  The shear free condition is studied for dissipative relativistic
self-gravitating fluids in the quasi-static approximation. It is shown that, in
the Newtonian limit, such condition implies the linear homology law for the
velocity of a fluid element, only if homology conditions are further imposed on
the temperature and the emission rate. It is also shown that the shear-free
plus the homogeneous expansion rate conditions are equivalent (in the Newtonian
limit) to the homology conditions. Deviations from homology and their
prospective applications to some astrophysical scenarios are discussed, and a
model is worked out.
