Periodic Flow of a Second Grade Fluid Due to the Disks Executing Non-Torsional Oscillations in an Orthogonal Rheometer Under the Influence of a Magnetic Field

The present paper studies the periodic flow of a second grade fluid generated by non-torsional oscillations of the disks rotating in the eccentric form under the application of a magnetic field. Subsequent to the rotational motion of the disks at a common angular velocity about two vertical axes, they perform oscillations horizontally in a symmetrical manner. The exact analytical solutions are derived for both the velocity field and the tangential force per unit area exerted on one of the disks by the fluid. Special attention is paid to the influence of the applied magnetic field and it is investigated how the magnetic field controls the flow when the frequency of oscillation is less than or equal to or greater than the angular velocity of the disks. It is found that the application of the magnetic field leads to thinner boundary layers developed on the disks and the changes in the values of the shear stress components which represent the tangential force exerted on the disks occur at larger amplitude.