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

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