  I study non-radiative cooling of X-ray emitting gas via heat conduction along
magnetic field lines inside magnetic flux loops in cooling flow clusters of
galaxies. I find that such heat conduction can reduce the fraction of energy
radiated in the X-ray band by a factor of 1.5-2. This non-radiative cooling
joins two other proposed non-radiative cooling processes, which can be more
efficient. These are mixing of cold and hot gas, and heat conduction initiated
by magnetic fields reconnection between hot and cold gas. These processes when
incorporated into the moderate cooling flow model lead to a general cooling
flow model with the following ingredients. (1) Cooling flow does occur, but
with a mass cooling rate about 10 times lower than in old versions of the
cooling flow model. Namely, heating occurs such that the effective age of the
cooling flow is much below the cluster age, but the heating can't prevent
cooling altogether. (2) The cooling flow region is in a non-steady state
evolution. (3) Non-radiative cooling of X-ray emitting gas can bring the model
to a much better agreement with observations. (4) The general behavior of the
cooling flow gas, and in particular the role played by magnetic fields, make
the intracluster medium in cooling flow clusters similar in some aspects to the
active solar corona.
