  The transport coefficients of a multi-component hadronic gas at zero and
non-zero baryon chemical potential are calculated using the Chapman-Enskog
method. The calculations are done within the framework of an $S$-matrix based
interacting hadron resonance gas model. In this model, the phase-shifts and
cross-sections are calculated using $K$-matrix formalism and where required, by
parameterizing the experimental phase-shifts. Using the energy dependence of
cross-section, we find the temperature dependence of various transport
coefficients such as shear viscosity, bulk viscosity, heat conductivity and
diffusion coefficient. We finally compare our results regarding various
transport coefficients with previous results in the literature.
