Buoyancy-driven convection in a horizontal porous layer saturated by a power-law fluid: The effect of an open boundary

Celli, Michele; Impiombato, Andrea Natale; Barletta, Antonio

doi:10.1016/j.ijthermalsci.2020.106302

Cited by 9 publications

(5 citation statements)

References 10 publications

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“…A review of buoyancy-driven instability of non-Newtonian fluids in horizontal or vertical porous configuration can be found in Lazzari and colleagues. [12][13][14][15][16][17] Further papers that deal with the viscous dissipation effect or different boundary conditions can be examined in Brandao and colleagues. [18][19][20][21] More details concerning the heat transfer in porous media saturated by different non-Newtonian fluid models can be seen in Shoney's book.…”

Section: Introductionmentioning

confidence: 99%

“…The presence of thermal instability can lead to changes in the fluid's viscosity and shear rate as well, which can, in turn, affect the convective flow patterns that form. A review of buoyancy‐driven instability of non‐Newtonian fluids in horizontal or vertical porous configuration can be found in Lazzari and colleagues 12–17 . Further papers that deal with the viscous dissipation effect or different boundary conditions can be examined in Brandao and colleagues 18–21 .…”

Section: Introductionmentioning

confidence: 99%

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Onset of instability in Darcy–Forchheimer porous layer with power‐law saturating fluid

EL Fakiri,

Lagziri,

Lahlaouti

et al. 2024

Heat Trans

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The paper investigates the effects of the Forchheimer term (form drag) and vertical pressure gradient on the buoyancy‐induced instability of power‐law saturating fluid in a porous plane medium. Two isobaric permeable layers are assumed to sandwich the horizontal porous plane. In the meantime, Dirichlet and Neumann equations are the thermal boundary conditions considered for the lower and upper layers. A base flow developed analytically via the governing equations is just in function of the Péclet number , with no dependence on the characteristic parameter of the power law fluid. A linear stability analysis consists of substituting a base flow with a small perturbation into the governing equations leads to a four‐order eigenvalue problem. An analytical solution is performed for the asymptotic cases of an infinite wavelength. The Runge–Kutta solver is applied together with the shooting technique to evaluate numerical solutions for the general case of nonnegligible wave numbers. Among the findings is the contribution of the Forchheimer term in the variation of the threshold Péclet number whose value can switch the wave numbers from zero to nonzero and increase the stability of the system.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Onset of instability in Darcy–Forchheimer porous layer with power‐law saturating fluid

EL Fakiri,

Lagziri,

Lahlaouti

et al. 2024

Heat Trans

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“…In a porous horizontal layer, a third kind of thermal boundary conditions have been imposed and the impact of throughflow of a power‐law fluid has been examined by Kumari and Murthy 27 by considering viscous dissipation and internal heating. Considering the open boundary effect, Celli et al 28 addressed the horizontal throughflow in porous media which is saturated with power‐law fluid. Recently, in addition to the impact of internal thermal source, Reddy and Ravi 29 also discussed vertical throughflow along with thermal instability analysis by considering both positive and negative Péclet number values.…”

Section: Introductionmentioning

confidence: 99%

Dissolution‐driven convection of a power‐law fluid in a porous medium in the presence of chemical reaction

Reddy,

Ragoju,

Reddy

et al. 2023

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The flow through porous medium accounts for numerous applications in various fields namely, agriculture, geothermal sciences, and engineering. Furthermore, dissolution‐driven convection in porous media has grabbed great attention in recent years due to its practical applications in long‐term geological storage of carbon dioxide, in the production of mineral deposits, and other industrial applications. In this regard, the current numerical analysis focuses on addressing the thermal instability of dissolution‐driven convective phenomena of a power‐law fluid through a porous horizontal domain with a first‐order chemical reaction. For linear stability analysis, the method of normal modes has been employed to solve governing dimensionless equations which give rise to an eigenvalue problem. The bvp4c routine in MATLAB R2020a has been used to solve the raised problem for the onset of convection. The impact of Damköhler number, Péclet number, and power‐law index on the onset of convection has been investigated. The role of these critical parameters is found to be highly significant in stabilizing the system. An increase in the power‐law index causes stabilization or destabilization in the system, depending on the Péclet number. An enhancement in the magnitude of Damköhler number makes the system stable for all values of the Péclet number. Also, Damköhler and critical Rayleigh number are inter‐related, that is, an increment in Damköhler number results in the enhancement of critical Rayleigh numbers, which in turn leads to stabilization of the system. The critical wave number is observed to have a remarkable influence on Damköhler number as well as power‐law index.

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“…For instance, Barletta et al have examined the impact of vertical pressure gradient in HRL problem with a working fluid-type PL model [10]. Celli et al have dealt with the case where the Prats problem is present and saturated with PL fluid [11]. For high flow rates, the inertia effect takes place which renders the Darcy model inapplicable.…”

Section: Introductionmentioning

confidence: 99%

Forchheimer–Bénard Instability of the Non-Newtonian Fluid

El Fakiri,

Lagziri,

Moussa

et al. 2023

E3S Web of Conf.

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The present paper examines the effect of vertical throughflow on the onset of convective instability in a horizontal porous layer filled with a non-Newtonian power-law fluid (PL). The permeable boundary layers are exposed to two different uniform constant temperature conditions, The Oberbeck-Boussinesq hypothesis is considered with the Darcy-Forchheimer model. A fourth-order eigenvalue problem is stemmed from the performance of the linear stability analysis, and the critical values are obtained using the shooting method combined with the Runge-Kutta method. The non-Newtonian Darcy-Rayleigh number (R), the Péclet number (Pe), the Forchheimer number (G), and the power-law index (n) are the parameters whose value play a crucial role in the onset of instability. The finding shows more stabilizing effects arise in pseudoplastic fluid than dilatant one at Peclet number Pe << 1 where the inverse behaviour takes place at large Peclet number even with the existence of the drag number or without it.

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Buoyancy-driven convection in a horizontal porous layer saturated by a power-law fluid: The effect of an open boundary

Cited by 9 publications

References 10 publications

Onset of instability in Darcy–Forchheimer porous layer with power‐law saturating fluid

Onset of instability in Darcy–Forchheimer porous layer with power‐law saturating fluid

Dissolution‐driven convection of a power‐law fluid in a porous medium in the presence of chemical reaction

Forchheimer–Bénard Instability of the Non-Newtonian Fluid

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