Oscillatory Flow of a Magnetic Fluid in a Pipe at Low Frequency Range Under a Magnetic Field: Phase Difference of Pressure

We made on numerical analysis of phase difference between pressure along the pipe axis and given oscillatory flow velocity in an straight pipe under a nonuniform steady magnetic field. In the analysis, a few cases under the assumption of numerical condition were conducted on: the first is taking into account the least compressibility of the fluid with using the obtained experimental data of the bulk modulus, the second taking into account the nonuniform distribution of mass concentration of particles, and the thrid taking into account the aggregation with the number of aggregated particles proposing as a prorate spheroid. By considering the three effects of the least compressibility and the nonuniform distribution of mass concentration, the aggregation as a prorate spheroid, the phase difference varies quantitatively at the lowest Womersley number range. And then, the numerical results were compared with the experimental data.