  Advection is believed to be the dominant cooling mechanism in optically thin
advection-dominated accretion flows (ADAF's). When outflow is considered,
however, the first impression is that advection should be of opposite sign in
the inflow and the outflow, due to the opposite direction of radial motion.
Then how is the energy balance achieved simultaneously? We investigate the
problem in this paper, analysing the profiles of different components of
advection with self-similar solutions of ADAF's in spherical coordinates
($r\theta\phi$). We find that for $n < 3\gamma/2-1$, where $n$ is the density
index in $\rho \propto r^{-n}$ and $\gamma$ is the heat capacity ratio, the
radial advection is a heating mechanism in the inflow and a cooling mechanism
in the outflow. It becomes 0 for $n = 3\gamma/2-1$, and turns to a cooling
mechanism in the inflow and a heating mechanism in the outflow for $n >
3\gamma/2-1$. The energy conservation is only achieved when the latitudinal
($\theta$-direction) advection is considered, which takes an appropriate value
to maintain energy balance, so that the overall effect of advection, no matter
the parameter choices, is always a cooling mechanism that cancels out the
viscous heating everywhere. For the extreme case of $n=3/2$, latitudinal motion
stops, viscous heating is balanced solely by radial advection, and no outflow
is developed.
