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Direct numerical simulations and linear stability analysis are carried out tostudy mixed convection in a horizontal duct with constant-rate heating appliedat the bottom and imposed transverse horizontal magnetic field. Atwo-dimensional approximation corresponding to the asymptotic limit of verystrong magnetic field effect is validated and applied, together with fullthree-dimensional analysis, to investigate the flow's behaviour in thepreviously unexplored range of control parameters corresponding to typicalconditions of a liquid metal blanket of a nuclear fusion reactor (Hartmannnumbers up to $10^4$ and Grashof numbers up to $10^{10}$). It is found that theinstability to quasi-two-dimensional rolls parallel to the magnetic fielddiscovered at smaller Hartmann and Grashof numbers in earlier studies alsooccurs in this parameter range. Transport of the rolls by the mean flow leadsto magnetoconvective temperature fluctuations of exceptionally high amplitudes.It is also demonstrated that quasi-two-dimensional structure of flows at veryhigh Hartmann numbers does not guarantee accuracy of the classicaltwo-dimensional approximation. The accuracy deteriorates at the highest Grashofnumbers considered in the study.

Magnetoconvection in a horizontal duct flow at very high Hartmann and Grashof numbers