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. 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-twodimensional 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.

Abstract.The results of the direct numerical simulation (DNS) of the MHD heat transfer in turbulent flow of liquid metal (LM) in a horizontal pipe under the joint influence of a longitudinal magnetic field (MF) and thermo-gravitational convection (TGC) are presented. Discusses the characteristics of hydrodynamics and heat transfer in the longitudinal MF in the absence of TGC. Suppression of turbulent transport is observed with an increase in the Hartmann number: the heat transfer coefficients, the friction coefficient. The authors calculated the effect of TGC in a strong longitudinal MF for a homogeneous heating. Investigated the averaged fields of velocity and temperature, heat transfer characteristics, the distribution of wall temperature along the perimeter of the cross section of the pipe. The effect of TGC on the velocity field is affected stronger than in the temperature field.

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