  We study the single electron spectra from $D-$ and $B-$meson semileptonic
decays in Au+Au collisions at $\sqrt{s_{\rm NN}}=$200, 62.4, and 19.2 GeV by
employing the parton-hadron-string dynamics (PHSD) transport approach that has
been shown to reasonably describe the charm dynamics at RHIC and LHC energies
on a microscopic level. In this approach the initial heavy quarks are produced
by using the PYTHIA which is tuned to reproduce the FONLL calculations. The
produced heavy quarks interact with off-shell massive partons in QGP with
scattering cross sections which are calculated in the dynamical quasi-particle
model (DQPM). At energy densities close to the critical energy density the
heavy quarks are hadronized into heavy mesons through either coalescence or
fragmentation. After hadronization the heavy mesons interact with the light
hadrons by employing the scattering cross sections from an effective
Lagrangian. The final heavy mesons then produce single electrons through
semileptonic decay. We find that the PHSD approach well describes the nuclear
modification factor $R_{\rm AA}$ and elliptic flow $v_2$ of single electrons in
d+Au and Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 200 GeV and the elliptic flow
in Au+Au reactions at $\sqrt{s_{\rm NN}}=$ 62.4 GeV from the PHENIX
collaboration, however, the large $R_{\rm AA}$ at $\sqrt{s_{\rm NN}}=$ 62.4 GeV
is not described at all. Furthermore, we make predictions for the $R_{\rm AA}$
of $D-$mesons and of single electrons at the lower energy of $\sqrt{s_{\rm
NN}}=$ 19.2 GeV. Additionally, the medium modification of the azimuthal angle
$\phi$ between a heavy quark and a heavy antiquark is studied. We find that the
transverse flow enhances the azimuthal angular distributions close to $\phi=$ 0
because the heavy flavors strongly interact with nuclear medium in relativistic
heavy-ion collisions and almost flow with the bulk matter.
