Onset of Rayleigh-Bénard Convection in Porous Bodies

Recent interest in the effects of viscous dissipation on convective flows in porous media has centred almost exclusively on forced convection flows. In this paper, we investigate the manner in which it affects the onset and early stages of convection in Darcy-Bénard convection. A weakly nonlinear theory is described briefly, and it is shown that hexagonal cells are preferred over rolls when the Rayleigh number is sufficiently close to 4π 2 . At higher Rayleigh numbers, two-dimensional rolls are preferred. When weak form drag is included, then subcritical convection eventually disappears as the Forchheimer parameter increases, yielding a highly novel situation wherein hexagonal convection arises supercritically. The range of stability of hexagons is found to increase.

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“…Detailed accounts of the development of the subject may be found in the reviews by Nield and Bejan [3], Rees [4], Tyvand [5] and Barletta [6].…”

Section: Introductionmentioning

confidence: 99%

Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag

Rees

Magyari

2017

Fluids

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“…decades, several new results have been achieved on this subject surveyed, for instance, by Rees (2000), Tyvand (2002), Nield and Bejan (2006) and Barletta (2011). In particular, recent studies have shown the role played by temperature boundary conditions of the third kind, describing a wall heat transfer regime intermediate between the first kind (Dirichlet-type) temperature conditions, and the second kind (Neumann-type) temperature conditions.…”

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confidence: 99%

Onset of Convection in a Porous Rectangular Channel with External Heat Transfer to Upper and Lower Fluid Environments

Barletta

Storesletten

2012

Transp Porous Med

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The conditions for the onset of convection in a horizontal rectangular channel filled with a fluid saturated porous medium are studied. The vertical sidewalls are assumed to be impermeable and adiabatic. The horizontal upper and lower boundary walls are considered as impermeable and subject to external heat transfer, modelled through a third-kind boundary condition on the temperature field. The external fluid environments above and below the channel, kept at different temperatures, provide the heating-from-below mechanism which may lead to the onset of the thermal instability in the porous medium. The linear response of the fluid saturated porous channel, in a basic motionless state, is tested with respect to threedimensional normal mode disturbances of the temperature field and of the pressure field. The linearised disturbance equations are solved analytically leading to an implicit-form expression of the neutral stability condition, formulated as a functional relationship between the Darcy-Rayleigh number and the continuous longitudinal wave number of the normal modes, for any assigned aspect ratio of the cross-section and for any given Biot number. The analysis of the neutral stability is carried out. The analysis is extended to the case of a channel with a finite length in the longitudinal direction, and with adiabatic and impermeable capped ends.

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“…Interest for these studies is motivated by the role that thermoconvective instability may play in many applications ranging from the analysis of geothermal systems to the strategies for inhibiting the dispersion of liquid pollutants in the soil. Most of the investigations dealing with the so-called Darcy-Bénard instability [1][2][3] and the many variants of this classical problem, based on different assignments of the boundary conditions and on the modelling of the momentum transfer in the porous medium, [3][4][5][6] are relative to plane layers as well as to rectangular cavities or channels.…”

Section: Introductionmentioning

confidence: 99%

Effect of a finite external heat transfer coefficient on the Darcy-Bénard instability in a vertical porous cylinder

Barletta

Storesletten

2013

Physics of Fluids

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The onset of thermal convection in a vertical porous cylinder is studied by considering the heating from below and the cooling from above as caused by external forced convection processes. These processes are parametrised through a finite Biot number, and hence through third-kind, or Robin, temperature conditions imposed on the lower and upper boundaries of the cylinder. Both the horizontal plane boundaries and the cylindrical sidewall are assumed to be impermeable; the sidewall is modelled as a thermally insulated boundary. The linear stability analysis is carried out by studying separable normal modes, and the principle of exchange of stabilities is proved. It is shown that the Biot number does not affect the ordering of the instability modes that, when the radius-to-height aspect ratio increases, are displayed in sequence at the onset of convection. On the other hand, the Biot number plays a central role in determining the transition aspect ratios from one mode to its follower. In the limit of a vanishingly small Biot number, just the first (non-axisymmetric) mode is displayed at the onset of convection, for every value of the aspect ratio. C 2013 American Institute of Physics. [http://dx

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Onset of Rayleigh-Bénard Convection in Porous Bodies

Cited by 49 publications

References 24 publications

Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag

Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag

Onset of Convection in a Porous Rectangular Channel with External Heat Transfer to Upper and Lower Fluid Environments

Effect of a finite external heat transfer coefficient on the Darcy-Bénard instability in a vertical porous cylinder

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