  We study the complete conformal geometry of shear-free spacetimes with
spherical symmetry and do not specify the form of the matter content. The
general conformal Killing symmetry is solved and we can explicitly exhibit the
vector. The existence of a conformal symmetry places restrictions on the model.
The conditions on the gravitational potentials are expressed as a system of
integrability conditions. Timelike sectors and inheriting conformal symmetry
vectors, which map fluid flow lines conformally onto fluid flow lines, are
generated and the integrability conditions are shown to be satisfied. As an
example, a spacetime, which is expanding and accelerating, is identified which
contains a spherically symmetric conformal symmetry.
