A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios.
Bibliographical noteCopyright © 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids 20, 024102 (2008) and may be found at https://doi.org/10.1063/1.2837175