Fluid Saturated Darcy Porous Medium Research Articles

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.

MHD forces on double diffusive free convection process along a vertical wavy surface embedded in a doubly stratified fluid-saturated Darcy porous medium under the influence of Soret and Dufour effect

The objective of this paper is to investigate the combined heat and mass transfer process near a vertical wavy semiinfinite surface embedded in a doubly stratified electrically conducting fluid-saturated Darcy porous medium under the influence of Soret and Dufour effects. The governing coupled non-dimensional partial differential equations are transformed to boundary layer equations using the two point local non-similarity transformation which is obtained by scale analysis. The resulting boundary layer equations are solved numerically by applying the Keller Box finite difference scheme. The heat and mass transfer has been analysed by plotting the Local, Average Nusselt and Sherwood numbers for various values of parameters influencing the model like: Mg (Magnetic field effect), a (amplitude of wavy surface), ST and SC (Thermal and Mass Stratification), Sr (Soret number), Df (Dufour number), Buoyancy ratio (B), Lewis number (Le).

Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium

The stability of the thermal convection in a fluid-saturated rotating anisotropic porous material is investigated. We take into account the rotation of a layer of saturated porous medium about an axis orthogonal to the planes bounding the layer. The permeability is allowed to be an anisotropic tensor. In particular, we restrict our attention to the case where the permeability in the vertical direction is different to that in the horizontal plane. The linear instability and nonlinear stability analysis, in the case where the inertial term vanishes, are performed. It is shown, by using an energy method, that the nonlinear critical Rayleigh numbers coincide with those of the linear analysis. The results reveal that the system becomes more stable when the rotation is present.

Exchange of stability in Cattaneo–LTNE porous convection

We investigate a problem of convection in local thermal non-equilibrium (LTNE) porous media. This is where the solid skeleton and the fluid may have different temperatures. However, due to increasing interest in thermal wave motion, especially at micro–nano-scales and particularly in solids, we analyse a model for thermal convection in a fluid saturated Darcy porous medium allowing the solid and fluid parts to be at different temperatures. This theory employs thermodynamics for the fluid based on Fourier’s law of heat conduction, whereas for the solid skeleton heat is transferred by means of the Cattaneo heat flux theory. Under appropriate conditions oscillatory convection is found whereas for the standard LTNE Darcy model this does not exist. In this article we concentrate on a transition which is found when the heat transfer interaction coefficient reaches a critical level and this leads to an exchange of stability for a certain porosity level.

Chemical reaction and radiation effects on mixed convection heat and mass transfer over a vertical plate in power-law fluid saturated porous medium

Abstract Mixed convection heat and mass transfer along a vertical plate embedded in a power-law fluid saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically.

Mixed Convection on a Vertical Plate in a Power-law Fluid Saturated Porous Medium with Cross Diffusion Effects

Mixed convection heat and mass transfer along a vertical plate embedded in a power-law fluid saturated Darcy porous medium with Soret and Dufour effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically.

Porous convection with local thermal non-equilibrium temperatures and with Cattaneo effects in the solid

There is increasing interest in convection in local thermal non-equilibrium (LTNE) porous media. This is where the solid skeleton and the fluid may have different temperatures. There is also increasing interest in thermal wave motion, especially at the microscale and nanoscale, and particularly in solids. Much of this work has been based on the famous model proposed by Carlo Cattaneo in 1948. In this paper, we develop a model for thermal convection in a fluid-saturated Darcy porous medium allowing the solid and fluid parts to be at different temperatures. However, we base our thermodynamics for the fluid on Fourier's law of heat conduction, whereas we allow the solid skeleton to transfer heat by means of the Cattaneo heat flux theory. This leads to a novel system of partial differential equations involving Darcy's law, a parabolic fluid temperature equation and effectively a hyperbolic solid skeleton temperature equation. This system leads to novel physics, and oscillatory convection is found, whereas for the standard LTNE Darcy model, this does not exist. We are also able to derive a rigorous nonlinear global stability theory, unlike work in thermal convection in other second sound systems in porous media.

Mixed convection heat and mass transfer over a vertical plate in a power-law fluid-saturated porous medium with radiation and chemical reaction effects

Mixed convection heat and mass transfer from a vertical plate embedded in a power-law fluid-saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using the shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21058

Soret and Dufour effects on mixed convection from a vertical plate in power-law fluid saturated porous medium

Mixed convection heat and mass transfer along a vertical plate embedded in a power-law fluid saturated Darcy porous medium with Soret and Dufour effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using shooting method. The effect of Soret and Dufour parameters, power law index and mixed convection parameter on non-dimensional velocity, temperature and concentration fields are discussed. The variation of different parameters on heat and mass transfer rates is presented in tabular form.

Double diffusive natural convection in power-law fluid saturated porous medium with Soret and Dufour Effects

The effects of double diffusive natural convection heat and mass transfer along a vertical plate embedded in a power-law fluid saturated Darcy porous medium in the presence of Soret and Dufour effects are studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically.

Soret and Dufour effects on free convection along a vertical wavy surface in a fluid saturated Darcy porous medium

In this article, free convection of heat and mass transfer along a vertical wavy surface in a Newtonian fluid saturated Darcy porous medium is studied by considering cross diffusion (namely the Soret and the Dufour effects) in the medium. The vertical wavy wall and the flow governing equations are transformed to a plane geometry case by using a suitable transformation. Then a similarity solution to this problem is presented under the large Darcy–Rayleigh number assumption. The governing partial differential equations are reduced to a set of ordinary differential equations that are integrated using numerical methods to study the nature of the non-dimensional heat and mass transfer coefficients in the medium. The results are presented for a range of the flow governing parameters such as the diffusivity ratio parameter, the buoyancy ratio parameter, the Soret parameter, the Dufour parameter and the amplitude of the wavy surface.

Natural convection from point source embedded in Darcian porous medium

The buoyancy induced convection arising from a point heat source in a fluid saturated Darcy porous medium bounded by an adiabatic conical surface, of apex angle 2 θ ω , has been studied. The point heat source is located at the apex and the axis of the conical surface coincides with the direction of bouyant force vector. The self-similar equations are obtained for 0 < θ ω < π and Rayleigh number Ra from zero to infinity. The numerical solutions of self-similar equations have been obtained for θ ω (free plume), 3π,/4, π/2 (plume bounded by horizontal surface), and π/4. It is shown that for a given Ra, the centre line velocity and temperature increases as π ω (the bounding space) decreases. A perturbation solution for Ra → 0 also been studied to present closed form solution.