A number of studies have shown that the convective stability criterion for the intracluster medium (ICM) is very differentfromtheSchwarzchildcriterion,duetotheeffectsofanisotropicthermalconductionandcosmicrays.Buildingonthesestudies,wedevelopamodeloftheICMinwhichacentralactivegalacticnucleus(AGN)accreteshotintracluster plasma at the Bondi rate and produces cosmic rays that cause the ICM to become convectively unstable. The resulting convection heats the intracluster plasma and regulates its temperature and density profiles. By adjusting a single parameter in the model (the size of the cosmic-ray acceleration region), we are able to achieve a good match to the observed density and temperature profiles in a sample of eight clusters. Our results suggest that convection is an important process in cluster cores. An interesting feature of our solutions isthat the cooling rate is more sharply peaked abouttheclustercenterthanistheconvectiveheatingrate.Asaresult,inseveraloftheclustersinoursample,acompact coolingflowarisesinthecentralregionwithasizercf thatistypicallyafewkpc.ThecoolingflowmatchesontoaBondi flow at smaller radii. The mass accretion rate in the Bondi flow is equal to, and controlled by, the rate at which mass flowsinthroughthecoolingflow.Oursolutionssuggest thattheAGNregulatesthemassaccretionrateintheseclusters bycontrollingrcf: if the AGN power rises above the equilibrium level,rcf decreases, the mass accretion rate drops, and the AGN power drops back down to the equilibrium level. Subject headingg convection — cooling flows — galaxies: active — galaxies: clusters: general — magnetic fields — turbulence