Impact of magnetic field and permeability on the unsteady slow rotation of a sphere: slip condition

This study investigates the unsteady rotational motion of a solid spherical particle with slip at its surface, immersed in an incompressible viscous fluid saturating a porous medium, under the influence of an external magnetic field. The flow dynamics are governed by the unsteady Brinkman equation coupled with the Lorentz force. To obtain analytical expressions, the Laplace transform technique is employed, and a slip boundary condition is applied at the surface of the sphere. The torque acting on the sphere is derived in the Laplace domain. The combined influence of the permeability, magnetic field, and slip condition on the torque is examined for three distinct cases: damping oscillatory motion, accelerating velocity, and impulsive motion. Graphical representations are provided to illustrate the variation of torque with time for different values of the Hartmann number, slip parameter, and permeability parameter. The results demonstrate that the Hartmann number and slip parameter enhance the torque in all cases, while the torque decreases with increasing value of the permeability parameter. In the limiting cases, the present results reduce to earlier findings in the absence of magnetic effect and permeability.