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The study of oscillating flow of a Couple Stress fluid past a permeable sphere is considered. Analytical solution for the flow field in terms of stream function is obtained using modified Bessel functions. The formula for Drag acting on the sphere due external flow is evaluated. Pressure field for the flow region past and inside the sphere is obtained. Effects of physical parameters like couple stress parameter, permeability, frequency and geometric parameters on the drag due to internal and external flows are represented graphically. It is observed that the drag for viscous fluid flow will be less than the case of couple-stress fluid flow and hence couple stress fluids offer resistance for flow.

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