  The problem of burning of high-velocity gas streams in channels is revisited.
Previous treatments of this issue are found to be incomplete. It is shown that
despite relative smallness of the transversal gas velocity, it plays crucial
role in determining flame structure. In particular, it is necessary in
formulating boundary conditions near the flame anchor, and for the proper
account of the flame propagation law. Using the on-shell description of steady
anchored flames, a consistent solution of the problem is given. Equations for
the flame front position and gas-velocity at the front are obtained. It is
demonstrated that they reduce to a second-order differential equation for the
front position. Numerical solutions of the derived equations are found.
