In this paper an attempt has been made to study the flow characteristics of a magnetic fluid flowing through a channel under the action of magnetic field keeping the magnet along axial direction and changing its length considering FHD phenomenon with respect to the formation of recirculating bubbles, velocity contour and average stagnation pressure. The continuity and momentum equations have been discretized by a control volume based finite difference method. Power law scheme is used to discretize the convective terms. The discretized equations have been solved iteratively by SIMPLE algorithm, using line-by-line ADI method. The distribution of grid nodes is non-uniform and staggered in both coordinating directions. The shape and size of the bubble and average stagnation pressure have a greater importance in case of various practical applications, such as magnetic hyperthermia, targeted transport of drugs, magnetic wound or cancer tumour treatment, opening the blockage in the artery etc.