Steady Three-Dimensional Convectivie Heat Transfer in a Porous Box via Multigrid

Dawood, Amir S.; Burns, Patrick

doi:10.1080/10407789208944764

Cited by 18 publications

(8 citation statements)

References 31 publications

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“…The expression on the right-hand side of (5) is the Pdclet number, Pe, of the problem. From (5) and (3) we can see that under steady-state precipitation takes place as long as the Pdclet number exceeds its critical value, Pe* Pe >Pe* -ln w* 02 0…”

Section: Opdh O-fidh Dhmentioning

confidence: 99%

“…According to the distribution described by (5), water near ground surface is more saline and, hence, denser than that at larger depths. This is a potentially unstable situation which may result in convective currents.…”

Section: Opdh O-fidh Dhmentioning

confidence: 99%

“…We shall use the multigrid approach which was successfully applied to the simulation of thermally induced convection in a pure liquid (e.g., Thompson et al [14], Wesseling [15]) as well as in a porous medium (Dawood and Bums [5]). For this purpose, we shall discretize the steady-state equations using the Finite Volume Element Method due to McCormick [10], arriving at a set of nonlinear algebraic equations, and then solve them by the Full Approximation Storage Algorithm [ 13].…”

Section: Simulation Of Convective Flowsmentioning

confidence: 99%

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The influence of free convection on soil salinization in arid regions

Gilman

Bear

1996

Transp Porous Med

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Evaporation of groundwater in a region with a shallow water table and small natural replenishment causes accumulation of salts near the ground surface. Water in the upper soil layer becomes denser than in the depth. This is a potentially unstable situation which may result in convective currents. When free convection takes place, estimates of the salinity profile, salt precipitation rate, etc., obtained within the framework of a 1-D (vertical) model fail.Very simplified model of the process is proposed, in which the unsaturated zone is represented by a horizontal soil layer at a constant water saturation, and temperature changes are neglected. The purpose of the model is to obtain a rough estimate of the role of natural convection in the salinization process.A linear stability analysis of a uniform vertical flow is given, and the stability limit is determined numerically as a function of evaporation rate, salt concentration in groundwater, and porous medium dispersivity. The loss of stability corresponds to quite realistic Rayleigh numbers. The stability limit depends in nonmonotonic way on the evaporation rate.The developed convective regime was simulated numerically for a 2-D vertical domain, using finite volume element discretization and FAS multigrid solver. The dependence of the average salt concentration in the upper layer on the Rayleigh number was obtained.

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Section: Opdh O-fidh Dhmentioning

confidence: 99%

Section: Opdh O-fidh Dhmentioning

confidence: 99%

Section: Simulation Of Convective Flowsmentioning

confidence: 99%

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The influence of free convection on soil salinization in arid regions

Gilman

Bear

1996

Transp Porous Med

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“…Its importance and studies associating convective heat transfer in porous medium are shown [1][2][3][4][5]. Few researchers such as: Caltagirone [6], Chan and Banerjee [7], Dawood and Burns [8], Holst and Aziz [9], Horne [10], Mojtabi [11], Ozoe et al [12], Rao et al [13], Gerald and Straus [14,15], Chongbin et al [16], Hidalgo et al [17], etc., have investigated convection process due to side or bottom heating, under Darcian assumptions in three dimensional fluid saturated porous enclosure. The literature shows that very few studies on 3-dimensional natural/free convection fluid flow through porous media.…”

Section: Introductionmentioning

confidence: 99%

A parallel finite element study of 3D mixed convection in a fluid saturated cubic porous enclosure under injection/suction effect

Murthy

Kumar

Nigam

2015

Applied Mathematics and Computation

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“…[1][2][3], only few can be found considering 3D enclosure heated from the side e.g. [4][5][6]. Furthermore, some 3D results of double diffusive natural convection, with combined actions of thermal and solutal buoyancy forces in porous enclosures can be found in [7] and [8].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional natural convection in a porous cavity by the boundary element method

Jecl¹,

Kramer²,

Ravnik³

et al. 2011

WIT Transactions on the Built Environment

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A thee-dimensional numerical simulation of convective flow in porous media using an algorithm based on a combination of a single domain and a subdomain boundary element method (BEM) is presented. The fluid flow in porous media is modeled with the modified Navier-Stokes equations (Brinkman-extended Darcy formulation with inertial term included) coupled with the energy and species equations using the Boussinesq approximation. The velocity-vorticity formulation is adopted to solve the governing set of equations, which results in decoupling of the computational scheme into the kinematic and kinetic computational parts. The boundary vorticity values are calculated by a single domain BEM solution of the kinematics equation, while the subdomain BEM is used to solve the vorticity, energy and species transport equations. Computations are performed for various governing parameters (Rayleigh number, Darcy number, Lewis number, buoyancy coefficient) and, simulation results are compared to the results of some published studies. Heat and mass flux through the cavity and flow fields are analyzed, focusing on the 3D nature of the phenomena.

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Steady Three-Dimensional Convectivie Heat Transfer in a Porous Box via Multigrid

Cited by 18 publications

References 31 publications

The influence of free convection on soil salinization in arid regions

The influence of free convection on soil salinization in arid regions

A parallel finite element study of 3D mixed convection in a fluid saturated cubic porous enclosure under injection/suction effect

Three-dimensional natural convection in a porous cavity by the boundary element method

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