  The viscosity of dark matter in cosmological models may cause an accelerated
expansion and when this effect is sufficiently large, it can explain the dark
energy. In this work, attributing the origin of viscosity to self-interaction
of dark matter, we study the viscous cosmology at small redshift $(0\leq
z\leq2.5)$. Assuming the cluster scale to be virialized and by modeling a power
law behavior of velocity gradients, we calculate the Hubble expansion rate,
$H(z)$ and the deceleration parameter, $q(z)$. We then perform a $\chi^{2}$
analysis to estimate the best fit model parameters. By using the best fit
values, we explain the cosmic chronometer and type Ia supernova data. We
conclude that if the dissipative effects become prominent only at the late time
of cosmic evolution and are smaller at higher redshift, we can explain the
observational data without requiring any dark energy component. Our analysis is
independent of any specific model of self interacting dark matter.
