Buoyancy driven instability in a horizontal layer of electrically conducting fluid in the presence of a vertical magnetic field

Linear stability theory is applied to the problem of the onset of buoyancy driven instability in a horizontal layer of electrically conducting fluid heated from below in the presence of a vertical magnetic field. Under the proper boundary conditions on the magnetic field perturbations, the Chebyshev collocation method is adopted to obtain the eigenvalue equation, which is then solved numerically. The critical Rayleigh number R-c, the critical wavenumber a(c) and the critical frequency omega(c) are obtained for wide ranges of the Prandtl number P-r, the magnetic Prandtl number P-m and the Chandrasekhar number Q. A necessary and sufficient condition for overstability to occur is also obtained. (C) 1998 Elsevier Science Ltd. All rights reserved.