  A hydrodynamic model for the energy transport between the components of a
contact binary is presented. Energy is transported by a large-scale, steady
circulation carrying high entropy matter from the primary to secondary
component. The circulation is driven by the baroclinic structure of the common
envelope, which is a direct consequence of the nonuniform heating at the inner
critical Roche lobes due to unequal emergent energy fluxes of the components.
The mass stream flowing around the secondary is bound to the equatorial region
by the Coriolis force and its width is determined primarily by the flow
velocity. Its bottom is separated from the underlying secondary's convection
zone by a radiative transition layer acting as an insulator. For a typically
observed degree of contact the heat capacity of the stream matter is much
larger than radiative losses during its flow around the secondary. As a result,
its effective temperature and entropy decrease very little before it returns to
the primary. The existence of the stream changes insignificantly specific
entropies of both convective envelopes and sizes of the components. Substantial
oversize of the secondaries, required by the Roche geometry, cannot be
explained in this way. The situation can, however, be explained by assuming
that the primary is a main sequence star whereas the secondary is in an
advanced evolutionary stage with hydrogen depleted in its core. Such a
configuration is reached past mass transfer with mass ratio reversal. Good
agreement with observations is demonstrated by model calculations applied to
actual W UMa-type binaries. In particular, a presence of the equatorial bulge
moving with a relative velocity of 10-30 km/s around both components of AW UMa
is accounted for.
