  We determine the hydrodynamic relaxation times $\tau_\eta$ for the shear
viscosity and $\tau_\kappa$ for the thermal conductivity in the normal phase of
a unitary Fermi gas confined in a box potential. Using a kinetic theory
relaxation model, we extract $\tau_\eta$ and $\tau_\kappa$ from the
time-dependent free-decay of a spatially periodic density perturbation,
yielding the universal density-shift coefficients for the shear viscosity and
thermal conductivity.
