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Context. The simultaneous occurrence of flows and time damped small-amplitude oscillations in solar prominences is a common phenomenon. These oscillations are mostly interpreted in terms of magnetohydrodynamic (MHD) waves. Aims. We study the time damping of linear non-adiabatic MHD waves in a flowing partially ionised plasma with prominence-like physical conditions. Methods. Considering non-adiabatic single fluid equations for a partially ionised hydrogen plasma, we have solved our dispersion relations for the complex frequency, ω, and we have analysed the behavior of the period, damping time and the ratio of the damping time to the period, versus the real wavenumber k, for Alfven, fast, slow, and thermal waves. Results. While in the case without flow there is a critical wavenumber at which the period of Alfven and fast waves goes to infinite, when a flow is present two different critical wavenumbers appear. The smaller wavenumber depends on the flow speed and causes the period of the high-period branch to go to infinite. When the second critical wavenumber is attained the period of both branches become equal. In general, the time damping of Alfven and fast waves is dominated by resistive effects, and its damping ratio is very inefficient when compared to observations. The damping of slow and thermal waves is basically dominated by non-adiabatic effects, and for slow waves it is possible to obtain a damping ratio close to observations, although it would correspond to long period oscillations with large damping times not often observed. The consideration of a structured medium produces new features such as the apparition of four critical wavenumbers for Alfven waves, and one critical wavenumber for slow waves. For fast waves, constrained propagation substantially improves, within the range of observed wavelengths, the ratio of the damping time to period. Conclusions. The presence of a background flow in a partially ionised plasma gives place to new interesting features when the time damping of MHD waves is studied. In general, the results point out that ion-neutral collisions are an inefficient mechanism to explain the observed time damping of prominence oscillations if they are produced by Alfven and fast waves. If the oscillations are produced by slow waves, only long period oscillations with large damping times produce damping ratios in agreement with observations.

Time damping of non-adiabatic magnetohydrodynamic waves in a partially ionised prominence medium: Effect of a background flow