MHD Couette Flow in Cylindrical Porous Annulus with Perfectly Conducting Walls

Abstract

This work obtained an analytical solution for a steady cylindrical MHD Couette flow in a porous medium between two perfectly conducting rotating cylinders under the influence of a non-uniform radial magnetic field. Since part of the analytical solution is expressed in terms of the integral of the Modified Bessel function of the first and second kinds of variable order, numerical integration was performed. Current results indicate that the flow may become more uniform when the strength of the external magnetic field is increased. The magnetic fluid tends to slow down if the permeability of the porous medium decreases. If the porous annulus is thick, the momentum of the flow is more difficult to propagate from the outer cylinder into the inner part of the annulus. If both the inner and outer cylinders rotate, the shear effect the inner cylinder imposes is only relatively influential in the region close to it. A decrease in Da no less than 10-2 may increase the amount of magnetic field induced. The transfer of momentum across the annular space is easier in a thin porous annulus than a thick one and hence induces a stronger magnetic field. If the inner cylinder rotates in the direction opposite of the outer one, the magnetic field in the clockwise direction will be induced in some region.