Problems in suppressing cooling flows in clusters of galaxies by global heat conduction

I use a simple analytical model to show that simple heat conduction models cannot significantly suppress cluster cooling flows. I build a static medium where heat conduction globally balances radiative cooling, and then perturb it. I show that a perturbation extending over a large fraction of the cooling flow region will grow to the non-linear regime within a Hubble time. Such perturbations are reasonable in clusters which frequently experience mergers and/or AGN activity. This result strengthens previous findings which show that a steady solution does not exist for a constant heat conduction coefficient.