  In this article, the theoretical model on heat and momentum transfer for
Rayleigh-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 recent
experimental and numerical studies the model is simplified and extended to the
full range of Hartmann numbers, reproducing the results of the Grossmann-Lohse
theory in the limit of vanishing magnetic fields. The revised model is compared
to experimental results in liquid metal magnetoconvection and shows that the
heat transport is described satisfactorily. The momentum transport, represented
by the Reynolds number, agrees less well which reveals some shortcomings in the
theoretical treatment of magnetoconvection.
