Analysis of a conducting fluid in a thin annulus with rotating insulated walls under radial magnetic effect

This work considers an electrically conducting fluid filled between two concentric cylindrical walls relatively close to each other. A theoretical solution for the steady Taylor-Couette flow between these two electrically insulated rotating cylinders under the influence of a radial magnetic field is provided in this work. By solving the appropriate set of governing equations simultaneously, the profiles of fluid tangential velocity component and induced magnetic field were obtained as complicated functions involving the modified Bessel functions of the first and second kinds of the first-order in terms of radial coordinates and Hartmann number. A computational study was also performed to validate the present theoretical solution. The analytical and computational results are identical when Ha = 1 while these results only slightly deviate from each other as Ha increases. Current results show that, the presence of the external magnetic field causes the flow close to the slower cylinder to accelerate while that close to the faster cylinder to decelerate. This has clearly implied the fact that an external magnetic field tends to make the velocity distribution across the inner and outer cylinders more uniform.