Vertical structure of Advection dominated Accretion Flows
  We solve the set of hydrodynamic (HD) equations for optically thin Advection
Dominated Accretion Flows (ADAFs) by assuming radially self-similar in
spherical coordinate system $ (r, \theta, \phi) $. The disk is considered to be
steady state and axi-symmetric. We define the boundary conditions at the pole
and the equator of the disk and to avoid singularity at the rotation axis, the
disk is taken to be symmetric with respect to this axis. Moreover, only the $
\tau_{r \phi} $ component of viscous stress tensor is assumed and we have set $
v_{\theta} = 0 $. The main purpose of this study is to investigate the
variation of dynamical quantities of the flow in the vertical direction by
finding an analytical solution. As a consequence, we found that the advection
parameter, $ f^{adv} $, varies along the $ \theta $ direction and reaches to
its maximum near the rotation axis. Our results also show that, in terms of
no-outflow solution, thermal equilibrium still exists and consequently
advection cooling can balance viscous heating.
