  We analyze two time-dependent cluster cooling flow models in spherical
symmetry. The first assumes that the intracluster gas resides in a static
external potential, and includes the effects of optically thin radiative
cooling and mass deposition. This corresponds to previous steady-state cooling
flow models calculated by White & Sarazin (1987). Detailed agreement is found
between steady-state models and time-dependent models at fixed times in the
simulations. The mass accretion rate is found either to increase or remain
nearly constant once flows reach a steady state. The time rate of change of the
accretion rate is strongly sensitive to the value of the mass deposition
parameter q, but only mildly sensitive to the ratio beta of gravitational
binding energy to gas temperature. We show that previous scaling arguments
presented by Bertschinger (1988) and White (1988) are valid only for mature
cooling flows with weak mass deposition (q ~< 1). The second set of models
includes the effects of a secularly deepening cluster potential and secondary
infall of gas from the Hubble flow. We find that such heating effects do not
prevent the flows from reaching a steady state within an initial central
cooling time.
