Horizontal Layer Of Porous Medium Research Articles

Effect of Three Types of Gravity Modulation on Rivlin Ericksen Nanofluid Saturated in Porous Medium with Internal Heating

In this paper, authors have studied the Rivlin-Ericksen elastico-viscous nanofluid thermal instability with internal heating under three types of gravity modulation in a horizontal layer of porous medium using both linear and nonlinear ways. Linear stability analysis is done using normal mode approach, whereas nonlinear stability analysis is done using truncated Fourier series method. The results demonstrate that the internal heating, modified diffusivity ratio, and concentration Rayleigh number advance the initiation of convective motion in the system. On the other hand, Darcy number stabilize the system. To understand the behaviour of mass/heat transfer in the system two different approaches viz Mathematica NDSolve and Runge-Kutta-Fehlberg method (RKF-45) are used, and it is found that the rate of heat/mass transfer is exactly the same in both cases. In comparison to other gravity modulation profiles, day-night gravity modulation profile accelerates mass/heat transfer more quickly than the other two types of gravity modulation profiles. Steady state graph has demonstrated, convection occurs earlier when internal heating and amplitude values are increased. Moreover, it is also observed that heat/mass transport is very much affected by the variation of kinematic viscoelasticity parameter.

Thermal instability of an Oldroyd-B fluid-saturated porous layer: implications of pressure gradient and LTNE temperatures

A local thermal nonequilibrium model is used to investigate the instability of an Oldroyd-B fluid-saturated horizontal layer of porous medium by imposing a constant pressure gradient in the horizontal direction and maintaining a constant temperature difference between the boundaries. The flow in the porous medium is studied by a modified Darcy–Oldroyd-B model. The problem has been transformed into a generalized complex eigenvalue problem and solved numerically by utilizing the Galerkin method. The pressure gradient and/or the viscoelasticity of the fluid instill oscillatory instability. The influence of constant horizontal pressure gradient is to hasten the onset of oscillatory convection: a result of contrast noticed in Newtonian fluids. The impact of constant horizontal pressure gradient is to increase the critical frequency of oscillations and to increase the size of convection cells. Besides, the effect of viscoelastic parameters on the oscillatory onset diminishes in the presence of pressure gradient. For the Maxwell fluid, instability sets in earlier compared to an Oldroyd-B fluid. The numerical results obtained under the limiting case are shown to be in excellent agreement with the published ones.

Convective Transport of Nanofluid Saturated with Porous Layer

In the present article, the onset of convection in a horizontal layer of porous medium saturated by ananofluid is investigated analytically using linear and weakly nonlinear analysis. The model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. The effect of Raleigh-Darcy number, Lewis number, modified diffusivity ratio, on the stability of the system is investigated. Stationary and Oscillatory modes of convections has been studied. The linear stability analysis is based on normal mode technique, while then on linear theory is based on the truncated representation of Fourier series method. A weekly nonlinear analysis is used to obtain the concentration and thermal Nusselt number. The behavior of the concentration and thermal Nusselt number is investigated by solving the finite amplitude equations. Obtained results have been presented graphically and discussed in details.

Inertia effects on rotating porous convection

The problem of thermal convection in a rotating horizontal layer of porous medium is considered. The porous medium is described by the equations of Darcy with the fluid inertia retained. The aim of this paper is to investigate the effect of inertia when the boundary conditions are of Robin type, with special emphasis on the case of prescribed heat flux. A detailed explanation is provided for the inertia effect coupled with the effects of rotation and the thermal boundary conditions.

Rotating porous convection with prescribed heat flux

The problem of thermal convection in a rotating horizontal layer of porous medium is considered. The porous medium is described by the equations of Darcy. A novel aspect of this work is to consider boundary conditions for the temperature of Newton–Robin type with heat flux prescribed as a limiting case. The effect of rotation is found to be crucial. For the Taylor number small enough the critical wave number is zero but we find a threshold such that for Taylor numbers beyond this non-zero critical wave numbers are found. The threshold is verified via a weakly nonlinear analysis. Finally, a sharp global nonlinear stability analysis is given.

Convection induced by inclined thermal and solutal gradients, with horizontal mass flow, in a shallow horizontal layer of a porous medium

A theoretical examination is made of convection, induced by applied thermal and solutal coplanar gradients inclined to the vertical and with net horizontal mass flux, in a shallow horizontal layer of a saturated porous medium. The horizontal components of these gradients induce a Hadley circulation superimposed on the net horizontal flow. The combined flow becomes unstable when the vertical components are sufficiently large. The solid matrix of the saturated medium is assumed adiabatic (heat capacity ratio/porosity = 1). A linear stability analysis is carried out, and calculations are made using Galerkin approximation for the various modes of instability. The orientation of the preferred mode and the other critical quantities are determined for representative parameter values. Our results, when complemented with results found in the literature for different parameter values, indicate that the horizontal gradient effect switches from stabilizing to destabilizing as the magnitude of the gradient increases.

Convection induced by inclined thermal and solutal gradients in a shallow horizontal layer of a porous medium

A theoretical examination is made of convection, induced by applied thermal and solutal gradients inclined to the vertical, in a shallow horizontal layer of a saturated porous medium. The horizontal components of these gradients induce a Hadley circulation, which becomes unstable when the vertical components are sufficiently large. A linear stability analysis is carried out, and calculations are made using a low-order Galerkin approximation for the various modes of instability. The orientation of the preferred mode and the other critical quantities are determined for representative parameter values.

Double-diffusive convection in a porous medium

An experimental study has been carried out to examine double-diffusive convection in a porous medium. The experiments were performed in a horizontal layer of porous medium consisting of 3 mm diameter glass beads contained in a box 24 cm × 12 cm × 4 cm high. The top and bottom walls were made of brass and were kept at different constant temperatures by separate baths, with the bottom temperature higher than that of the top. The onset of convection was detected by a heat flux sensor and by the temperature distribution in the porous medium. When the porous medium was saturated with distilled water, the onset of convection was marked by a change in slope of the heat flux curve. The temperature distribution in the longitudinal direction in the middle of the layer indicated a convection pattern consisting of two-dimensional rolls with axes parallel to the short side. This pattern was confirmed by flow visualization. When the porous medium was saturated with salinity gradients of 0.15% cm−1 and 0.225% cm−1, the onset of convection was marked by a dramatic increase in heat flux at the critical ΔT, and the convection pattern was three-dimensional. When the temperature difference was reduced from supercritical to subcritical values, the heat flux curve established a hysteresis loop. Results from linear stability theory, taking into account effects of temperature-dependent viscosity, volumetric expansion coefficients, and a nonlinear basic state salinity profile, are discussed.

Theory on Thermal Instability of Binary Gas Mixtures in Porous Media

A theory is developed which predicts the instability of a horizontal layer of porous medium saturated with a binary gas mixture. The lower boundary of the system is maintained at a higher temperature and the upper one at low temperature. The transport equations and coefficients are developed on the basis of kinetic theory. A linear perturbation technique is employed to reduce the governing equations for momentum, heat, and mass transfer to eigenvalue differential equations which are solved by the Finlayson method, the combination of the Galerkin method and the Routh-Hurwitz stability criterion. Only neutral stationary stability is found to occur in the system. Its criterion can be predicted by a simple algebraic equation. Both the critical Rayleigh and wave numbers for the onset of convection are governed by five independent dimensionless parameters, two of which are most influential. The critical Rayleigh number may be lower or greater than that for pure fluid layer depending upon whether thermal diffusion induces the heavier component of the mixture to move toward the cold or hot boundary, respectively. The theory compares well with the experimental results.