On magnetic inhibition of thermal convection

The effect of an imposed vertical magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. Solutions are found over a wide range of conditions, for free boundaries, by a combination of numerical and analytic techniques. Quantitative estimates are made of the significant modifications to the heat transfer which are brought about by the presence of the magnetic field. It is found that the general properties of nonlinear steady cellular convection seem to persist in the face of magnetic inhibition.