  We analyse various flow coefficients of anisotropic momentum distribution of
final state particles in mid-central ($b$ $=$ 5--9 $fm$) Au + Au collisions in
the beam energy range $\rm E_{\rm Lab}$ $=$ $1A -158A$ GeV. Different variants
of the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, namely the
pure transport (cascade) mode and the hybrid mode, are employed for this
investigation. In the hybrid UrQMD model, the ideal hydrodynamical evolution is
integrated with the pure transport calculation for description of the evolution
of the fireball. We opt for the different available equations of state (EoS)
replicating the hadronic as well as partonic degrees of freedom together with
possible phase transitions, viz. hadron gas, chiral + deconfinement EoS and bag
model EoS, to investigate their effect on the properties of the final state
particles. We also attempt to gain insights about the dynamics of the medium by
studying different features of particle production such as particle ratios and
net-proton rapidity distribution. The results and conclusions drawn here would
be useful to understand the response of various observables to the underlying
physics of the model as well as to make comparisons with the upcoming
measurements of the future experiments at Facility for Antiproton and Ion
Research (FAIR) and Nuclotron-based Ion Collider fAcility (NICA).
