  Conduction may play an important role in reducing cooling flows in galaxy
clusters. We analyse a sample of sixteen objects using Chandra data and find
that a balance between conduction and cooling can exist in the hotter clusters
(T > 5 keV), provided the plasma conductivity is close to the unhindered
Spitzer value. In the absence of any additional heat sources, a reduced mass
inflow must develop in the cooler objects in the sample. We fit cooling flow
models to deprojected data and compare the spectral mass deposition rates found
to the values required to account for the excess luminosity, assuming
Spitzer-rate heat transfer over the observed temperature gradients. The mass
inflow rates found are lower than is necessary to maintain energy balance in at
least five clusters. However, emission from cooling gas may be partially
absorbed. We also compute the flux supplied by turbulent heat transport (Cho et
al. 2003) and find conductivity profiles which follow a strikingly similar
temperature dependence to the conductivity values required to prevent cooling.
Finally, we show that the cluster radio luminosities vary by over five orders
of magnitude in objects with X-ray luminosities differing by no more than a
factor of a few. This suggests that there is unlikely to be a straightforward
correlation between the mechanical power provided by the radio lobes and the
rate of energy loss in cooling flow clusters.
