The effects of viscosity dependence on the local strength of magnetic field are investigated numerically in a cylindrical geometry. The increase of viscosity resulting from the presence of magnetic field, which has been commonly neglected in most of the simulations, is found to have significant damping effect on the flow field. There exists a critical magnetic strength that leads to different effects in the flow field. The flow is perturbed more significantly for higher magnetic strength if not exceeding the critical value. However beyond the critical magnetic strength, the damping effects overpower the influences of magnetic force to the flow.