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In this article, the theoretical model on heat and momentum transfer forRayleigh-B\'enard convection in a vertical magnetic field by Z\"urner et al.(Phys. Rev. E 94, 043108 (2016)) is revisited. Using new data from recentexperimental and numerical studies the model is simplified and extended to thefull range of Hartmann numbers, reproducing the results of the Grossmann-Lohsetheory in the limit of vanishing magnetic fields. The revised model is comparedto experimental results in liquid metal magnetoconvection and shows that theheat transport is described satisfactorily. The momentum transport, representedby the Reynolds number, agrees less well which reveals some shortcomings in thetheoretical treatment of magnetoconvection.

Refined mean field model of heat and momentum transfer in magnetoconvection