Double-diffusive parallel flow induced in a horizontal Brinkman porous layer subjected to constant heat and mass fluxes: analytical and numerical studies

Amahmid, A.; Hasnaoui, M.; Mamou, Mahmoud; Vasseur, P.

doi:10.1007/s002310050343

Cited by 47 publications

(29 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In cases of small Lewis numbers Le → 0 the values of Sherwood numbers tend to unity (Sh → 1), which implies, that the mass transfer is dominated by diffusion. The same conclusions are also published in [1]. In the case of Da = 10 −1 the values of N u and Sh are equal to 1, which means that heat and mass transfer are governed by diffusion.…”

Section: N U Shsupporting

confidence: 72%

“…The Rayleigh number in this case is beyond the critical value required for the beginning of convective motion. The relationship between the critical Rayleigh number and the Darcy number is given in [1] The buoyancy effect in this case is due entirely to temperature gradients, so the concentration field is a result of the flow driven by the temperature gradients and the imposed concentration difference between the upper and bottom boundaries. From the fig.…”

Section: N U Shmentioning

confidence: 99%

“…In cases where the density differences are a result of combined temperature and concentration gradients, the critical Rayleigh number is a function of the Darcy number, Lewis number and buoyancy coefficient [1]. The flow structure in these cases becomes multi-cellular and is also called a Rayleigh-Benard flow structure [2].…”

Section: Introductionmentioning

confidence: 99%

“…The Brinkman extended Darcy model, on the other hand accounts for friction due to macroscopic shear is thus more appropriate when describing fluid flows in the porous matrix. This model was used in [1] to investigate the onset and development of double-diffusive convection in a horizontal porous layer with uniform heat and mass fluxes specified at the horizontal boundaries. The obtained analytical solutions are compared to some numerical results for different values of governing parameters.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Boundary Element Method for double diffusive natural convection in a horizontal porous layer

Kramer¹,

Jecl²,

Skerget³

2007

WIT Transactions on Modelling and Simulation, Vol 44

View full text Add to dashboard Cite

A numerical study of double-diffusive natural convection in porous media using the Boundary Element Method is presented. The studied configuration is a horizontal layer filled with fluid saturated porous media, where different temperature and concentration values are applied on the horizontal walls, while the vertical walls are adiabatic and impermeable. Transport phenomena in porous media are described with the use of modified Navier-Stokes equations in the form of conservation laws for mass, momentum, energy and species. The results for different governing parameters (Rayleigh number, Darcy number, buoyancy ratio and Lewis number) are presented and compared with those in published studies.

show abstract

Section: N U Shsupporting

confidence: 72%

Section: N U Shmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Boundary Element Method for double diffusive natural convection in a horizontal porous layer

Kramer¹,

Jecl²,

Skerget³

2007

WIT Transactions on Modelling and Simulation, Vol 44

View full text Add to dashboard Cite

show abstract

“…In Chapter 1, the Darcy model for fluid flow in porous media was adopted. However, Amahmid et al [4] propose that for sparsely packed porous media (more appropriate to the physical problem as potential refraction is decreased) the Brinkman model, which accounts for friction due to macroscopic shear, is more appropriate to describe fluid flows in a porous matrix, which forms the motivation behind the development of this chapter.…”

Section: Nonlinear Stability Analysismentioning

confidence: 99%

Convection in Porous Media

2013

Convection Heat Transfer

View full text Add to dashboard Cite

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source• a link is made to the metadata record in Durham E-Theses• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. AbstractThe subject of thermal convection in fluid and porous media is investigated, coupled with the development of efficient spectral finite element methods to improve on the more commonly used techniques for these types of problems.Convection induced by the selective absorption of radiation in a porous medium is DeclarationThe work in this thesis is based on research carried out at the Numerical Analysis

show abstract

Convection in Porous Media

2004

Fundamentals of the Finite Element Method for Heat and Fluid Flow

View full text Add to dashboard Cite

The subject of thermal convection in fluid and porous media is investigated, coupled with the development of efficient spectral finite element methods to improve on the more commonly used techniques for these types of problems. Convection induced by the selective absorption of radiation in a porous medium is investigated in the first four chapters. For the Darcy and Brinkman models for fluid flow the thresholds of the linear and nonlinear theories are shown to be extremely close, demonstrating that the linear theory is accurate enough to predict the onset of convective motion. The exploration of a quadratically modelled internal heat source is discussed next. It is shown that the linear and nonlinear thresholds are close unless the quadratic term becomes dominant over the linear term. Developing a doublediffusive model yields a critical parameter for which no oscillatory convection occurs when it is exceeded. This is an unobservea phenomenon in the present literature. Thermal convection in a linearly viscous fluid in a finite box is also explored. It is demonstrated that the linear and nonlinear thresholds do not coincide, which contradicts results by Georgescu & Mansutti [25]. Legendre and Chebyshev polynomial based spectral methods are also developed for the evaluation of eigenvalues and eigenfunctions inherent in stability analysis in porous media, drawing on the experience of the implementation of the well established techniques in the previous work. These generate sparse matrices, where the standard homogeneous boundary conditions for both porous and fluid media problems are contained within the method.

show abstract

Double-diffusive parallel flow induced in a horizontal Brinkman porous layer subjected to constant heat and mass fluxes: analytical and numerical studies

Cited by 47 publications

References 16 publications

Boundary Element Method for double diffusive natural convection in a horizontal porous layer

Boundary Element Method for double diffusive natural convection in a horizontal porous layer

Convection in Porous Media

Convection in Porous Media

Contact Info

Product

Resources

About