Journal of Applied MathematicsVolume 2005, Issue 3, Pages 183-203http://dx.doi.org/10.1155/JAM.2005.183

## Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers

1Department of Mathematics, Pondicherry Engineering College, Pondicherry 605014, India
2Department of Physics, Pondicherry Engineering College, Pondicherry 605014, India
3Department of Applied Mathematics, Ideal College of Arts and Sciences, Kakinada 530003, India

Received 26 November 2004; Revised 11 April 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Steady incompressible flow around a circular cylinder in an external magnetic field that is aligned with fluid flow direction is studied for Re (Reynolds number) up to 40 and the interaction parameter in the range 0N15 (or 0M30), where M is the Hartmann number related to N by the relation M=2NRe, 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 Re=10 is suppressed completely when N<1 and it started growing again when N9. For Re=20 and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing when N3. The drag coefficient decreases for low values of N(<0.1) and then increases with increase of N. The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary with N. It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values of N(<0.1) and rear pressure inversion occurs with further increase of N. These results are in agreement with experimental findings.