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Due to off-center relativistic motion of the charged spectators and the localmomentum-imbalance of the participants, a short-lived huge magnetic field islikely generated, especially in relativistic heavy-ion collisions. Indetermining the temperature dependence of bulk and shear viscosities of the QCDmatter in vanishing and finite magnetic field, we utilize mean fieldapproximation to the SU($3$) Polyakov linear-sigma model (PLSM). We comparebetween the results from two different approaches; Green-Kubo correlation andBoltzmann master equation with Chapman-Enskog expansion. We find that bothapproaches have almost identical results, especially in the hadron phase. Inthe temperature dependence of bulk and shear viscosities relative to thermalentropy at the critical temperature, there is a rapid decrease in the chiralphase-transition and in the critical temperature with increasing magneticfield. As the magnetic field strength increases, a peak appears at the criticaltemperature ($T_c$). This can be understood from the small drop on the thermalentropy at $T_c$, which can be interpreted due to instability in thehydrodynamic flow of the quark-gluon plasma and soft statistical hadronization.It is obvious that, increasing magnetic field accelerates the transition fromhadron to QGP phases (inverse catalysis), i.e., taking place at lowertemperatures.

SU(3) Polyakov linear-sigma model: bulk and shear viscosity of QCD matter in finite magnetic field