A Note on Bénard Marangoni Instability in the Presence of a Magnetic Field

Explicit asymptotic expressions are derived for the first unstable mode of surface tension driven instability in an electrically conducting fluid subjected to a strong magnetic field. The spatial structure of the velocity, temperature, and electric current density is characterized in terms of Hartmann boundary layers - a concept that permits a physical explanation of the role of the magnetic field and an understanding of scaling laws derived in previous work.