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We determine the shear viscosity of the ultracold Fermi gas at unitarity inthe normal phase using hydrodynamic expansion data. The analysis is based on ageneralized fluid dynamic framework which ensures a smooth transition betweenthe fluid dynamic core of the cloud and the ballistic corona. We use expansiondata taken by Joseph et al. and measurements of the equation of state by Ku etal. We find that the shear viscosity to particle density ratio just above thecritical temperature is $\eta/n|_{T_c}=0.41\pm 0.11$. We also obtain evidencethat the shear viscosity to entropy density ratio has a minimum slightly above$T_c$ with $\eta/s |_{\it min}=0.50\pm 0.10$.

Determination of the density and temperature dependence of the shear viscosity of a unitary Fermi gas based on hydrodynamic flow