Quasistatic magnetoconvection: heat transport enhancement and boundary layer crossing

Abstract

We present a numerical study of quasistatic magnetoconvection in a cubic Rayleigh-Bénard (RB) convection cell subjected to a vertical external magnetic field. For moderate values of the Hartmann number Ha (characterising the strength of the stabilising Lorentz force), we find an enhancement of heat transport (as characterised by the Nusselt number N u). Furthermore, a maximum heat transport enhancement is observed at certain optimal Ha opt . The enhanced heat transport may be understood as a result of the increased coherency of the thermal plumes, which are elementary heat carriers of the system. To our knowledge this is the first time that a heat transfer enhancement by the stabilising Lorentz force in quasistatic magnetoconvection has been observed. We further found that the optimal enhancement may be understood in terms of the crossing between the thermal and the momentum boundary layers (BL) and the fact that temperature fluctuations are maximum near the position where the BLs cross. These findings demonstrate that the heat transport enhancement phenomenon in the quasistatic magnetoconvection system belongs to the same universality class of stabilising−destabilising (S-D) turbulent flows as the systems of confined Rayleigh-Bénard (CRB), rotating Rayleigh-Bénard (RRB) and double-diffusive convection (DDC). This is further supported by the findings that the heat transport, boundary layer ratio and the temperature fluctuations in magnetoconvection at the boundary layer crossing point are similar to the other three cases. A second type of boundary layer-crossing is also observed in this work. In the limit of Re Ha, the (traditionally defined) viscous boundary δ v is found to follow a Prandtl-Blasiustype scaling with the Reynolds number Re and is independent of Ha. In the other limit of Re Ha, δ v exhibits an approximate ∼ Ha −1 dependence, which has been predicted for a Hartmann boundary layer. Assuming the inertial term in the momentum equation is balanced by both the viscous and Lorentz terms, we derived an expression δ v = H/ √ c 1 Re 0.72 + c 2 Ha 2 for all values of Re and Ha, which fits the obtained viscous boundary layer well.

From Rayleigh–Bénard convection to porous-media convection: how porosity affects heat transfer and flow structure

“…In the future, it will be of interest to extend the study to the 3-D case, to allow for a one-to-one comparison with experiment. Following the comparative study of Chong et al (2017) and Lim et al (2019), it is also desirable to investigate further turbulent flows with different stabilizing forces, to get an even more complete understanding of various stabilizing-destabilizing flow systems.…”

Flow regimes of Rayleigh–Bénard convection in a vertical magnetic field

“…This in turn improves the convective heat transport and compensates the effect of an overall slower flow magnitude. In simulations of magnetoconvection at Pr ∼ 8, Lim et al (2019) even found an increase of Nu for an optimal Ha. Such an improvement of the transport properties is generally associated with the cross-over of the viscous and the thermal boundary layer (BL) (Chong et al 2017;Lim et al 2019).…”

Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field

“…The most significant discrepancies between the two datasets appear at higher values of ) data shows a lower slope in comparison with the simulations (both P r = 0.025 and P r = 1). Because this difference is largest at higher values of Ra, it might be due to, as suggested by Cioni et al (2000), the formation of a large-scale circulation in the experimental apparatus due to the eventual loss of magnetic constraint and flow anisotropy (Vogt et al 2018a;Lim et al 2019). Additional studies in cylindrical geometry are necessary to quantify this effect in more detail.…”