“…There have been numerous e orts using numerical, analytical, and experimental methods to study those overshoots, see the literature review presented in Reference [9]. The overshoots have been reported in the entrance region of many di erent ow geometries including parallel plates, pipes, annuli and semi-circular sections [1][2][3][9][10][11][12], di erent uid ow cases such as natural and forced convection heat transfer, non-Newtonian uids, pulsating ow ÿelds and moving boundaries [6,10,12,13], di erent inlet boundary conditions such as uniform entry, zero-vorticity and non-uniform entry proÿles [1-3, 9, 13] and di erent numerical approaches such as ÿnite volume, ÿnite element and ÿnite di erence methods [9,[11][12][13]. However, considerable care is needed observing overshoots in uid ow cases which normally have bulges in the vicinity of their solid boundaries, e.g.…”