This article presents an analytical and experimental study of magnetohydrodynamic Rayleigh–Bénard convection in a large aspect ratio, 20[ratio ]10[ratio ]1, rectangular box. The test fluid is a eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr≈0:02. The experimental setup covers Rayleigh numbers in the range 103< Ra<8×104 and Chandrasekhar numbers 0[les ]Q[les ]1.44×106 or Hartmann numbers 0[les ]M[les ]1200, respectively.When a horizontal magnetic field is imposed on a heated liquid metal layer, the electromagnetic forces give rise to a transition of the three-dimensional convective roll pattern into a quasi-two-dimensional flow pattern in such a way that convective rolls become more and more aligned with the magnetic field. A linear stability analysis based on two-dimensional model equations shows that the critical Rayleigh number for the onset of convection of quasi-two-dimensional flow is shifted to significantly higher values due to Hartmann braking at walls perpendicular to the magnetic field. This finding is experimentally confirmed by measured Nusselt numbers. Moreover, the experiments show that the convective heat transport at supercritical conditions is clearly diminished. Adjacent to the onset of convection there is a significant region of stationary convection with significant convective heat transfer before the flow proceeds to time-dependent convection. However, in spite of the Joule dissipation effect there is a certain range of magnetic field intensities where an enhanced heat transfer is observed. Estimates of the local isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport is accompanied by the formation of strong non-isotropic time-dependent flow in the form of large-scale convective rolls aligned with the magnetic field which exhibit a simpler temporal structure compared to ordinary hydrodynamic flow and which are very effective for the convective heat transport.

The influence of a vertical magnetic field on the integral heat transfer and the temporal dynamics of liquid metal Rayleigh–Bénard convection is studied in an experiment using a small Prandtl number (Pr≈0.02) sodium potassium alloy Na22Kr78 as a test fluid. The test section is a rectangular box of large aspect ratio 20 : 10 : 1 that covers a parameter range of Rayleigh numbers, 103&lt;Ra&lt;105, and Chandrasekhar numbers, 0&lt;Q&lt;1.44×104. The integral heat transfer across the layer is evaluated from the measured temperatures at the upper and the lower boundary and the applied heat flux. Local, time-dependent temperatures are obtained from a four-element temperature probe placed in the middle of the liquid metal layer. The noncoplanar arrangement of the thermocouples enables the evaluation of the time-dependent temperature gradient vector that allows us to estimate the local isotropy properties of the time-dependent flow. From the damping effect of Joule dissipation, the convective heat transport decreases monotonically with increasing Chandrasekhar numbers. Fluctuations of the temperature field are damped significantly by the magnetic field. However, this effect is selective with respect to frequency. Long period fluctuations are strongly damped whereas short period fluctuations are less damped or may even be amplified. The observations show that significant convective heat transport is practically always associated with time-dependent flow. The fluctuating part of the local temperature gradient confirms the horizontal isotropy of the velocity field; no predominant orientation of time-dependent flow structures is established either with or without a magnetic field.

This paper presents an experimental study of the momentum and heat transport in a turbulent magnetohydrodynamic duct flow with strong wall jets at the walls parallel to the magnetic field. Local turbulent flow quantities are measured by a traversable combined temperature-potential-difference probe. The simultaneous measurements of time-dependent velocity and temperature signals facilitates the evaluation of Reynolds stresses and turbulent heat fluxes. Integral quantities such as pressure drop and temperature at the heated wall are evaluated and compared with results from conservative design correlations. At strong enough magnetic fields the destabilizing effect of strong shear generated at the sidewalls wins the competition with the damping effect by Joule's dissipation and turbulent side layers are created. Due to the strong non-isotropic character of the electromagnetic forces, the turbulence structure is characterized by large-scale two-dimensional vortices with their axis aligned in the direction of the magnetic field. As most of the turbulent kinetic energy is concentrated in the near-wall turbulent side layers, the temperatures at the heated wall are governed by the development of the thermal boundary layer in the turbulent flow.

In this paper, a direct check is presented whether the turbulent wind in Rayleigh–Bénard convection is driven by turbulent Reynolds stresses, associated with the tilting plumes at the upper and the lower horizontal walls. This is done by evaluation of experimental data obtained from particle image velocimetry measurements in the centerplane of a cubic convection cell and two-dimensional solution of the Navier–Stokes equations in a square domain. Although, in both, there are regions of negative turbulent energy production P=−〈uiuj〉∂Ui/∂xj, meaning that, locally, energy is transferred from velocity fluctuations to the mean flow, the integral of turbulent energy production over the whole flow field is essentially positive. This implies that the turbulent wind is not driven by the turbulent Reynolds stresses. It is demonstrated from the numerical results that once the mean flow is established, the temperature of the fluid is larger at one side wall and smaller at the other and therefore, the mean flow is driven by the mean buoyant force at the side walls.