The stability of natural convection in a vertical layer of electrically conducting fluid in the presence of a transverse magnetic field

The stability of natural convection of an electrically conducting fluid which is confined between two parallel vertical plates maintained at constant and different temperatures and is permeated by a transverse magnetic field is analyzed using linear stability theory. In deriving the equations governing the stability, a simplification is made using the fact that the magnetic Prandtl number P_m for most electrically conducting fluids is extremely small. The Chebyshev collocation method is used to obtain the eigenvalue equation, which is then solved numerically. The critical Grashof number G_c, the critical wavenumber a_c, and the critical wave speed c_c are obtained for a wide range of the Prandtl number P and for several selected values of the Hartmann number M. It is found that the magnetic field has a stabilizing effect on the convection flow against both stationary and travelling-wave disturbances. The detailed values of P, G_c, a_c, and c_c, at the point of transition from stationary to travelling-wave mode are also obtained for several selected values of M.