Thermal convection for a Darcy-Brinkman rotating anisotropic porous layer in local thermal non-equilibrium
Florinda Capone, Jacopo A. Gianfrani
Abstract
Abstract The onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under the hypothesis of local thermal non-equilibrium, is analysed. Since the porosity of the medium is assumed to be high, the more suitable Darcy-Brinkman model is adopted. Linear instability analysis of the conduction solution is carried out. Nonlinear stability with respect to $$L^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -norm is performed in order to prove the coincidence between the linear instability and the global nonlinear stability thresholds. The effect of both rotation and thermal and mechanical anisotropies on the critical Rayleigh number for the onset of instability is discussed.