Ferrohydrodynamics (FHD) is of great interest because the fluids of concern possess a giant magnetic response. This gives rise to several striking phenomena with important applications. Among these are the spontaneous formation of a labyrinthine pattern in thin layers, the self-levitation of an immersed magnet, and of particular interest here, the enhanced convective cooling in a ferrofluid that has a temperature-dependent magnetic moment. The very well written book by Rosensweig (1985) is a perfect introduction to this fascinating subject. He very briefly refers to thermo-convective instability in FHD, which is what we concentrate on here. Another, more general, but again very readable account of ferromagnetism may by found in Landau et al. (1984). We now present the relevant equations for FHD, in the forms appropriate to this chapter. Then a brief account is given of a striking convective-like instability, before embarking on the thermo-ferro convection problem.
KeywordsRayleigh Number Sobolev Inequality Linear Instability Elliptic Estimate Force Representation
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