Hydrodynamic and hydromagnetic stability

Numerical study of double-diffusive natural convection in a porous cavity using the Darcy-Brinkman formulation

Thermal instability in Brinkman porous media with Cattaneo–Christov heat flux

In this paper, we study the effect of a homogeneous longitudinal through flow on the onset of convection in a horizontal porous layer saturated by a binary fluid and heated from below or above. The layer boundaries are subjected to a constant heat flux. The investigation is made by taking the Soret effect into account. It is found that in the case of positive separation ratio when the denser component moves toward the cooler wall, through flow has no effect on the stability threshold but exerts an orientating effect on the convective patterns. For negative separation ratio, a strong destabilization occurs of the spatially homogeneous state with respect to long-wave disturbances. The stability range for long-wavelength convective rolls is defined.

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Thermosolutal convection in a horizontal porous layer heated from below in the presence of a horizontal through flow

This paper reports an analytical and numerical study of the natural convection in a horizontal porous layer filled with a binary fluid. A uniform heat flux is applied to the horizontal walls while the vertical walls are impermeable and adiabatic. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the horizontal walls (double-diffusive convection, $a\,{=}\,0$ ) or by temperature gradients (Soret effects, $a\,{=}\,1$ ). The governing parameters for the problem are the thermal Rayleigh number, $R_T$ , the Lewis number, $Le$ , the solutal Rayleigh number, $R_S$ , the aspect ratio of the cavity, $A$ , the normalized porosity of the porous medium, $\varepsilon$ , and the constant $a$ . The onset of convection in the layer is studied using a linear stability analysis. The thresholds for finite-amplitude, oscillatory and monotonic convection instabilities are determined in terms of the governing parameters. For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained by assuming parallel flow in the core of the cavity. The critical Rayleigh numbers for the onset of supercritical, $R_{\hbox{\scriptsize\it TC}}^{\hbox{\scriptsize\it sup}}$ , or subcritical, $R_{\hbox{\scriptsize\it TC}}^{\hbox{\scriptsize\it sub}}$ , convection are predicted by the present theory. A linear stability analysis of the parallel flow pattern is conducted in order to predict the thresholds for Hopf bifurcation. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical prediction and the numerical simulations.

Double-diffusive and Soret-induced convection in a shallow horizontal porous layer

Anisotropic thermoconvective effects on the onset of double diffusive convection in a porous medium

The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model

Double diffusive convection in a porous layer using a thermal non-equilibrium model

The effect of rotation and anisotropy on the onset of double diffusive convection in a horizontal porous layer is investigated using a linear theory and a weak nonlinear theory. The linear theory is based on the usual normal mode technique and the nonlinear theory on the truncated Fourier series analysis. Darcy model extended to include time derivative and Coriolis terms with anisotropic permeability is used to describe the flow through porous media. The effect of rotation, mechanical and thermal anisotropy parameters, and the Prandtl number on the stationary and overstable convection is discussed. It is found that the effect of mechanical anisotropy is to allow the onset of oscillatory convection instead of stationary. It is also found that the existence of overstable motions in case of rotating porous medium is not restricted to a particular range of Prandtl number as compared to the pure viscous fluid case. The finite amplitude analysis is performed to find the thermal and solute Nusselt numbers. The effect of various parameters on heat and mass transfer is also investigated.

The Effect of Rotation on the Onset of Double Diffusive Convection in a Horizontal Anisotropic Porous Layer

The double diffusive convection in a horizontal anisotropic porous layer saturated with a Boussinesq binary fluid, which is heated and salted from below in the presence of Soret and DuFour effects is studied analytically using both linear and non-linear stability analyses. The linear analysis is based on the usual normal mode technique, while the non-linear analysis is based on a minimal representation of double Fourier series. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number, wavenumbers for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effects of anisotropy parameter, solute Rayleigh number, and Soret and DuFour parameters on the stationary, oscillatory convection, and heat and mass transfer are shown graphically. Some known results are recovered as special cases of the present problem.

M.S. Malashetty

Papers

Anisotropic thermoconvective effects on the onset of double diffusive convection in a porous medium

The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model

Double diffusive convection in a porous layer using a thermal non-equilibrium model

The Effect of Rotation on the Onset of Double Diffusive Convection in a Horizontal Anisotropic Porous Layer

Linear and Non-linear Double Diffusive Convection in a Fluid-Saturated Anisotropic Porous Layer with Cross-Diffusion Effects