Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field

Capone, Florinda; Luca, Roberta De; Gentile, Maurizio

doi:10.3390/fluids4040191

Cited by 5 publications

(5 citation statements)

References 37 publications

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“…Equations ( 23) -( 25) form an eigenvalue problem with R D as the eigenvalue and solved by applying the Galerkin technique. Accordingly, the dependent variables are expanded as below ... (26) where A i and B i are constants, W i and  i are the basis functions selected so that they fulfill the respective boundary conditions. Equation ( 26) is replaced back in Eqs.…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…Along with this, the combined result of density maximum and a uniform vertical throughflow on the onset of convection in a layer of Darcy porous medium has been discussed by Wu et al [23] using finite-difference as well as finiteelement methods. Recently, Capone et al [26] analyzed the effect of vertical throughflow on the onset of double diffusive magnetoconvection in a horizontal porous layer. The critical Rayleigh numbers for the onset of steady or oscillatory convection are obtained using a single-term Galerkin method.…”

Section: Introductionmentioning

confidence: 99%

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Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Yallappa¹

2022

jmmf

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The vertical throughflow effect is investigated on the onset of porous convection by considering a cubic density-temperature relationship and using the Forchheimer-Darcy model. The stability eigenvalue problem is explained numerically using the Galerkin technique. Contrary to the linear density-temperature relationship, the direction of throughflow alters the onset of convection. The throughflow dependent Péclet number is found to stabilize the fluid motion against convection and the upflow is found to be either stabilizing or destabilizing than the downflow depending on the values of thermal condition parameters λ1 and λ2. A destabilizing effect on the onset is observed with increasing λ1 and λ2. The Darcy number Da and the Forchheimer drag co-efficient, cb instability characteristics have been investigated and depicted graphically.

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Section: Methods Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Yallappa¹

2022

jmmf

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“…1 Its counterpart in a porous medium has also been investigated in the past. [2][3][4][5] In a separate development, free convective flow of Newtonian/non-Newtonian fluids in the presence of MHD and Hall current effects have been investigated extensively by Veera Krishna and his co-workers. [6][7][8][9][10][11] In EHD, the fluid motion is largely controlled by electrical body forces rather than magnetic forces.…”

Section: Introductionmentioning

confidence: 99%

“…Thermal convection in a conducting fluid layer in the presence of a uniform vertical magnetic field, called magnetoconvection, has been studied extensively 1 . Its counterpart in a porous medium has also been investigated in the past 2‐5 . In a separate development, free convective flow of Newtonian/non‐Newtonian fluids in the presence of MHD and Hall current effects have been investigated extensively by Veera Krishna and his co‐workers 6‐11 …”

Section: Introductionmentioning

confidence: 99%

Volumetric heating and AC electric field effects on porous convection with general boundary conditions

Rachitha,

Nanjundappa,

Shivakumara

2024

Heat Trans

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The onset of convective instability in an internally heated dielectric fluid‐saturated porous layer under the influence of a uniform AC electric field for different types of boundary conditions is investigated. The flow in the porous medium is described by the Brinkman model with fluid viscosity different from effective viscosity. The lower adiabatic and the top with finite heat transfer coefficient to the external environment boundaries are considered to be either rigid or stress‐free. The presence of a uniform volumetric heat source alters the conduction profile of the temperature field from linear to quadratic in the vertical coordinate. A modal linear stability analysis of the basic motionless state is carried out and the general regime of linear instability is investigated by solving the stability eigenvalue problem numerically using the Galerkin method of weighted residual technique. The neutral stability condition as well as the critical value of the thermal Rayleigh number is computed for rigid–rigid, free–free, and rigid–free boundaries for various values of governing parameters. It is seen that the nature of boundaries affect the stability of the system only quantitatively, though not qualitatively. The rigid–rigid boundaries offer a more stabilizing effect against convection in comparison with rigid–free and free–free boundaries. The study found that the effect of increasing thermal electric Rayleigh number and the Darcy number is to hasten the onset of instability, while the opposite trend is perceived with an increase in the ratio of viscosities and Biot number. The outcomes of this investigation are found to be in good agreement with past studies under the limiting cases.

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“…Ferrofluid and other magnetized nanofluids may also be learned from Hayat et al (2016). It was shown in Capone et al (2019) that binary mixture porous layer permeated by an external magnetic field is stabilized. The stabilizing impacts of exerted magnetic field were also deliberated in Zaydan et al (2020) on the Buongiorno's nanofluid model convection.…”

Section: Introductionmentioning

confidence: 99%

Uniform magnetic field impact on absolute versus convective onset of Darcy–Benard convection with horizontal throughflow

Türkyılmazoğlu

2023

HFF

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Purpose The onset of Darcy–Benard convection in a fluid-saturated porous layer within channeled walls can be through either the convectively amplified perturbations or absolutely unstable modes. The convective type route to formation of cellular forms has received much more interest in the literature than the absolute mode. This paper aims to explore the absolute instability mechanism on triggering the Benard convection in the presence of a uniform magnetic field acting perpendicular to the channel walls. Design/methodology/approach Pursuing a completely theoretical linear stability approach, the locus of wavenumbers and critical Rayleigh numbers with respect to varying Peclet numbers leading to zero complex group velocity, and hence the absolute instability onset, is formulated in closed form. The formulae also incorporate the influence of fluid movement through the porous layer. Findings Wanenumbers are found to be increasing in magnitude under the effect of the magnetic field. Although the magnetic field expectedly behaves in favor of stabilizing the convection through both convective and absolute instabilities by pushing the threshold value of Rayleigh number to higher values, a peculiarity exists in such a manner that the stabilizing effect of magnetic field can no longer compete against the absolute instability mechanism within the magnetized field after some critical location possessing negative part of the wavenumber. Originality/value The significant outcome is attributed to the exchange of instabilities as far as the absolute instability mechanism is concerned. Magnetic field is always stabilizing and no such trend is observed regarding the convective type instability.

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Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field

Cited by 5 publications

References 37 publications

Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Volumetric heating and AC electric field effects on porous convection with general boundary conditions

Uniform magnetic field impact on absolute versus convective onset of Darcy–Benard convection with horizontal throughflow

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