Multiple steady states for unicellular natural convection in an inclined porous layer

Sen, Mihir; Vasseur, P.; Robillard, L.

doi:10.1016/0017-9310(87)90089-5

Cited by 63 publications

(26 citation statements)

References 16 publications

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“…By assuming a shallow cavity A 1 and by using the parallel flow approximation [21][22][23], Kimura et al [17] found that the analytical solution for the monocellular flow consists of: a horizontal asymmetric velocity with a zero mean along any vertical section,…”

Section: Nonlinear Solution and Formulation Of Its Linear Stabilitymentioning

confidence: 99%

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Gueye

Ouarzazi

Hirata

et al. 2017

Fluids

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Abstract:We analyze the thermal convection thresholds and linear characteristics of the primary and secondary instabilities for viscoelastic fluids saturating a porous horizontal layer heated from below by a constant flux. The Galerkin method is used to solve the eigenvalue problem by taking into account the elasticity of the fluid, the ratio between the viscosity of the solvent and the total viscosity of the fluid and the lateral confinement of the medium. For the primary instability, we found out that depending on the rheological parameters, two types of convective structures may appear when the basic conductive solution loses its stability: stationary long wavelength instability as for Newtonian fluids and oscillatory convection. The effect of the lateral confinement of the porous medium by adiabatic walls is to stabilize the oblique and longitudinal rolls and therefore selects transverse rolls at the onset of convection. In the range of the rheological parameters where stationary long wave instability develops first, we use a parallel flow approximation to determine analytically the velocity and temperature fields associated with the monocellular convective flow. The linear stability analysis of the monocellular flow is performed, and the critical conditions above which the flow becomes unstable are determined. The combined influence of the viscoelastic parameters and the lateral confinement on the characteristics of the secondary instability is quantified. The major new findings concerning the secondary instabilities may be summarized as follows: (i) For concentrated viscoelastic fluids, computations showed that the most amplified mode of convection corresponds to oscillatory transverse rolls, which appears via a Hopf bifurcation. This pattern selection is independent of both the fluid elasticity and the lateral confinement of the porous medium; (ii) For diluted viscoelastic fluids, the preferred mode of convection is found to be oscillatory transverse rolls for a very laterally-confined medium. Otherwise, stationary or oscillatory longitudinal rolls may develop depending on the fluid elasticity. Results also showed the destabilizing effect of the relaxation fluid elasticity and the stabilizing effect of the viscosity ratio for the onset of both primary and secondary instabilities.

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Section: Nonlinear Solution and Formulation Of Its Linear Stabilitymentioning

confidence: 99%

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Gueye

Ouarzazi

Hirata

et al. 2017

Fluids

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“…There exists two papers which present detailed numerical solutions for layers with constant heat flux boundary conditions, namely those by Vasseur et al (1987) and Sen et al (1987). The former concentrates on finite, but high aspect ratio cavities, and provides a careful comparison between a theoretical analysis based on a parallel flow approximation and fully nonlinear solutions.…”

mentioning

confidence: 99%

Linear Instability of the Isoflux Darcy–Bénard Problem in an Inclined Porous Layer

Rees

Barletta

2011

Transp Porous Med

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The linear stability for convection in an inclined porous layer is considered for the case where the plane bounding surfaces are subjected to constant heat flux boundary conditions. A combined analytical and numerical study is undertaken to uncover the detailed thermoconvective instability characteristics for this configuration. Neutral curves and decrement spectra are shown. It is found that there are three distinct regimes between which the critical wavenumber changes discontinuously. The first is the zero-wavenumber steady regime which is well known for horizontal layers. The disappearance of this regime is found using a small-wavenumber asymptotic analysis. The second consists of unsteady modes with a nonzero wavenumber, while the third consists of a steady mode. Linear stability corresponds to inclinations which are greater than 32.544793 • from the horizontal.

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“…Besides, Prasad and Kulacki [6], Sen et al [7], Baytas and Pop [8], Nithiarasu et al [9], Moya et al [10], Al-Amiri [11], Lauriat and Prasad [12], Saeid and Pop [13], have made numerical studies to investigate the phenomenon in differentially heated enclosures. In all studies, entire wall has constant temperature or adiabatic.…”

Section: Introductionmentioning

confidence: 97%

Natural convection in partially cooled and inclined porous rectangular enclosures

Öztop

2007

International Journal of Thermal Sciences

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Multiple steady states for unicellular natural convection in an inclined porous layer

Cited by 63 publications

References 16 publications

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Linear Instability of the Isoflux Darcy–Bénard Problem in an Inclined Porous Layer

Natural convection in partially cooled and inclined porous rectangular enclosures

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