Longitudinal oscillations of a circular cylinder in a micro-polar fluid: case of resonance

The problem of the longitudinal oscillations of a circular cylinder along its axis of symmetry in an incompressible micro-polar fluid and the flow generated due to these oscillations in the fluid is considered. The Stokes flow is considered by neglecting nonlinear convective terms in the equations of motion on the assumption that the flow is so slow that oscillations’ Reynolds number is less than unity. Here we get a rare, but distinct special case referred to as resonance in which material constants are interrelated in a particular way. In non-resonance case, all material constants are independent and are not related. The solution in this case cannot be obtained as limiting case of a non-resonance problem. The velocity and micro-rotation components of the flow for the case of resonance and non-resonance are obtained. The skin friction acting on the cylinder is evaluated and the effect of physical parameters like micro-polarity and couple stress parameter on the skin friction due to oscillations is shown through graphs.