Transport Coefficients of Hadronic Matter near $T_c$

A hadron resonance gas model including all known particles and resonances with masses $m<2$ GeV and an exponentially rising density of Hagedorn states for $m>2$ GeV is used to obtain an upper bound on the shear viscosity to entropy density ratio, $\eta/s\approx1/(4\pi)$, of hadronic matter near $T_c$. We found a large trace anomaly and small speed of sound near $T_c$, which agree well with recent lattice calculations. We comment on the bulk viscosity to entropy density ratio close to $T_c$.