  We study the influence of converging cooling flow bulk motions on the
Sunyaev-Zel'dovich (SZ) effect. To that purpose we derive a modified Kompaneets
equation which takes into account the contribution of the accelerated electron
media of the cooling flow inside the cluster frame. The additional term is
different from the usual kinematic SZ-effect, which depends linearly on the
velocity, whereas the contribution described here is quadratic in the
macroscopic electron fluid velocity, as measured in the cluster frame. For
clusters with a large cooling flow mass deposition rate and/or a small central
electron density, it turns out that this effect becomes relevant.

Astrophysics