Considering the condition on conservation of energy momentum tensor (EMT), we study late time cosmological solutions in the context of $f(R,T)=R+\alpha T^{n}$ gravity (where $\alpha$ and $n$ are constants) in a flat FLRW spacetime. The present model discusses the case of a barotropic perfect fluid as the matter content of the Universe, along with the case when dissipative effects are taken into account. Briefly, assuming a single perfect fluid we find that the mentioned model is not capable of presenting an observationally consistent picture of the late time accelerated expansion of the Universe; nevertheless, the model leads to admissible solutions when the bulk viscosity is included. In this regard, a consistent setting is found considering the Eckart, Truncated and Full Israel-Stewart theories which determine the behavior of bulk viscosity. In the presence of bulk viscosity, the behavior of the deceleration parameter (DP) shows that the underlying model can describe an acceptable evolution even if the isotropic pressure of matter content of the Universe is negligible.
