  We investigate the efficiency and time-dependence of thermally and cosmic ray
driven galactic winds for the metal enrichment of the intra-cluster medium
(ICM) using a new analytical approximation for the mass outflow. The spatial
distribution of the metals are studied using radial metallicity profiles and 2D
metallicity maps of the model clusters as they would be observed by X-ray
telescopes like XMM-Newton. Analytical approximations for the mass loss by
galactic winds driven by thermal and cosmic ray pressure are derived from the
Bernoulli equation and implemented in combined N-body/hydrodynamic cosmological
simulations with a semi-analytical galaxy formation model. Observable
quantities like the mean metallicity, metallicity profiles, and 2D metal maps
of the model clusters are derived from the simulations. We find that galactic
winds alone cannot account for the observed metallicity of the ICM. At redshift
$z=0$ the model clusters have metallicities originating from galactic winds
which are almost a factor of 10 lower than the observed values. For massive,
relaxed clusters we find, as in previous studies, a central drop in the
metallicity due to a suppression of the galactic winds by the pressure of the
ambient ICM. Combining ram-pressure stripping and galactic winds we find radial
metallicity profiles of the model clusters which agree qualitatively with
observed profiles. Only in the inner parts of massive clusters the observed
profiles are steeper than in the simulations. Also the combination of galactic
winds and ram-pressure stripping yields too low values for the ICM
metallicities. The slope of the redshift evolution of the mean metallicity in
the simulations agrees reasonably well with recent observations.
