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

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 behavior in the previously unexplored range of control parameters corresponding to typical conditions of a liquid metal blanket of a nuclear fusion reactor (the Hartmann numbers up to 10⁴ and the Grashof numbers up to 10¹⁰). 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. The fluctuations are not suppressed or even significantly reduced in amplitude by the very strong magnetic field. It is also demonstrated that the quasi-two-dimensional structure of flows at very high Hartmann numbers does not guarantee the accuracy of the classical two-dimensional approximation. The accuracy deteriorates at the highest Grashof numbers considered in the study.