  The downward flow in a vertical duct with one heated and three thermally
insulated walls is analyzed numerically using the two-dimensional approximation
valid in the asymptotic limit of an imposed strong transverse magnetic field.
The work is motivated by the design of liquid metal blankets with poloidal
ducts for future nuclear fusion reactors, in which the main component of the
magnetic field is perpendicular to the flow direction and very strong heating
is applied at the wall facing the reaction chamber. The flow is found to be
steady-state or oscillating depending on the strengths of the heating and
magnetic field. A parametric study of the instability leading to the
oscillations is performed. It is found among other results that the flow is
unstable and develops high-amplitude temperature oscillations at the conditions
typical for a fusion reactor blanket.
