Stability analysis of penetrative convection in anisotropic porous media with variable permeability

Harfash, Akil J.

doi:10.1515/jnet-2014-0009

Cited by 14 publications

(6 citation statements)

References 23 publications

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“…Firstly, the systems is transformed onto the Chebyshev domain (−1, 1) and the solutions W, θ and φ treated as independent variables and expanded in a series of Chebyshev polynomials (36) then, we insert (36) into the Eqs. (17)- (18), and then substitute the Gauss-Labatto points which are defined by (37) Thus, we obtain 3N−3 algebraic equations for 3N+3 unknowns W 0 , …, W N , Θ 0 , …, Θ N , Φ 0 , …, Φ N .…”

Section: Numerical Techniquementioning

confidence: 99%

“…To achieve this we transform the problem into a vorticity-pseudostream function formulation and utilise second order finite difference schemes. Recently, in [32][33][34][35][36], the accuracy of the linear instability thresholds are tested using three-dimensional simulations. Our results show that the linear threshold accurately predicts on the onset of instability in the basic steady state.…”

Section: Introductionmentioning

confidence: 99%

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Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media

Harfash

Alshara

2015

Korean J. Chem. Eng.

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A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source and subjected to a vertical magnetic field and variable gravity effect. The validity of both the linear instability and global nonlinear stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good prediction on the onset of instability in the steady state throughflow. It is known that as R c increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as R c increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.

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Section: Numerical Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media

Harfash

Alshara

2015

Korean J. Chem. Eng.

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“…One of the most widely employed mechanisms to describe penetrative convection is internal heating.Aninternal heat source (or sink) can give rise to a situation where one part of a layer is naturally convecting while the other remains stable, allowing penetrative convection to occur. Recently, mathematical models to describe penetrative convection have been developed and analyzed intensely by Harfash [17][18][19][20].…”

Section: The Effect Of Boundary Conditions On Convective Instabilitymentioning

confidence: 99%

“…The boundary conditions which w must satisfy are derived from the conditions (18) and (19) and the incompressibility condition…”

Section: The Effect Of Boundary Conditions On Convective Instabilitymentioning

confidence: 99%

Numerical Methods for Solving Some Hydrodynamic Stability Problems

Harfash

2015

Int. J. Appl. Comput. Math

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In this paper we solve the stability problem of the thermal convection in a thin fluid layer with free-free, slip-slip, and fixed-slip boundary conditions. We use different numerical methods to check their flexibility and accuracy where we use the following numerical methods: finite difference, High order finite difference, p order finite element, Chebyshev collocation-1, Chebyshev collocation-2 and Chebyshev tau. Moreover, we solve the equations of Poiseuille flow in a Brinkman porous media with slip-slip boundary conditions using p order finite element, Chebyshev collocation-1 and Chebyshev collocation-2 methods. The advantage and disadvantage of each method have been discussed. According to our result, we believe that the finite difference and finite element methods are very flexible methods and we can apply them to solve any problem easily. However, the accuracy of the the finite difference and finite element methods is less than the accuracy of the Chebyshev methods.

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“…11 An enormous amount of literature is available on the subject of anisotropy of the porous medium, and how it influences the onset of convection. [12][13][14][15] Beyond the validity of Darcy-Brinkman law and anisotropy of the porous medium, the usual assumption made in these studies is that liquid and solid phase is with local thermal equilibrium (LTE) conditions. However, under highly unsteady conditions, a sensible difference exists between the two phases' thermal conductivity, as Straughan 16 mentioned.…”

Section: Introductionmentioning

confidence: 99%

The onset of anisotropic Darcy–Brinkman penetrative convection with local thermal nonequilibrium due to heat generation and extraction

Nandal

2023

Heat Trans

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An anisotropic, fluid‐saturated porous medium with local thermal nonequilibrium is the subject of this paper's analysis of the stability of the commencement of convection caused by internal heat generation. The classical Darcy's momentum equation is applied with the Brinkman model. To observe the thermal instabilities in the fluid layer, it is assumed that there is steady heat extraction through the bottom boundary and constant heat generation inside the fluid layer. The critical internal Darcy Rayleigh and associated wave numbers are computed using linear instability and energy approaches using the Chebyshev pseudospectral method to determine the existence of instability or otherwise. The fluid layer becomes unstratified as a result of heat generation inside the fluid, which encourages the occurrence of any subcritical instability. The critical Darcy–Rayleigh number has been found to be significantly influenced by a number of parameters, including the anisotropy parameter, internal heat parameter, porosity‐modified conductivity ratio, inter‐phase heat transfer parameter, and Darcy–Brinkman number.

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Stability analysis of penetrative convection in anisotropic porous media with variable permeability

Cited by 14 publications

References 23 publications

Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media

Magnetic field and throughflow effects on double-diffusive convection in internally heated anisotropic porous media

Numerical Methods for Solving Some Hydrodynamic Stability Problems

The onset of anisotropic Darcy–Brinkman penetrative convection with local thermal nonequilibrium due to heat generation and extraction

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