Convection In Horizontal Porous Layer Research Articles

Solutal convection in horizontal porous layer with immobilization and clogging

The paper is devoted to the investigation of the solutal convection in a horizontal layer of porous media with horizontal seepage of the mixture and solute immobilization. The flow through porous media is modelled within the standard Darcy–Bousinesq model and immobilization is described by the mobile/immobile media (MIM) approach. The high concentrations of solute are considered which lead to taking into account the dependence of media permeability on porosity. The variation of porosity is modelled as a linear function of solute concentration in the immobile phase. It is shown that immobilisation leads to the stabilization of homogeneous filtration regime and to slow down of the perturbation dynamics. The increasing of critical parameters with the intensification of sorption is not monotonous due to saturation of porous matrix with the adsorbed solute.

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.

Laterally Penetrative Onset of Convection in a Horizontal Porous Layer

The onset of Darcy–Bénard convection in an unlimited horizontal porous layer is studied theoretically. The thermomechanical boundary conditions of Dirichlet or Neumann type at the lower and upper plane are switched from one type to another, at certain values of the horizontal x-coordinate. A semi-infinite portion of the lower boundary is defined as thermally conducting and impermeable, while the remaining boundary is open and with given heat flux. At the upper boundary, the same thermomechanical conditions are applied, but with a relative spatial displacement L and in the opposite spatial order. A domain of local destabilization around the origin is generated between the lines of discontinuity x = pm ,L/2. The marginal state of convection is triggered centrally, while it is penetrative in the domains exterior to the central domain. The onset problem is solved numerically, with a general 3D mode of disturbance, but 2D disturbances are preferred in most cases. The critical Rayleigh number is given as a function of the dimensionless gap width L and the wavenumber k in the y direction along the lines of discontinuity in the boundary conditions. An asymptotic formula for 2D penetrative eigenfunctions is shown to be in agreement with the numerical results.

Soret phenomenon in porous Magneto-Hydrodynamics

The onset of double-diffusive convection in horizontal porous layers filled by an electrically conducting fluid embedded in a magnetic field, is investigated on taking into account of Soret phenomenon. Sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained. Conditions guaranteeing that Hopf convection in the absence of Soret phenomenon, turns into steady convection by the Soret parameter, have been found.

Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term

The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal conduction solution, is proved. Necessary and sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained.

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

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.

Oscillatory mixed convection in horizontal porous layers locally heated from below

Oscillatory mixed convection in horizontal porous layers locally heated from below

Experimental study of free and mixed convection in horizontal porous layers locally heated from below

Experimental results are reported for free and mixed convection in liquid saturated, horizontal porous layers with localized heating from below. Three different sizes of heat source have been considered which give a relative heater size (axial length/layer depth) of 1.0–5.0. For natural convection, Nusselt numbers have been obtained for Rayleigh numbers of practical interest, 1 ⩽ Ra h ⩽ 1000, while for mixed convection, results cover 1 ⩽ Ra h ⩽ 1000 and 0.1 ⩽ Pe h ⩽ 120. Based on dimensional analysis and nonlinear regression, correlations for Nusselt number against Rayleigh and Peclet numbers have been obtained. Experimental Nusselt numbers compare very well with numerically calculated values. Improved agreement between calculations and measurements can be obtained through use of an effective thermal conductivity. The stability of the flow and temperature fields are also carefully examined. The existence of a Peclet number for which the overall heat transfer rate is a minimum is confirmed by experiment.

Free and mixed convection in horizontal porous layers with multiple heat sources

Free and mixed convection has been studied numerically for horizontal porous layers heated from below by multiple, isothermal, discrete sources. Steady-state results have been obtained for natural convection with up to eight sources and for mixed convection with up to four sources. Rayleigh numbers are varied from 10 to 500, and Peclet numbers from 0.1 to 100. For natural convection, the vertical sidewalls for the two-dimensional domain considered have little effect on Nusselt numbers if the distance between the outermost source and wall is greater than three times the length of the heat source. As the number of heat sources increases, heat-transfer coefficients for the second outermost sources are a minimum. In mixed convection, overall Nusselt numbers increase with both the number of sources and Rayleigh number. If the individual heat source is considered, heat-transfer coefficients are determined only by its location. For Rayleigh numbers greater than 50, there exists a critical Peclet number for which the overall Nusselt number is a minimum. Unstable, oscillatory flow and temperature fields are observed for Rayleigh numbers greater than 50. Nomenclature c = specific heat of fluid at constant pressure, J/kg-K D - length of the heat sources, m DN = nth discrete heat source d = distance between two discrete heat sources, m g = acceleration of gravity, m/s2 H = height of the porous layer, m h = local heat-transfer coefficient, W/m2-K h = average heat-transfer coefficient for the bottom sur

