Convective Instability in a Horizontal Porous Channel with Permeable and Conducting Side Boundaries

Barletta, Antonio; Schio, Eugenia Rossi di; Storesletten, L.

doi:10.1007/s11242-013-0198-y

Cited by 10 publications

(4 citation statements)

References 14 publications

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“…A few papers are devoted to the transition from 2D to 3D onset modes of convection. Barletta et al [13] made a similar analysis to the present one for a 3D porous box problem where the side boundaries are permeable and conducting, but these boundary conditions differ too much from ours for the sake of detailed comparisons.…”

Section: Summarizing Discussionmentioning

confidence: 75%

A Non-normal-mode Marginal State of Convection in a Porous Box with Insulating End-Walls

Tyvand

Nøland

2019

Transp Porous Med

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The 4th order Darcy-Bénard eigenvalue problem for the onset of thermal convection in a 3D rectangular porous box is investigated. We start from a recent 2D model [1] for a rectangle with hand-picked boundary conditions defying separation of variables so that the eigenfunctions are of nonnormal mode type. In this paper, the previous 2D model [1] is extended to 3D by a Fourier component with wavenumber k in the horizontal y direction, due to insulating and impermeable sidewalls. As a result, the eigenvalue problem is 2D in the vertical xz-plane, with k as a parameter. The transition from a preferred 2D mode to 3D mode of convection onset is studied with a 2D non-normal mode eigenfunction. We study the 2D eigenfunctions for a unit width in the lateral y direction to compare the four lowest modes k m = mπ (m = 0, 1, 2, 3), to see whether the 2D mode (m = 0) or a 3D mode (m ≥ 1) is preferred. Further, a continuous spectrum is allowed for the lateral wavenumber k, searching for the global minimum Rayleigh number at k = k c and the transition between 2D and 3D flow at k = k * . Finally, these wavenumbers k c and k * are studied as functions of the aspect ratio.

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Section: Summarizing Discussionmentioning

confidence: 75%

A Non-normal-mode Marginal State of Convection in a Porous Box with Insulating End-Walls

Tyvand

Nøland

2019

Transp Porous Med

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“…Figure (17) below shows the comparison process to distribute local temperatures against the length of the test section between the current study and a previous study[11] of the same phenomenon. Table(5) below shows the comparison details, as the distribution of temperatures is gradually increasing with the progress of the fluid flow through the test section, and therefore the behavior is identical between the current study and the previous study.…”

mentioning

confidence: 58%

“…The study showed that the Nusselt number increases gradually with the increase of the Rayleigh number and decreases gradually with the increase in the length of the space. Antonio Barletta et al [5] A fluid-saturated, horizontal porous channel with a rectangular cross-section is created for the stability investigation. A uniform flux is used to simulate the heating from below, and the top wall is considered to be isothermal.…”

Section: Introductionmentioning

confidence: 99%

Investigating Heating Transfer and Turbulent Flow in a Channel for Different Cross Sections Full-Filled of Glass Spheres as a Porous Media

2023

IJSER

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In recent years various modern improvements have been used to raise the performance of heat systems in various engineering and industrial applications. One of these improvements is the use of porous material. This research focuses on conducting a theoretical study (numerical simulation) via forced convection heat transfer of three channels of various cross-sections (square, rectangular, and triangular) with an equal hydraulic diameter of (0.15 m) with glass spheres filled of a diameter (0.012 m) as a porous martial. The lower surface of the test section is subjected to a uniform heat flux along the fluid flow of (5000 W/m 2 ), while the upper surface is thermally insulated. The type of model used in this study (k-epsilon turbulent model) to simulate and analyze fluid flow inside three channels. This study aims to enhance the thermal properties of the fluid (water) and study its effect on the distribution of temperature, velocity, and pressure, respectively. The results showed that the channel with a triangular cross-section gives the highest distribution of temperature and pressure compared to the rest, and therefore it is considered the optimal design for the channels.

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“…They considered effect of finite Prandtl-Darcy number in the relation for the critical Darcy-Rayleigh number. Barletta et al (2013Barletta et al ( , 2016Barletta 2016) studied convective and absolute instability in horizontal porous channels with different physical boundary conditions, such as permeable and conducting side boundaries and variable-viscosity dissipation. Barletta and Celli (1224) investigated the onset of two-dimensional convective instability in steadystate mixed convection in a vertical porous layer including the effects of dynamic boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Convective Instability in Slip Flow in a Vertical Circular Porous Microchannel

2021

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The paper represents an analysis of convective instability in a vertical cylindrical porous microchannel performed using the Galerkin method. The dependence of the critical Rayleigh number on the Darcy, Knudsen, and Prandtl numbers, as well as on the ratio of the thermal conductivities of the fluid and the wall, was obtained. It was shown that a decrease in permeability of the porous medium (in other words, increase in its porosity) causes an increase in flow stability. This effect is substantially nonlinear. Under the condition Da > 0.1, the effect of the porosity on the critical Rayleigh number practically vanishes. Strengthening of the slippage effects leads to an increase in the instability of the entire system. The slippage effect on the critical Rayleigh number is nonlinear. The level of nonlinearity depends on the Prandtl number. With an increase in the Prandtl number, the effect of slippage on the onset of convection weakens. With an increase in the ratio of the thermal conductivities of the fluid and the wall, the influence of the Prandtl number decreases. At high values of the Prandtl numbers (Pr > 10), its influence practically vanishes.

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Convective Instability in a Horizontal Porous Channel with Permeable and Conducting Side Boundaries

Cited by 10 publications

References 14 publications

A Non-normal-mode Marginal State of Convection in a Porous Box with Insulating End-Walls

A Non-normal-mode Marginal State of Convection in a Porous Box with Insulating End-Walls

Investigating Heating Transfer and Turbulent Flow in a Channel for Different Cross Sections Full-Filled of Glass Spheres as a Porous Media

Convective Instability in Slip Flow in a Vertical Circular Porous Microchannel

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