  We explore the influence of a temperature-dependent shear viscosity over
entropy density ratio $\eta/s$ on the azimuthal anisotropies v_2 and v_4 of
hadrons at various rapidities. We find that in Au+Au collisions at full RHIC
energy, $\sqrt{s_{NN}}=200$ GeV, the flow anisotropies are dominated by
hadronic viscosity at all rapidities, whereas in Pb+Pb collisions at the LHC
energy, $\sqrt{s_{NN}}=2760$ GeV, the flow coefficients are affected by the
viscosity both in the plasma and hadronic phases at midrapidity, but the
further away from midrapidity, the more dominant the hadronic viscosity is. We
find that the centrality and rapidity dependence of the elliptic and
quadrangular flows can help to distinguish different parametrizations of
$(\eta/s)(T)$. We also find that at midrapidity the flow harmonics are almost
independent of the decoupling criterion, but show some sensitivity to the
criterion at back- and forward rapidities.
