Flow generated by slow steady rotation of a permeable sphere in a micro-polar fluid

The analytical study of the flow generated by the slow steady rotation of a permeable sphere in an incompressible micro-polar fluid is considered. Both the flows internal and external to the sphere are coupled. The result will degenerate to independent equations for the case of viscous fluids for the inner and external flows. The flow field in the form of velocity w and micro rotation function φ are obtained in terms of modified Bessel functions and Gegenbauer polynomials. The flow pattern is shown in the form of graphs. It is interesting to note that the velocity and micro-rotation functions within the sphere are constant at distances from the axis of rotation since it represents a rigid body rotation. Effects of physical parameters on the Couple are also shown in the form of graphs.