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Abstract:
In magnetoconvection, the flow of an electromagnetically conductive fluid is driven by a combination of buoyancy forces, which create the fluid motion due to thermal expansion and contraction, and Lorentz forces, which distort the convective flow structure in the presence of a magnetic field. The differences in the global flow structures in the buoyancy-dominated and Lorentz-force-dominated regimes lead to different heat transport properties in these regimes, reflected in distinct dimensionless scaling relations of the global heat flux (Nusselt number Nu) versus the strength of buoyancy (Rayleigh number Ra) and electromagnetic forces (Hartmann number Ha). Here, we propose a theoretical model for the transition between these two regimes for the case of a static vertical magnetic field applied across a convective fluid layer confined between two isothermal, a lower warmer and an upper colder, horizontal surfaces. The model suggests that the scaling exponents γ in the buoyancy-dominated regime, Nu∼Raγ, and ξ in the Lorentz-force-dominated regime, Nu∼(Ha−2Ra)ξ, are related as ξ=γ/(1−2γ), and the onset of the transition scales with Ha−1/γRa. These theoretical results are supported by our direct numerical simulations for 10≤Ha≤2000, Prandtl number Pr=0.025 and Ra up to 109 and data from the literature.
