  We extend our hybrid model HydHSD by taking into account shear viscosity
within the Israel-Stewart hydrodynamics. The influence of different forms of
$\pi^{\mu\nu}$ constraints on observables is analyzed. We show that the form of
the corresponding condition plays an important role for the sensitivity of
viscous hydrodynamics to the ratio of shear viscosity to the entropy density,
$\eta/s$. It is shown that the constraint used in the vHLLE model, results in
most sensitivity of rapidity distributions and transverse momentum spectra to a
change of the $\eta/s$ ratio; however, their applicability for large values of
$\eta/s$ is doubtful. On the contrary, the strict constraints from
\cite{MNR2010} are very strong but most established. We also found that
$\eta/s$ as a function of the collision energy probably has an extremum at
$E_{\rm lab}=10.7$ AGeV. However, we obtain that any considered condition does
not allow to reproduce simultaneously pion and proton experimental data within
our model.
