Anisotropy and the Onset of the Thermoconvective Instability in a Vertical Porous Layer

The thermoconvective instability of the parallel vertical flow in a fluid saturated porous layer bounded by parallel open boundaries is studied. The open boundaries are assumed to be kept at constant uniform pressure while their temperatures are uniform and different, thus forcing a horizontal temperature gradient across the layer. The anisotropic permeability of the porous layer is accounted for by assuming the principal axes to be oriented along the directions perpendicular and parallel to the layer boundaries. A linear stability analysis based on the Fourier normal modes of perturbation is carried out by testing the effect of the inclination of the normal mode wave vector to the vertical. The neutral stability curves and the critical Rayleigh number for the onset of the instability are evaluated by solving numerically the stability eigenvalue problem.

Thermo-convective instability in a rotating ferromagnetic fluid layer with temperature modulation

We study the thermoconvective instability in a rotating ferromagnetic fluid confined between two parallel infinite plates with temperature modulation at the boundaries. We use weakly nonlinear stability theory to analyze the stationary convection in terms of critical Rayleigh numbers. The influence of parameters such as the Taylor number, the ratio of the magnetic force to the buoyancy force and the magnetization on the flow behaviour and structure are investigated. The heat transfer coefficient is analyzed for both the in-phase and the out-of-phase modulations. A truncated Fourier series is used to obtain a set of ordinary differential equations for the time evolution of the amplitude of convection for the ferromagnetic fluid flow. The system of differential equations is solved using a recent multi-domain spectral collocation method that has not been fully tested on such systems before. The solutions sets are presented as sets of trajectories in the phase plane. For some supercritical values of the Rayleigh number, spiralling trajectories that transition to chaotic solutions are obtained. Additional results are presented in terms of streamlines and isotherms for various Rayleigh numbers.

Instability of Combined Forced and Free Flow in an Inclined Porous Channel

The aim of this paper is to analyze the onset of convective instability in a plane porous channel inclined to the horizontal. A net upslope or downslope flow is considered, so that mixed convection takes place as caused by the uniform and symmetric heat fluxes prescribed on the impermeable bounding walls. The thermoconvective instability of the basic flow is studied versus small-amplitude wavelike perturbations. The hybrid analytical–numerical technique adopted in this paper, in order to track and illustrate the parametric changes of neutral stability curves, is Galerkin’s method of weighted residuals. Numerical values at significant points on the neutral stability curves are obtained by employing an accurate Runge–Kutta solver combined with the shooting method.

Unstable mixed convection in a heated inclined porous channel

This paper presents a stability analysis of a mixed convection problem in an inclined parallel-plate channel with uniform heating (or cooling) from the top and bottom. The channel is filled with a saturated homogeneous porous medium and the momentum equation is given by Darcy’s model. A forced through-flow is prescribed across the channel. Linear stability analysis is thus employed to determine the onset of thermoconvective instability. The channel inclination is shown to play an important role in the stability of the problem, where two different regimes can be present: a buoyancy-assisted regime and a buoyancy-opposed regime. The analysis of the problem leads to a differential eigenvalue problem composed of a system of four complex-valued equations that are used to determine the critical values of the Rayleigh number leading to an instability under different problem configurations. This eigenproblem is solved by employing the generalised integral transform technique (GITT), in which simpler real eigenfunction bases are used to expand the complex eigenproblem. The results indicate that the longitudinal rolls are always more unstable than oblique and transverse rolls. For a buoyancy-opposed regime, even with a very small channel inclination angle, the basic through-flow is always unstable. This result has an important implication for experimental research, as it shows that a perfect alignment must be employed for horizontal mixed-convection experiments to avoid instabilities that arise in the buoyancy-opposed regime.

Stability analysis of soret effect on thermohaline convection in dusty ferrofluid saturating a Darcy porous medium

<p>The Soret–driven ferro thermoconvective instability of multi–component fluid in a porous medium heated from below and salted from above in the presence of dust particles subjected to a transverse uniform magnetic field has been analyzed using Darcy model for various values of permeability of the porous medium. The salinity effect has been contained in magnetization and density of the ferrofluid. A small thermal perturbation imparted on the basic state and a linear stability analysis is used for this model for which normal mode technique is applied. An exact solution is obtained for the case of two free boundaries and both stationary and oscillatory instabilities have been investigated. It is found that the system destabilizes only through stationary mode. The non-buoyancy magnetization parameter, the dust particle parameter and the permeability of the porous medium are found to destabilize the system. The results are depicted graphically.</p>

On Hadley flow in a porous layer with vertical heterogeneity

The onset of thermoconvective instability in a horizontal porous layer with a basic Hadley flow is studied, under the assumption of weak vertical heterogeneity. Hadley flow is a single-cell convective circulation induced by horizontal linear changes of the layer boundary temperatures. When combined with heating from below, these thermal boundary conditions yield a temperature gradient inclined to the vertical, in the basic state. The linear stability of the basic state is studied by considering small-amplitude disturbances of the velocity field and the temperature field. The linearized governing equations for the disturbances are then solved both by Galerkin’s method of weighted residuals and by a combined use of the Runge–Kutta method and the shooting method. The effect of weak heterogeneity of the permeability and the effective thermal conductivity of the porous medium is studied with respect to neutral stability conditions. It is shown that, among the normal mode disturbances, the most unstable are longitudinal rolls, that is, plane waves with a wave vector perpendicular to the imposed horizontal temperature gradient. The effect of heterogeneity becomes important only for high values of the horizontal Rayleigh number, associated with the horizontal temperature gradient, approximately greater than 60. In this regime, the effect of heterogeneity is destabilizing. It is shown that heterogeneity with respect to thermal conductivity is of major importance in the onset of instability.