Theoretical and observational arguments suggest that there is a large amount of hot ($sim 10^6$ K), diffuse gas residing in the Milky Ways halo, while its total mass and spatial distribution are still unclear. In this work, we present a general model for the gas density distribution in the Galactic halo, and investigate the gas evolution under radiative cooling with a series of 2D hydrodynamic simulations. We find that the mass inflow rate in the developed cooling flow increases with gas metallicity and the total gas mass in the halo. For a fixed halo gas mass, the spatial gas distribution affects the onset time of the cooling catastrophe, which starts earlier when the gas distribution is more centrally-peaked, but does not substantially affect the final mass inflow rate. The gravity from the Galactic bulge and disk affects gas properties in inner regions, but has little effect on the final inflow rate either. We confirm our results by investigating cooling flows in several density models adopted from the literature, including the Navarro-Frenk-White (NFW) model, the cored-NFW model, the Maller & Bullock model, and the $beta$ model. Typical mass inflow rates in our simulations range from $sim 5 M_{odot}$ yr$^{-1}$ to $sim 60 M_{odot}$ yr$^{-1}$, and are much higher than the observed star formation rate in our Galaxy, suggesting that stellar and active galactic nucleus feedback processes may play important roles in the evolution of the Milky Way (MW) and MW-type galaxies.
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