Efficacy of transverse magnetic field towards suppressing nanofluidic flow instabilities over bluff objects

•The coupled effect of nanoparticle concentration and externally imposed transverse magnetic field is analyzed for the free stream flow of Cu-H2O nanofluid over bluff objects.•The critical magnetic parameters for the transformation of the flow from (i) the steady separated pattern to an attached flow pattern and (ii) from an unsteady periodic pattern to a steady separated flow are estimated for a range of Reynolds number and solid volume fraction of the nanofluid.