Cosmic acceleration with bulk viscosity in modified $f(Q)$ gravity

In this article, we have investigated the role of bulk viscosity to study the accelerated expansion of the universe in the framework of modified $f(Q)$ gravity. The gravitational action in this modified gravity theory has the form $f(Q)$, where $Q$ denote the non-metricity scalar. In the present manuscript, we have considered a bulk viscous matter-dominated cosmological model with the bulk viscosity coefficient of the form $\xi =\xi _{0}+\xi _{1}H+\xi _{2}\left( \frac{\dot{H}}{H}+H\right)$ which is proportional to the velocity and acceleration of the expanding universe. Two sets of limiting conditions on the bulk viscous parameters $\xi _{0},$ $\xi _{1},$ $$ and model parameter $\alpha$ arose here out of which one condition favours the present scenario of cosmic acceleration with a phase transition and corresponds to the universe with a Big Bang origin. Moreover, we have discussed the cosmological behaviour of some geometrical parameters. Then, we have obtained the best fitting values of the model parameters $\xi _{0},$ $\xi _{1},$ $\xi _{2}$ and $\alpha$ by constraining our model with updated Hubble datasets consisting of $57$ data points and recently released Pantheon datasets consisting of $1048$ data points which show that our obtained model has good compatibility with observations. Further, we have also included the Baryon Acoustic Oscillation (BAO) datasets of six data points with the Hubble \& Pantheon datasets and obtained slightly different values of the model parameters. Finally, we have analyzed our model with the statefinder diagnostic analysis and found some interesting results and are discussed in details.