A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer heated from below, in the stress-free boundary case. By introducing a suitable generalized energy functional, a rigorous nonlinear stability result is derived for a thermoconvective magnetized ferrofluid. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic body and inertia forces. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of the linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, in the case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter, M 3, on subcritical instability region has also been analysed. It is shown that with the increase of magnetic parameter, M 3, the subcritical instability region between the two theories decreases quickly. We also demonstrate coupling between the buoyancy and the magnetic forces in the nonlinear energy stability analysis.

https://www.jstor.org/stable/info/20209392

A nonlinear stability analysis for magnetized ferrofluid heated from below

The stability of Soret-driven thermosolutal convection in a shallow horizontal layer of a porous medium subjected to inclined thermal and solutal gradients of finite magnitude is investigated theoretically by means of a linear stability analysis. The horizontal components of these gradients induce a Hadley circulation, which becomes unstable when vertical components are sufficiently large. We employed a two-term Galerkin approximation for various modes of instability. The effect of the Soret parameter on the mechanism of instability of the thermosolutal convection is investigated. Results are presented for various values of the governing parameters of the flow. It is observed that the Soret parameter has a significant effect on convective instability and this is discussed.

Soret-driven thermosolutal convection induced by inclined thermal and solutal gradients in a shallow horizontal layer of a porous medium

A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted Due to the immenseness of the literature volume, the survey

Zongchun Qiao

Papers

Non-linear convection in a porous medium with inclined temperature gradient and variable gravity effects

Non-linear stability of convection in a porous medium with inclined temperature gradient

Non-linear convection in a porous medium with inclined temperature gradient and vertical throughflow