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We find an analytical solution to relativistic viscous hydrodynamics for a1+1 dimensional Landau flow profile. We consider relativistic Navier-Stokesform of the dissipative hydrodynamic equation, for a non-conformal system witha constant speed of sound, and employ the obtained solution to fit rapidityspectrum of observed pions in $\sqrt{s_{NN}}=$ 200, 17.3, 12.3, 8.76, 7.62,6.27, 4.29, 3.83, 3.28 and 2.63 GeV collision energies. We find that at thefreeze-out hypersurface with improved Landau's freeze-out prescription, theviscous corrections do not affect the rapidity spectra. We demonstrate that thesolution of the non-conformal Landau flow lead to a better agreement with theexperimental data compared to the conformal ideal solution. We also extractspeed of sound from fit to the rapidity spectra for various collision energiesand find a monotonous decrease with decreasing collision energies. Appealing tothe fact that viscosity has negligible effect on rapidity spectra for Landau'sfreeze-out scenario, we argue that our calculations provides a framework forextracting the average value of speed of sound in relativistic heavy-ioncollisions.

Viscosity, non-conformal equation of state and sound velocity in Landau hydrodynamics