  We provide complete and global solutions of transonic flows around black
holes, in presence of advection, rotation, heating and cooling. We show that
for any degree of advection, there may exist two critical viscosity parameters
$\alpha_{c1, c2}$ such that for $\alpha <\alpha_{c1}$ the flow may pass through
the inner sonic point only. For $\alpha_{c1} <\alpha<\alpha_{c2}$, the flow may
have shock waves, and for $\alpha>\alpha_{c2}$, the flow may again pass through
the inner sonic point, depending on flow parameters. No new topologies emerge
other than what we found earlier while studying viscous isothermal transonic
flows. These findings indicate that the newly discovered advection dominated
flows do not constitute any new solutions.
