Numerical simulation of magnetic control of heat transfer in thermal convection

We report on numerical study of effects of orientation and distribution of an external magnetic field on the reorganization of convective structures and heat transfer in thermal convection in electrically conductive fluids. The simulations were performed using a transient RANS (T-RANS) approach in which the large-scale deterministic structures are numerically resolved in time and space and the unresolved contribution is modelled using an algebraic stress–flux three-equation subscale model. For low Prandtl (Pr) fluids the subscale model was extended to include Pr-dependent molecular dissipation of heat flux. The method was first validated in natural convection in a side-heated cubical enclosure subjected to magnetic fields of different orientation, strength and penetration depth, showing good agreement with the previous benchmark studies. Subsequently, a series of simulations was performed of turbulent Rayleigh–Bénard convection subjected to different magnetic fields over a range of Rayleigh (Ra) and Hartmann (Ha) numbers. The computed Nusselt number showed good agreement with the available experimental results. Numerical visualization of instantaneous flow patterns showed dramatic differences in the convective structures and local heat transfer for different orientation of the magnetic field with respect to the gravitation vector. A gradual, step-like increase in the magnetic strength revealed an interesting outcome of the “competition” between the buoyancy and the Lorentz forces, leading first to chaotic transition and eventually to laminarization. For specific ranges of Ha, it was found that a local magnetic field confined to the wall boundary layer along the thermally active walls provides almost equal effects as the homogeneous field over the whole flow, indicating an interesting possibility for controlling thermal convection and associated heat transfer.