Steady incompressible flow around a circular cylinder in an
external magnetic field that is aligned with fluid flow direction
is studied for $\mathrm{Re}$ (Reynolds number) up to 40 and the
interaction parameter in the range $0\leq N \leq 15$ (or $0\leq M \leq 30$ ), where $M$ is the Hartmann number related to $N$ by the
relation $M = \sqrt{2 N \mathrm{Re}}$ , 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 $\mathrm{Re} = 10$
is suppressed completely when $N \lt 1$ and it started growing again
when $N\geq 9$ . For $\mathrm{Re} = 20$ and 40, the suppression is not
complete and in addition to that the rear separation bubble
started increasing when $N\geq 3$s . The drag coefficient decreases
for low values of $N$ $(\lt 0.1)$ and then increases with increase
of $N$ . The pressure drag coefficient, total drag coefficient, and
pressure at rear stagnation point vary with $\sqrt{N}$ . It is also found that the upstream and downstream pressures on the surface of
the cylinder increase for low values of $N$ $(\lt 0.1)$ and rear pressure inversion occurs with further increase of $N$ . These results are in agreement with experimental findings.