Unsteady rotational motion of a composite sphere in a viscous fluid using stress jump condition

The unsteady rotational motion of a composite sphere, consisting of a solid core surrounded by a porous shell, in an incompressible viscous fluid is discussed using Brinkman's formula. The composite sphere is assumed to rotate about z-axis with time-dependent angular velocity. Laplace transform technique is utilized to obtain the solution of the problem. The inversion of Laplace transform is obtained analytically using contour integration. An analytical and numerical interpretation of the Torque exerted by the fluid on the porous surface is obtained. The effect of stress jump condition and permeability coefficient is discussed and some special cases are deduced.