  Considering ($1+1$)-dimensional fluid in presence of gravitational trace
anomaly, as an effective description of higher-dimensional fluid, the
hydrodynamics is discussed through a first order thermodynamic description.
Contrary to the existing approaches which are second order in nature, the fluid
velocity is identified through the auxiliary field required to describe the
Polyakov action for the effective description of relevant energy-momentum
tensor. The thermodynamic and fluid quantities, on a static black hole
spacetime, are calculated both near the horizon as well as at the asymptotic
infinity. The Unruh vacuum appears to be suitable one for the present analysis,
in contrast to Israel-Hartle-Hawking vacuum which is consistent with second
order description. As in anomaly cancellation approach to find the Hawking flux
the Unruh vacuum is consistent with the required conditions, in reverse way we
interpret this fluid description as an alternative approach to find these
required conditions to calculate the same in anomaly cancellation approach.
