Numerical simulation of three-dimensional double-diffusive natural convection in porous media by boundary element method

Stajnko, Janja Kramer; Ravnik, Jure; Jecl, R.

doi:10.1016/j.enganabound.2016.12.007

Cited by 12 publications

(4 citation statements)

References 26 publications

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“…Expression (10) and the recognized expressions ΔC C ( / ) 1 C ≪ and ΔT T ( / ) 1 C ≪ are used to modify the dimensional Equations ( 1)- (6) to nondimensional equations as shown below:…”

Section: Modelmentioning

confidence: 99%

“…As the aspect ratio of the fluid interface increases, the heat transfer rate increases significantly, and as the Rayleigh number increases, the heat transfer decreases slightly. Stajnko et al 6 performed a numerical study on the double-diffusive regular convection in a porous cubic crater. In their research, the influence of permeability number and buoyancy force was greatly analyzed, and it was observed that the increase in buoyancy and permeability significantly enhanced mass and heat transportation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Three‐dimensional tilted hydromagnetic natural double‐diffusive convection in a rectangular cuboid filled with nanofluids based on magnetic nanoparticles

et al. 2021

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three‐dimensional tilted hydromagnetic natural double‐diffusive convection in a rectangular cuboid filled with nanofluids based on magnetic nanoparticles

et al. 2021

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“…With the prosperous development of numerical methods in computational mechanics, there was a tendency towards boundary-type methods, in addition to the domain-type methods. To name but a few, the boundary domain integral method was applied to study the double diffusive natural convection in porous media [4]; the boundary element method was introduced to simulate three-dimensional double-diffusive natural convection in porous media [5]. As the meshfree methods get rid of mesh constraint and the strong form methods discard domain integral, a growing number of studies appear and are reported as follows: the local radial basis collocation method was used to solve the two-dimensional double diffusion and natural convection problem in 2012 [6]; the exponentially convergent scalar homotopy algorithm was introduced as the nonlinear solver.…”

Section: Introductionmentioning

confidence: 99%

Direct Collocation with Reproducing Kernel Approximation for Two-Phase Coupling System in a Porous Enclosure

Yang

Liao

2021

Mathematics

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The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As the convection behavior in the fluid-saturated porous media involves phase coupling, the resulting system is highly nonlinear in nature. To this end, the local approximation is adopted in conjunction with Newton–Raphson method. Nevertheless, to unveil the performance of the method in the nonlinear analysis, only single thermal natural convection is of major concern herein. A unit square is designated as the model problem to investigate the parameters in the system related to the convergence; several benchmark problems are used to verify the accuracy of the approximation, in which the stability of the method is demonstrated by considering various initial conditions, disturbance of discretization, inclination, aspect ratio, and reproducing kernel support size. It is shown that a larger support size can be flexible in approximating highly irregular discretized problems. The derivation of explicit operators with two-phase variables in solving the nonlinear system using the direct collocation is carried out in detail.

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“…Based on numerical simulations and laboratory experiments, Sezai and Mohamad (1999) found that, for a certain range of parameters (Lewis and Rayleigh numbers), the convective flow is strictly three‐dimensional. Stajnko et al (2017) developed a 3‐D solution based on the boundary element method and investigated the effect of governing parameters on convective flow and rate of heat and mass transfer. Zhu et al (2017) studied the influence of heterogeneity on entropy generation associated to the THC.…”

Section: Introductionmentioning

confidence: 99%

A Fourier Series Solution for Transient Three‐Dimensional Thermohaline Convection in Porous Enclosures

Tabrizinejadas

Fahs

Ataie-Ashtiani³

et al. 2020

Water Resources Research

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Thermohaline convection (THC) in porous media is frequently investigated using the problem of porous enclosure. Most of the existing modeling-based studies are limited to 2-D simulations, because 2-D assumption is widely used to deal with computational requirement of 3-D numerical solutions. Analytical solutions serve as an alternative to deal with computational requirement of numerical solutions. Existing analytical solutions of THC are mostly limited to 2-D and also under steady-state regime. In this work, we develop a meshless 3-D semianalytical solution for the problem of THC in a porous box under crossed thermal and solute gradients, for both steady state and transient regimes. The semianalytical solution is developed using the Fourier series (FS) method applied to the vector potential form of the governing equations. The extension to transient solutions represents an important technical feature of this work, as the applications of the FS method to density-driven problems have been limited to steady-state conditions. The FS solution is validated against a finite element solution obtained using COMSOL Multiphysics. Numerical experiments show the worthiness of the developed FS solution as a benchmark because it clearly allows making distinction between different numerical techniques. The effects of governing parameters on three-dimensional THC have not been investigated previously. We perform a detailed parameter sensitivity analysis to address this gap. A vortex convective flow is observed and the orientation and intensity of the flow is sensitive to the gravity number. The increase in the temperature gradient reduces the salinity flux.

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Numerical simulation of three-dimensional double-diffusive natural convection in porous media by boundary element method

Cited by 12 publications

References 26 publications

Three‐dimensional tilted hydromagnetic natural double‐diffusive convection in a rectangular cuboid filled with nanofluids based on magnetic nanoparticles

Three‐dimensional tilted hydromagnetic natural double‐diffusive convection in a rectangular cuboid filled with nanofluids based on magnetic nanoparticles

Direct Collocation with Reproducing Kernel Approximation for Two-Phase Coupling System in a Porous Enclosure

A Fourier Series Solution for Transient Three‐Dimensional Thermohaline Convection in Porous Enclosures

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