Rayleigh–Bénard convection in liquid metal layers under the influence of a horizontal magnetic field

Abstract

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.

Convection patterns in a liquid metal under an imposed horizontal magnetic field

“…That may cause the increase in the number of rolls from 4 to 5 for steady roll convection. The results of the laboratory experiment is mainly for Ra/Q 1 with very large Q ∼ 10 6 [17], having no overlapping region with the present experiment except for nonmagnetic cases. However, behaviors observed in the present experiment have features common with that by temperature measurements.…”

“…[2]. The rise of Ra c at large Q values was confirmed by laboratory experiments in the same paper [17]. Their stability analysis also predicts a slight variation in the critical wave number.…”

“…The flow direction deduced by the four-element temperature probe in the experiment in Ref. [17] is isotropic when Q is zero. The 063020-10 present result by direct measurements of flow velocity for Q = 0 is consistent with that.…”

“…The delay of the onset of oscillatory convection by magnetic fields has been confirmed in laboratory experiments and further transitions to chaos or turbulence have been reported [11][12][13][14][15][16][17]. However, previous experimental studies lacked the possibility to directly measure flow velocities and therefore have not fully elucidated the convection pattern in the presence of a magnetic field.…”

“…[17] indicated that the horizontal magnetic field raises the critical Ra for onset of convection depending on the horizontal scale of the layer because of the emergence of sidewall Hartmann layers. This is in contrast to the situation for a horizontally infinite layer in Ref.…”