  In mean field approximation, the grand canonical potential of SU(3) Polyakov
linear-$\sigma$ model (PLSM) is analysed for chiral phase-transition,
$\sigma_l$ and $\sigma_s$ and for deconfinement order-parameters, $\phi$ and
$\phi^*$ of light- and strange-quarks, respectively. Various PLSM parameters
are determined from the assumption of global minimization of the real part of
the potential. Then, we have calculated the subtracted condensates
($\Delta_{l,s}$). All these results are compared with recent lattice QCD
simulations. Accordingly, essential PLSM parameters are determined. The
modelling of the relaxation time is utilized in estimating the conductivity
properties of the QCD matter in thermal medium, namely electric
[$\sigma_{el}(T)$] and heat [$\kappa(T)$] conductivities. We found that the
PLSM results on the electric conductivity and on the specific heat agree well
with the available lattice QCD calculations. Also, we have calculated bulk and
shear viscosities normalized to the thermal entropy, $\xi/s$ and $\eta/s$,
respectively, and compared them with recent lattice QCD. Predictions for $(\xi
/s)/(\sigma_{el}/T)$ and $(\eta/s)/(\sigma_{el}/ T)$ are introduced. We
conclude that our results on various transport properties show some essential
ingredients, that these properties likely come up with, in studying QCD matter
in thermal and dense medium.
