  We use high-resolution hydrodynamic re-simulations to investigate the
properties of the thermal Sunyaev-Zel'dovich (SZ) effect from galaxy clusters.
We compare results obtained using different physical models for the
intracluster medium (ICM), and show how they modify the SZ emission in terms of
cluster profiles and scaling relations. We also produce realistic mock
observations to verify whether the results from hydrodynamic simulations can be
confirmed. We find that SZ profiles depend marginally on the modelled physical
processes, while they exhibit a strong dependence on cluster mass. The central
and total SZ emission strongly correlate with the cluster X-ray luminosity and
temperature. The logarithmic slopes of these scaling relations differ from the
self-similar predictions by less than 0.2; the normalization of the relations
is lower for simulations including radiative cooling. The observational test
suggests that SZ cluster profiles are unlikely to be able to probe the ICM
physics. The total SZ decrement appears to be an observable much more robust
than the central intensity, and we suggest using the former to investigate
scaling relations.
