Effect of radial magnetic field on the natural convection in a semi-circular curved enclosure for different aspect ratios

Abstract

The problem of natural convection in a (2D) semi-circular curved enclosure in the presence of a radial magnetic field is numerically studied in this paper. The selected configuration is such that the convective flow is driven by a mean temperature gradient also directed radially, and the effects of enclosure aspect ratio and the strength of the applied magnetic field are considered. Numerical simulations are carried out using a (3D) MHD code developed by our research group, first at a fixed \(Ra = 10^5 \) and \(Pr = 0.71\) for aspect ratios \(A = 2, 4, 6, 8\) and Hartmann numbers in the range \(Ha = 0-100\). As the aspect ratio is increased, a Rayleigh–Bénard-like convection with the convective cells formed near the symmetric central portion of the enclosure, where the mean temperature gradient is anti-parallel to the gravity, is found to be triggered. Except at the transition, the effect of the imposed radial magnetic field is found to decrease the fluid motion in general, and the convective motion is completely suppressed at \(Ha = 100\) irrespective of the aspect ratio. The critical Hartmann number for the onset of (R–B-like) convection is found to decrease with an increase in the aspect ratio. Numerical simulations are also attempted at a fixed \(A = 10\) and \(Ra = 8000\) for Prandtl numbers \(Pr = 10, 0.1, 0.01\) and Hartmann numbers \(Ha = 0,3,6,9,12\). In the absence of the applied magnetic field, the flow is found to exhibit periodic oscillations of increased amplitude and time-period when Pr is decreased, except at \(Pr = 10\), where a steady-state solution is found. For \(Pr = 0.01\), the oscillatory flow is observed to persist even when the magnetic field strength is increased in the range \(Ha = 3 - 12\). Moreover, the temporal frequency of these flow oscillations is found to be nearly the same for \(Ha \le 9\).