Steady incompressible flow around a circular cylinder in an external magnetic field that is aligned with fluid flow direction is studied for (Reynolds number) up to 40 and the interaction parameter in the range (or ), where is the Hartmann number related to by the relation , using finite difference method. The pressure-Poisson equation is solved to find pressure fields in the flow region. The multigrid method with defect correction technique is used to achieve the second-order accurate solution of complete nonlinear Navier-Stokes equations. It is found that the boundary layer separation at rear stagnation point for is suppressed completely when and it started growing again when . For and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing when . The drag coefficient decreases for low values of and then increases with increase of . The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary with . It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values of and rear pressure inversion occurs with further increase of . These results are in agreement with experimental findings.
T. V. S. Sekhar. R. Sivakumar. T. V. R. Ravi Kumar. "Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers." J. Appl. Math. 2005 (3) 183 - 203, 30 June 2005. https://doi.org/10.1155/JAM.2005.183