Sharp fronts observed by Chandra satellite between dense cool cluster cores moving with near-sonic velocity through the hotter intergalactic gas , require strong suppression of thermal conductivity across the boundary . This may be due to magnetic fields tangential to the contact surface separating the two plasma components . We point out that a super-Alfvenic motion of a plasma cloud ( a core of a merging galaxy ) through a weakly magnetized intercluster medium leads to ” magnetic draping ” , formation of a thin , strongly magnetized boundary layer with a tangential magnetic field . For supersonic cloud motion , M _ { s } \geq 1 , magnetic field inside the layer reaches near-equipartition values with thermal pressure . Typical thickness of the layer is \sim L / M _ { A } ^ { 2 } \ll L , where L is the size of the obstacle ( plasma cloud ) moving with Alfvén Mach number M _ { A } \gg 1 . To a various degree , magnetic draping occurs both for sub- and supersonic flows , random and ordered magnetic fields and it does not require plasma compressibility . The strongly magnetized layer will thermally isolate the two media and may contribute to the Kelvin-Helmholtz stability of the interface . Similar effects occur for radio bubbles , quasi-spherical expanding cavities blown up by AGN jets ; in this case the thickness of the external magnetized layer is smaller , \sim L / M _ { A } ^ { 3 } \ll L .