On scaling laws in turbulent magnetohydrodynamic Rayleigh-Benard convection

Abstract

We invoke the concepts of magnetic boundary layer and magnetic Rayleigh number and use the magnetic energy dissipation rates in the bulk and the boundary layers to derive some scaling laws expressing how Nusselt number depends on magnetic Rayleigh number, Prandtl number and magnetic Prandtl number for the simple case of turbulent magnetohydrodynamic Rayleigh-Benard convection in the presence of uniform vertical magnetic field.Comment: This is typos-corrected version of the earlier version. It has some minor changes. This brief work is not, in any sense, complete. Certain ideas have been put forward whose applicability and validity have to be checked. More work is on the way; constructive critisisms are most welcom