Thermal influence of boundaries on the onset of Rayleigh-Bénard convection

Cerisier, P.; Rahal, Samir; Cordonnier, J.; Lebon, Georgy

doi:10.1016/s0017-9310(97)00364-5

Cited by 24 publications

(17 citation statements)

References 15 publications

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“…Notice that when X increases the critical values in both figures change from the fixed temperature case to the fixed heat flux case. The results are similar to those of Cericier et al [6] and were plotted using a formula calculated from a low order Galerkin approximation. It is important to observe that in the middle range of X the thickness of the walls play a relevant roll producing large differences between the critical values, for fixed X.…”

Section: The Velocity With the Scaling Is Defined As U =( ∂ψ/∂Z0−ǫ∂supporting

confidence: 84%

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Viscoelastic Natural Convection

Dávalos‐Orozco¹

2012

Viscoelasticity - From Theory to Biological Applications

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Section: The Velocity With the Scaling Is Defined As U =( ∂ψ/∂Z0−ǫ∂supporting

confidence: 84%

“…The effect of the thickness and heat conductivity of the wall on natural convection has been investigated by Cericier et al [6]. The goal is to be able to obtain more realistic critical values of the Rayleigh number and wavenumber.…”

Section: The Velocity With the Scaling Is Defined As U =( ∂ψ/∂Z0−ǫ∂mentioning

confidence: 99%

Viscoelastic Natural Convection

Dávalos‐Orozco¹

2012

Viscoelasticity - From Theory to Biological Applications

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“…This extension to the problem of convection has been presented in Ref. [2], and studied by Cerisier et al [7] and Howle [1], among others.…”

Section: The Problem Of Convection In a Fluid Layermentioning

confidence: 82%

“…The bounding surfaces have become an interesting topic of study since the boundary conditions are mathematically written according to their nature [6,7]. The thickness and thermal conductivity of the walls and the fluid layer are strongly related to the familiar eigenvalue Rayleigh number and to the wavenumber.…”

Section: Introductionmentioning

confidence: 99%

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Thickness and Thermal Conductivities of the Walls and Fluid Layer Effects on the Onset of Thermal Convection in a Horizontal Fluid Layer Heated from Below

Pérez-Reyes¹,

Vargas-Aguilar²,

Gómez‐Benítez³

et al. 2017

Vortex Structures in Fluid Dynamic Problems

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The thermal boundary conditions have important effects on the hydrodynamics of a thermo-convective fluid layer. These effects are introduced through the Biot number under the Robin type boundary conditions. The thermal conductivity and thicknesses of the walls are key properties to bridge two known ideal situations widely studied: the fluid layer bounded by two insulating walls and the fluid layer bounded by two perfect thermal conducting walls. This chapter is devoted to the physical mechanisms involved in the thermal boundary conditions, its influence on the linear stability of the fluid layer and its implications with the pattern formation. A review of very important investigations on the subject is also given. The role of the thermal conductivities and thicknesses of the walls is explained with help of curves of criticality for the thermoconvection in a horizontal Newtonian fluid layer.

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Natural convection in shear‐thinning yield stress fluids in a square enclosure

Magnin

Métivier

2015

AIChE Journal

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International audienceThe influence of viscoplastic rheological features on the Rayleigh-Bénard convection is investigated by numerical means in order to compare with first experimental results given by Darbouli et al. The fluid is modeled by a regularized Herschel-Bulkley law which is often used to fit numerous pasty fluids. Natural convection in a two-dimensional square cavity heated from below is considered. Critical values of Oldroyd number Od and yield number Y are provided. Numerical results highlight a stabilizing effect of the yield stress as well as a destabilizing effect of increasing shear-thinning coefficient n as the increase in n enhances the heat transfer in the range of our calculations. Unyielded regions are located in the square corners of the cavity and in the cavity where convection occurs. The unyielded zones size increases with the increase in Od and can invade all the cavity for sufficiently large values of Od

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Thermal influence of boundaries on the onset of Rayleigh-Bénard convection

Cited by 24 publications

References 15 publications

Viscoelastic Natural Convection

Viscoelastic Natural Convection

Thickness and Thermal Conductivities of the Walls and Fluid Layer Effects on the Onset of Thermal Convection in a Horizontal Fluid Layer Heated from Below

Natural convection in shear‐thinning yield stress fluids in a square enclosure

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