Natural Convection in Horizontal Porous Layers: Effects of Darcy and Prandtl Numbers

Natural convection in horizontal porous layers heated from below is studied by employing a formulation based on the Brinkman–Forchheimer–extended Darcy equation of motion. The numerical solutions show that the convective flow is initiated at lower fluid Rayleigh number Raf than that predicted by the linear stability analysis for the Darcy flow model. The effect is considerable, particularly at a Darcy number Da greater than 10−4. On the other hand, an increase in the thermal conductivity of solid particles has a stabilizing effect. Also, the Rayleigh number Raf required for the onset of convection increases as the fluid Prandtl number is decreased. In the stable convection regime, the heat transfer rate increases with the Rayleigh number, the Prandtl number, the Darcy number, and the ratio of the solid and fluid thermal conductivities. However, there exists an asymptotic convection regime where the porous media solutions are independent of the permeability of the porous matrix or Darcy number. In this regime, the temperature and flow fields are very similar to those obtained for a fluid layer heated from below. Indeed, the Nusselt numbers for a porous medium with kf = ks match with the fluid results. The effect of Prandtl number is observed to be significant for Prf < 10, and is strengthened with an increase in Raf, Da, and ks/kf. An interesting effect, that a porous medium can transport more energy than the saturating fluid alone, is also revealed.

Mixed Convection in Horizontal Porous Layers Heated From Below

Numerical studies are reported for steady, mixed convection in two-dimensional horizontal porous layers with localized heating from below. The interaction mechanism between the forced flow and the buoyant effects is examined for wide ranges of Rayleigh number Ra* and Peclet number Pe*. The external flow significantly perturbs the buoyancy-induced temperature and flow fields when Pe* is increased beyond unity. For a fixed Peclet number, an increase in Rayleigh number produces multicellular recirculating flows in a domain close to the heat source. This enhances heat transfer by free convection. However, for a fixed Ra*, an increase in forced flow or Peclet number does not necessarily increase the heat transfer rate. Hence, there exists a critical Peclet number as a function of Ra* for which the overall Nusselt number is minimum. The heat transfer is, generally, dominated by the buoyant flows for Pe* < 1 whereas the contribution of free convection is small for Pe* > 10 when Ra* ≤ 10.

Effects of Stratification on Thermal Convection in Horizontal Porous Layers With Localized Heating From Below

The purpose of the present work is to study numerically the natural convection in a horizontal porous layer in the presence of a stable, linear thermal gradient. The geometry considered is a two-dimensional horizontal cavity filled with a fluid-saturated porous medium whose bottom surface is cooled at a constant temperature {Tc}, except for a central portion of the surface where isothermal heat source exists. The temperature on the side walls varies linearly from the bottom surface temperature {Tc} to the top wall temperature T{sub t}. Detailed flow and temperature field solutions are obtained for various values of thermal stratification ratio S. When S = 0, the present problem reduces to natural convection in horizontal porous layers with localized heating from below.

Natural Convection in Horizontal Porous Layers With Localized Heating From Below

Convective flow of fluid through saturated porous media heated from below is of considerable interest, and has been extensively studied. Most of these studies are concerned with either infinite horizontal porous layers or rectangular (or cylindrical) porous cavities with adiabatic vertical walls. A related problem of practical importance occurs when only a portion of the bottom surface is heated and the rest of it is either adiabatic or isothermally cooled. This situation is encountered in several geothermal areas which consists of troughs of volcanic debris contained by walls of nonfragmented ignimbrite. Thus, the model region considered is a locally heated long trough of isotropic porous medium confined by impermeable and insulating surroundings. Also, the recent motivation to study this problem has come from the efforts to identify a geologic repository for nuclear waste disposal. The purpose of the present work is to consider the effects of aspect ratio and Rayleigh number on free convection heat transfer from an isothermal heat source centrally located on the bottom surface of a horizontal porous cavity.