Magnetohydrodynamic convection in a vertical slot with horizontal magnetic field

Abstract

This article presents an experimental study of magnetohydrodynamic convection in a tall vertical slot under the influence of a horizontal magnetic field. The test fluid is an eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr ≈ 0:02. The experimental setup covers Rayleigh numbers in the range 103 [lsim ] Ra [lsim ] 8×104 and Hartmann numbers 0 < M < 1600. The effect of the magnetic field on the convective heat transport is determined not only by damping as expected from Joule dissipation but also, for magnetic fields not too strong, the convective heat transfer may be considerably enhanced compared to ordinary hydrodynamic (OHD) flow. Estimates of the isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport accompanies the formation of strong local anisotropy of the turbulent eddies in the sense of an alignment of the main direction of vorticity with the magnetic field. The reduced three-dimensional nonlinearities in non-isotropic flow favour the formation of largescale vortex structures compared to OHD flow, which are more effective for convective heat transport. Along with the formation of quasi-two-dimensional vortex structures, temperature fluctuations may be considerably enhanced in a magnetic field that is not too strong. However, above Hartmann numbers M [gsim ] 400 the formerly strongly time-dependent flow suddenly becomes stationary with an extended region of high convective heat transport at stationary flow. Finally, for very high Hartmann numbers the convective motion is strongly suppressed and the heat transport is reduced to a state close to pure heat conduction.

Quasi-two-dimensional convection in a three-dimensional laterally heated box in a strong magnetic field normal to main circulation

“…2͒, which we consider as a good convergence. In 15 who reported the values of Rayleigh numbers Ra corresponding to the appearance of oscillations in the flow. These results were reported for a tall cavity with L = 0.1 as critical values of Ra versus the magnetic parameter M, which are connected with the present notations as Ra= Gr Pr L 3 and M =HdLD / 2.…”

“…4 of Ref. 15, the parameter M was varied there just by doubling its value starting from M = 100. Therefore, the numerical critical numbers, which correspond to zero oscillation amplitude, must be smaller than those reported in Ref.…”

“…result in significant three-dimensional effects, especially if the so-called parallel layers are involved. Examples of such flows include buoyant convection in a cavity in a vertical and transverse magnetic fields, 4,8,[13][14][15][16][17] flows with Hunt's jets, [18][19][20][21] flows in bends, 22,23 circular ducts in a nonuniform magnetic field, 24,25 etc. In some situations, usually involving a pair of parallel electrically insulating walls transverse to the sufficiently strong magnetic field, the flow becomes quasi-twodimensional ͑Q2D͒.…”

“…[13][14][15][16]; however, it assumes significantly larger Hartmann numbers for which the Q2D model is applicable. Note that comparing the results of two-dimensional ͑2D͒ stability of convection in long horizontal cavities with experimental data ͑without the magnetic field͒, Gelfgat et al 34 argued that the 2D model yields reliable results for width ratios larger than 5.…”

An approach to verification and validation of MHD codes for fusion applications

“…The differences can be related to both the experiment and the computations. As alternative benchmarks, one can consider experiments on MHD natural-convection flows in [30] and [31].…”