The effect of a vertical uniform magnetic field on Rayleigh-Benard convection is investigated experimentally. We confirm that the threshold of convection is in agreement with linear stability theory up to a Chandrasekhar number Q approximately 4x10(6), higher than in previous experiments. We characterize two convective regimes influenced by MHD effects. In the first one, the Nusselt number Nu proportional to the Rayleigh number Ra, which can be interpreted as a condition of marginal stability for the thermal boundary layer. For higher Ra, a second regime Nu approximately Ra0.43 is obtained.

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The ultimate regime of convection, long ago predicted by Kraichnan ͓Phys. Fluids 5, 1374 ͑1962͔͒, could be called elusive because some apparently equivalent experiments showed it while others did not, with no apparent reasons for this discrepancy. In this paper, we propose a model which accounts for the finite heat conductivity and heat capacity of real active boundaries. Bad thermal characteristics of the plates can explain differences between various experiments, in agreement with recent numerical simulations.