligible induced magnetic field, the governing momentum equation has been solved exactly by using the Laplace-transform technique. The flow formation near ramped motion of the plate has also been compared with the flow formation near a plate having constant motion (impulsive motion). It is observed that velocity of the fluid in the case of ramped motion of the plate is always less than that of the flow induced by impulsive motion of the plate.