  By simulating jet-inflated bubbles in cooling flows with the PLUTO
hydrodynamic code we show that mixing of high entropy shocked jet's material
with the intra-cluster medium (ICM) is the major heating process perpendicular
to the jets' axis. Heating by the forward shock is not significant. The mixing
is very efficient in heating the ICM in all directions, to distances of ~10kpc
and more. Although the jets are active for a time period of only 20 Myr, the
mixing and heating near the equatorial plane, as well as along the symmetry
axis, continues to counter radiative cooling for times of >10^8 yr after the
jets have ceased to exist. We discuss some possible implications of the
results. (i) The vigorous mixing is expected to entangle magnetic field lines,
hence to suppress any global heat conduction in the ICM near the center. (ii)
The vigorous mixing forms multi-phase ICM in the inner cluster regions, where
the coolest parcels of gas will eventually cool first, flow inward, and feed
the active galactic nucleus to set the next jet-activity episode. This further
supports the cold feedback mechanism. (iii) In cases where the medium outside
the region of r~10kpc is not as dense as in groups and clusters of galaxies,
like during the process of galaxy formation, the forward shock and the high
pressure of the shocked jets' material might expel gas from the system.
