Rotating Rayleigh–Bénard convection under the influence of transverse magnetic field

Abstract

In the present numerical study the effect of constant transverse magnetic field on convection of low Prandtl number liquid metal rotating in a cubical cavity with an aspect-ratio of 8:8:1 has been investigated. The bottom wall is heated while the top-wall is cooled and all the other walls are kept thermally insulated. The governing equations of mass, momentum, energy and magneto-hydrodynamic for a frame rotating with the enclosure, subject to Boussinesq approximation applied to gravity and centrifugal force terms, have been solved on a collocated grid using a semi-implicit finite difference method. The simulations have been carried out for liquid metal flows having a fixed Prandtl number Pr=0.01, Rayleigh number Ra=107, and magnetic Prandtl number Pm=4.0×10-4 while Chandrasekhar number Q varies from 5.0625×104 to 1.21×106 and non-dimensional rotation rate Ω is varied from zero to 105.The increase in strength of transverse magnetic field (from Ql=5.0625×104 to Qh=1.21×106) till Q≃Ta leads to slight increase in convective heat transfer as well as formation of two-dimensional coherent structures aligned along the direction of magnetic field. For cases pertaining to Q<Ta the two-dimensionality of the flow breaks down and the rolls distort in their alignment which leads to decrease in magnitude of vertical heat transfer. For cases where Q≪Ta, the increased Coriolis forces lead to generation of large-scale circulation which forms a large cylindrical rotating column of fluid in consonance with Taylor–Proudman theorem. On increasing the strength of magnetic field the component of rms velocity in the direction of magnetic field gets suppressed while there is increase in other two components.