An experimental review on heavy flavor $v_{2}$ in heavy-ion collision

For over a decade now, the primary purpose of relativistic heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) has been to study the properties of QCD matter under extreme conditions -high temperature and high density. The heavy-ion experiments at both RHIC and LHC have recorded a wealth of data in p+p, p+Pb, d+Au, Cu+Cu, Cu+Au, Au+Au, Pb+Pb and U+U collisions at energies ranging from $\sqrt{s_{NN}}$ = 7.7 GeV to 7 TeV. Heavy quarks are considered good probe to study the QCD matter created in relativistic collisions due to their very large mass and other unique properties. A precise measurement of various properties of heavy flavor hadrons provides an insight into the fundamental properties of the hot and dense medium created in these nuclei-nuclei collisions, such as transport coefficient and thermalization and hadronization mechanisms. The main focus of this paper is to present a review on the measurements of azimuthal anisotropy of heavy flavor hadrons and to outline the scientific opportunities in this sector due to future detector upgrade. We will mainly discuss the elliptic flow of open charmed meson ($D$-meson), $J/\psi$ and leptons from heavy flavor decay at RHIC and LHC energy.