  In this paper we have extended our previous modeling of energy balance in the
chromosphere-corona transition region to cases with particle and mass flows.
The cases considered here are quasi-steady, and satisfy the momentum and energy
balance equations in the transition region. We include in all equations the
flow velocity terms and neglect the partial derivatives with respect to time.
We present a complete and physically consistent formulation and method for
solving the non-LTE and energy balance equations in these situations, including
both particle diffusion and flows of H and He. Our results show quantitatively
how mass flows affect the ionization and radiative losses of H and He, thereby
affecting the structure and extent of the transition region. Also, our
computations show that the H and He line profiles are greatly affected by
flows. We find that line shifts are much less important than the changes in
line intensity and central reversal due to the effects of flows. In this paper
we use fixed conditions at the base of the transition region and in the
chromosphere because our intent is to show the physical effects of flows and
not to match any particular observations. However, we note that the profiles we
compute can explain the range of observed high spectral and spatial resolution
Lyman alpha profiles from the quiet Sun. We suggest that dedicated modeling of
specific sequences of observations based on physically consistent methods like
those presented here will substantially improve our understanding of the energy
balance in the chromosphere and corona.
