The steady-state problem of a magnetic fluid filling a porous annulus between two cylindrical walls under the influence of a nonuniform radially outward magnetic field has been investigated. The cylindrical walls are either electrically perfectly insulated or electrically perfectly conducting. The permeability of the porous annulus increases with its radial location. The governing partial differential equations were derived carefully and closed form solutions for the profiles of the velocity component and the induced magnetic component were obtained. The effect of the strength of the externally applied magnetic field, the permeability of the porous annulus, and the conductivity of the cylindrical walls were examined through the angular velocity components, as well as the induced magnetic field.
"Analytical Solution for MHD Flow of a Magnetic Fluid within a Thick Porous Annulus." J. Appl. Math. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/931732