Dynamic permeability of electrically conducting fluids under magnetic fields in annular ducts

The dynamic response of an electrically conducting fluid (either Newtonian or Maxwellian) flowing between straight concentric circular cylinders under a constant radial magnetic field, is analyzed. The isothermal flow is studied using the time Fourier transform, so that the dynamic generalization of Darcy's law in the frequency domain is obtained and analytical expressions for the dynamic permeability are derived. For the Newtonian case, the range of frequencies where the dynamic permeability approaches the static value is enlarged the smaller the gap between the cylinders and the higher the magnetic-field strength. For the Maxwell fluid, the presence of the inner cylinder shifts the frequencies that lead to the enhancement of the real part of the dynamic permeability to larger values and increases its maximum values relative to the case where the inner cylinder is absent. In addition, the Ohmic dissipation causes the damping of the amplitude of the response.