Effects of strong fringing magnetic fields on turbulent thermal convection

Abstract

We study the influence of fringing magnetic fields on turbulent thermal convection in a horizontally extended rectangular domain. The magnetic field is created in the gap between two semi-infinite planar magnetic poles, with the convection layer located near the edge of the gap. We employ direct numerical simulations in this set-up for fixed Rayleigh and small Prandtl numbers, but vary the fringe width by controlling the gap between the magnetic poles and the convection cell. The magnetic field generated by the magnets is strong enough to cease the flow in the high magnetic flux region of the convection cell. We observe that as the local vertical magnetic field strength increases, the large-scale structures become thinner and align themselves perpendicular to the longitudinal sidewalls. We determine the local Nusselt and Reynolds numbers as functions of the local Hartmann number (based on the vertical component of the magnetic field), and estimate the global heat and momentum transport. We show that the global heat transport decreases with increasing fringe width for strong magnetic fields but increases with increasing fringe width for weak magnetic fields. In the regions of large vertical magnetic fields, the convective motion becomes confined to the vicinity of the sidewalls. The amplitudes of these wall modes show a non-monotonic dependence on the fringe width.

Simulation of magnetohydrodynamic flows of liquid metals with heat transfer or magnetic stirring

“…In this paper, we numerically examined the effects of nonhomogeneous magnetic fields in liquid metal flows using a finite-difference flow solver. We briefly summarized the results of Bhattacharya et al [4] in which the influence of fringing magnetic fields on turbulent convection was studied. An important finding was that for strong magnetic fields, the global heat transport decreases with an increase of fringe-width, whereas for weak magnetic fields, the heat transport marginally increases with an increase of fringe-width.…”

“…These magnets extend from −∞ to ∞ in the 𝑥-direction, 𝑙 𝑦 ∕2 to ∞ in the 𝑦-direction, from near the top wall to ∞ in the positive 𝑧-direction, and from near the bottom wall to −∞ in the negative 𝑧 direction. For a detailed description of the setup, the readers are referred to Bhattacharya et al [4]. In this configuration, the lateral component of the magnetic field (𝐵 𝑥 ) vanishes, and the longitudinal and vertical components, respectively, are logarithmic and inversetangent functions of the spatial coordinates 𝑦 and 𝑧 and the gap 𝛿 between the magnetic poles and the horizontal walls.…”

“…Thus, it is important to understand the impact of spatially varying magnetic fields on MHD flows. Recently, Bhattacharya et al [4] studied the effects of spatially varying magnetic fields on MHD flows driven by buoyancy (magnetoconvection); these effects will be briefly summarized in this paper. There have been several studies on MHD duct flows with different configurations of spatially varying fields (see, for example, Sterl [5] and Prinz et al [6]); however, in this paper, we focus specifically on duct flows with a localized zone of applied magnetic field (henceforth referred to as magnetic obstacle).…”

“…Recently, Bhattacharya et al. [4] studied the effects of spatially varying magnetic fields on MHD flows driven by buoyancy (magnetoconvection); these effects will be briefly summarized in this paper. There have been several studies on MHD duct flows with different configurations of spatially varying fields (see, for example, Sterl [5] and Prinz et al.…”

Stability analysis of wall‐attached Bénard–Marangoni convection in a vertical magnetic field

“…damping [4][5][6][7][8]. This provides the main motivation for the present work, which is concerned with the effect of side walls on the linear instability of BMC in a magnetic field.…”