  Assuming that there exists a species of heavy sterile neutrinos($m_{\nu}>1$
keV) and their decays can serve as a heating source of the hot gas in galaxy
clusters, we study how the observational constraints on cooling flow limit the
mass of these sterile neutrinos. We predict a relation among the luminosity,
total mass and the redshift of a cluster, and we compare this relation with
data from 12 clusters to obtain an estimate of the decay rate of the sterile
neutrino.
