  The heavy quark collisional scattering on partons of the quark gluon plasma
(QGP) is studied in a QCD medium at finite temperature and chemical potential.
We evaluate the effects of finite parton masses and widths, finite temperature
$T$ and quark chemical potential $\mu_q$ on the different elastic cross
sections for dynamical quasi-particles (on- and off-shell particles in the QGP
medium as described by the dynamical quasi-particles model "DQPM") using the
leading order Born diagrams. Our results show clearly the decrease of the $qQ$
and $gQ$ total elastic cross sections when the temperature and the quark
chemical potential increase. These effects are amplified for finite $\mu_q$ at
temperatures lower than the corresponding critical temperature $T_c (\mu_q)$.
Using these cross sections we, furthermore, estimate the energy loss and
longitudinal and transverse momentum transfers of a heavy quark propagating in
a finite temperature and chemical potential medium. Accordingly, we have shown
that the transport properties of heavy quarks are sensitive to the temperature
and chemical potential variations. Our results provide some basic ingredients
for the study of charm physics in heavy-ion collisions at Beam Energy Scan
(BES) at RHIC and CBM experiment at FAIR.
