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Considering ($1+1$)-dimensional fluid in presence of gravitational traceanomaly, as an effective description of higher-dimensional fluid, thehydrodynamics is discussed through a first order thermodynamic description.Contrary to the existing approaches which are second order in nature, the fluidvelocity is identified through the auxiliary field required to describe thePolyakov action for the effective description of relevant energy-momentumtensor. The thermodynamic and fluid quantities, on a static black holespacetime, are calculated both near the horizon as well as at the asymptoticinfinity. The Unruh vacuum appears to be suitable one for the present analysis,in contrast to Israel-Hartle-Hawking vacuum which is consistent with secondorder description. As in anomaly cancellation approach to find the Hawking fluxthe Unruh vacuum is consistent with the required conditions, in reverse way weinterpret this fluid description as an alternative approach to find theserequired conditions to calculate the same in anomaly cancellation approach.

Hydrodynamics of $(1+1)$ dimensional fluid in the presence of gravitational anomaly from first order thermodynamics