Creeping motion of a micropolar fluid between two sinusoidal corrugated plates

The steady creeping motion of an incompressible micropolar fluid between two slightly corrugated plates is investigated using the perturbation technique up to the second order. Both normal and parallel flows to the corrugations are considered. The corrugations of the two walls are assumed to be either in phase or half-period out of phase. It is also, assumed that the corrugations are periodic sinusoidal waves of small amplitude. The assumption of low Reynolds number is applied so that the nonlinear inertial terms can be ignored. The effect of corrugations, the rate of flow and the mean velocity are illustrated versus the micropolarity, phase difference and wavelength of corrugations.