Velocity and pressure functions of an oscillating flow in a circular Hele-Shaw cell

In this study, we have investigated the form of velocity and pressure functions a fluid oscillating between two parallel glass sheets that circular Hele-Shaw cell. The flow has been considered to be radial, incompressible laminar. time-dependent Navier-Stokes equation solved in cylindrical coordinates using Fourier transform, across thickness cell obtained at different times. function unsteady state is related vertical component parabolic also inverse radial component. time dependence appears as simple harmonic with frequency equal oscillation frequency. maximum middle along its height gradually decreases from towards top or bottom plane reaches zero. Pressure does not depend on changes logarithmically radius. external frequency, but it phase shift respect velocity.