Instability and Convection in Rotating Porous Media: A Review

Abstract

A review on instability and consequent natural convection in rotating porous media is presented. Taylor-Proudman columns and geostrophic flows exist in rotating porous media just the same as in pure fluids. The latter leads to a tendency towards two-dimensionality. Natural convection resulting from density gradients in a gravity field as well as natural convection induced by density gradients due to the centripetal acceleration are being considered. The former is the result of gravity-induced buoyancy, the latter is due to centripetally-induced buoyancy. The effect of Coriolis acceleration is also discussed. Linear stability analysis as well as weak nonlinear solutions are being derived and presented.

Thermal convection for a Darcy-Brinkman rotating anisotropic porous layer in local thermal non-equilibrium

“…Furthermore, in many industrial applications, such as centrifugal filtration processes and rotating machinery, rotation plays an important role on the onset of convection, as well. When investigating these kind of situations where the solid matrix rotates, a rotating frame of reference needs to be introduced [12]. It turns out that a term due to Coriolis acceleration appears in the momentum equation.…”

Coriolis effect on thermal convection in a rotating bidispersive porous layer

“…There are many practical applications, in engineering, in the food process industry, in the chemical industry, where the porous layer is rotating about a vertical axis, see Vadasz [17][18][19], and references therein, Capone & Rionero [20], Capone & De Luca [21,22], De Luca & Rionero [23] and in the case of anisotropic porous media with local thermal non-equilibrium Capone & Gentile [24]. The effect of rotation on the flow in porous media with rotating solid matrix deserves a relevant significance in traditional and non-traditional fields.…”

Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media

“…Thermal convection in single porous layers has attracted-in the past as nowadays-the interest of many authors due to its numerous applications in industrial processes, in geophysics and in astronomy, for instance. Starting from a detailed theoretical analysis [20,26,[29][30][31], several mathematical models have been introduced in order to better describe different aspects of the phenomenon (see [1][2][3][4][8][9][10][11]14,17,18,[23][24][25] and the references therein). In particular, in [2] mixed convection flow has been numerically studied; in [4,11], the effect of an external magnetic field induced in an electrically conducting fluid has been investigated; in [17] doublediffusive convection is analysed, while [24] deals with double-diffusive convection according to the Brinkman model.…”