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

Shear Viscosity and Phase Diagram from Polyakov$-$Nambu$-$Jona-Lasinio model