  Direct numerical simulations and linear stability analysis are carried out to
study mixed convection in a horizontal duct with constant-rate heating applied
at the bottom and imposed transverse horizontal magnetic field. A
two-dimensional approximation corresponding to the asymptotic limit of very
strong magnetic field effect is validated and applied, together with full
three-dimensional analysis, to investigate the flow's behaviour in the
previously unexplored range of control parameters corresponding to typical
conditions of a liquid metal blanket of a nuclear fusion reactor (Hartmann
numbers up to $10^4$ and Grashof numbers up to $10^{10}$). It is found that the
instability to quasi-two-dimensional rolls parallel to the magnetic field
discovered at smaller Hartmann and Grashof numbers in earlier studies also
occurs in this parameter range. Transport of the rolls by the mean flow leads
to magnetoconvective temperature fluctuations of exceptionally high amplitudes.
It is also demonstrated that quasi-two-dimensional structure of flows at very
high Hartmann numbers does not guarantee accuracy of the classical
two-dimensional approximation. The accuracy deteriorates at the highest Grashof
numbers considered in the study.
