Impact of slippage on the wall correction rotation factor of MHD couple stress fluid between two concentric spheres

The creeping rotational motion of a magnetohydrodynamic couple stress fluid between two concentric spheres under the impact of slippages. The slippage conditions are applied on the surface of the inside sphere. In addition, the couple stresses on the boundary are assumed to vanish. The analytical solution to the problem is used to obtain the field functions of velocity, tangential stress, and couple stresses. The wall correction factor experienced by the fluid on the inner solid sphere is evaluated and plotted. However, in the presence of a magnetic field, the eddy current caused by rotating particles produces a torque that tends to rise because the assumption of the torque direction is the opposite direction of magnetic induction. Also, the first couple stress parameter, the angular velocity ratio, and slip condition did an improvement in the torque. On the other side, the wall correction factor slows down with slippage on the inner sphere and the size parameter. All results give limiting cases with no slippage and viscous fluid.