  We discuss a detailed study of the variation of shear viscosity, $\eta$, with
temperature and baryon chemical potential within the framework of
Polyakov$-$Nambu$-$Jona-Lasinio model. $\eta$ is found to depend strongly on
the spectral width of the quasi-particles present in the model. The variation
of $\eta$ across the phase diagram has distinctive features for different kinds
of transitions. These variations have been used to study the possible location
of the Critical End Point (CEP), and cross-checked with similar studies of
variation of specific heat. Finally using a parameterization of freeze-out
surface in heavy-ion collision experiments, the variation of shear viscosity to
entropy ratio has also been discussed as a function of the center of mass
energy of collisions.
