  The structure and evolution of low mass W UMa type contact binaries are
discussed by employing Eggleton's stellar evolution code. Assuming that these
systems completely satisfy Roche geometry, we calculate the relative radii of
both components of contact binaries in different contact depth between inner
and outer Roche lobes. We obtain a radius grid of contact binaries, and can
ensure the surfaces of two components lying on an equipotential surface by
interpolation using this radius grid when we follow the evolution of the
contact binaries. We assume that the energy transfer takes place in the
different regions of the common envelope to investigate the effects of the
region of energy transfer on the structure and evolution of contact binaries.
We find that the region of energy transfer has significant influence on the
structure and evolution of contact binaries, and conclude that the energy
transfer may occur in the outermost layers of the common convective envelope
for W-type systems, and this transfer takes place in the deeper layers of the
common envelope for A-type systems. Meanwhile, if we assume that the energy
transfer takes place in the outermost layers for our model with low total mass,
and find that our model steadily evolves towards a system with a smaller mass
ratio and a deeper envelope, suggesting that some A-type W UMa systems with low
total mass could be considered as the later evolutionary stages of W-subtype
systems, and that the surface temperature of the secondary excesses that of the
primary during the time when the primary expands rapidly, or the secondary
contracts rapidly, suggesting that W-subtype systems may be caused by expansion
of the primary, or by the contraction of the secondary.
