Abstract
The problem of natural convection in a horizontal layer of viscous thermally conducting fluid heated from below (Benard problem) is relevant in many physical situations and, in particular, in geophysics and astrophysics. Our goal is to give an account of the questions arising in the determination of the critical value that the Rayleigh number must exceed before the convection (instability) can manifest itself. We limit ourselves in considering the classical Benard problem, the magnetic Benard problem and the convection in a porous medium with internal heat source and variable gravity effects in the framework of linear and non-linear stability.
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