Rayleigh–Bénard convection in non-Newtonian fluids: Experimental and theoretical investigations

Bouteraa, Mondher; Varé, Thomas; Nouar, Chérif; Becker, Simon; Ouhajjou, Jamal

doi:10.1063/5.0070983

Cited by 4 publications

(5 citation statements)

References 41 publications

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“…Rayleigh-B enard convection (RBC) arises as buoyancy-driven instability in a fluid layer heated from below by a vertical temperature gradient. Owing to the significance of this heat transfer mechanism and its wide applicability in industry and natural processes, researchers have long been interested in this topic (Bodenschatz et al, 2000;Ouertatani et al, 2008;Tisserand et al, 2011;Park, 2015Aghighi et al, 2015Kaur and Singh, 2017;Mahanthesh et al, 2020;Bouteraa et al, 2021;Samuel et al, 2022). Over the past decade, increased processor power and advanced numerical methods have enabled researchers to study this problem under more complex conditions, such as viscoplastic fluids (Turan et al, 2012;Hassan et al, 2015;Aghighi and Ammar, 2017;Aghighi et al, 2018).…”

Section: Wall Slip Effects 1275mentioning

confidence: 99%

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

Aghighi,

Metivier,

Fakhri

2023

MMMS

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PurposeAccording to the research, viscoplastic fluids are sensitive to slipping. The purpose of this study is to determine whether slip affects the Rayleigh–Bénard convection of viscoplastic fluids in cavities and, if so, under what conditions.Design/methodology/approachThe wall slip was evaluated using a model created for viscoplastic (Bingham) fluids. The coupled conservation equations were solved numerically using the finite element method. Simulations were performed for various parameters: the Rayleigh number, yield number, slip yield number and friction number.FindingsWall slip determines two essential yield stresses: a specific yield stress value beyond which wall slippage is impossible (S_Yc); and a maximum yield stress beyond which convective flow is impossible (Y_c). At low Rayleigh numbers, Y_c is smaller than S_Yc. Hence, the flow attained a stable (conduction) condition before achieving the no-slip condition. However, for more significant Rayleigh numbers Y_c exceeded S_Yc. Thus, the flow will slip at low yield numbers while remaining no-slip at high yield numbers. The possibility of slipping on the wall increases the buoyancy force, facilitating the onset of Rayleigh–Bénard convection.Originality/valueAn essential aspect of this study lies in its comprehensive examination of the effect of slippage on the natural convection flow of viscoplastic materials within a cavity, which has not been previously investigated. This research contributes to a new understanding of the viscoplastic fluid behavior resulting from slipping.

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Section: Wall Slip Effects 1275mentioning

confidence: 99%

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

Aghighi,

Metivier,

Fakhri

2023

MMMS

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“…Park and Ryu, [18] Inaba et al, [19] Benouared et al, [20] Bouteraa et al, [21] Jenny et al, [22] Bouteraa and Nouar, [23] Yigit et al, [24] Bouteraa et al, [25] Henry et al [26] (c)…”

Section: Numerical Simulationmentioning

confidence: 99%

“…Therefore, the Carreau model is more suitable for numerical simulation. In fact, in recent numerical simulations of Rayleigh-Bénard convection with non-Newtonian fluids, [23,25] the Carreau model was employed.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…In these studies, the effective viscosity η eff is used to calculate the effective Ra (Ra eff ). However, the selection of the representative velocity, used for estimating the effective shear-rate (_ γ eff ), is different among these studies, [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] as tabulated in Table 1. This variance induces a difficulty in estimating the effective shear-rate (_ γ eff ).…”

Section: Introductionmentioning

confidence: 99%

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Representative velocity scale of Rayleigh‐Bénard convection with shear‐thinning fluids

Masuda,

Iyota,

Ohta

2023

Can J Chem Eng

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Although natural convection is frequently encountered in various chemical processes, Rayleigh number (Ra) cannot be defined fully in shear‐thinning fluid systems. In particular, the velocity scale, which is necessary to estimate the effective viscosity of the system, should be discussed carefully. Thus, in this study, the representative velocity scale of Rayleigh‐Bénard (RB) convection, which is a typical example of natural convection, with shear‐thinning fluids was investigated based on the velocity fields obtained using computational fluid dynamics. Numerical simulations revealed that the critical temperature difference at which RB convection starts to fully develop decreases with an increase in the shear‐thinning property. The shear‐thinning property also induced subcritical bifurcation. In addition, the velocity scale of convection increases with an increase in the shear‐thinning property. Thus, the shear‐thinning property is considered to accelerate convection. Compared with several types of velocity scales used by other researchers, significant deviations from the actual scale were observed. Therefore, a new type of velocity scale, including the buoyant to viscous force ratio, arbitrary parameter, and thermal diffusivity, was proposed. The proposed velocity scale allowed an approximate estimation of the actual velocity scale. Although further investigation of the validity is necessary with varying geometries and rheological parameters, this velocity scale will be useful for controlling RB convection with Newtonian/shear‐thinning fluids.

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“…Показано, что, как и в случае ньютоновской жидкости, никакие докритические неустойчивости невозможны. Результаты экспериментальных исследований конвекции Рэлея -Бенара в неньютоновских жидкостях приведены в [3]. Установлено, что для получения гексагональных ячеек в начале конвекции температурная зависимость параметров жидкости должна быть достаточно сильной.…”

Section: Introductionunclassified

Rayleigh — Benard problem for Polymer Solution

Pukhnachev,

Frolovskaya

2023

Известия АлтГУ

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There are three mathematical models describing the motion of aqueous solutions of polymers: the second grade fluid model (Rivlin — Eriksen), the hereditary model (Voitkunsky — Amfilokhiev — Pavlovsky), and its asymptotic simplification (Pavlovsky). This work considers the problem of fluid equilibrium stability in a horizontal fluid layer heated from below or from above. Also, equations of thermal gravitational convection for all three models are derived. Three types of boundary conditions are considered: two solid boundaries; the lower solid boundary and the upper free boundary; two free boundaries (the Rayleigh problem). For the case of heating from below, the principle of perturbation monotonicity is established that ensures the spectral problem eigenvalues to be of real type. This greatly simplifies the determination of the critical Rayleigh numbers. It turned out that these numbers coincide with the critical Rayleigh numbers in the classical Rayleigh — Benard problem. In the case of heating from above at large temperature gradients, the perturbation decrements become complex, but their real parts are negative. The conclusion that the relaxation properties of a second grade fluid and an aqueous solution of polymers do not lead to a change in the critical Rayleigh number may seem strange at first glance. According to our assumption, it is explained by the base state of the liquid being a state of rest.

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Rayleigh–Bénard convection in non-Newtonian fluids: Experimental and theoretical investigations

Cited by 4 publications

References 41 publications

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

Representative velocity scale of Rayleigh‐Bénard convection with shear‐thinning fluids

Rayleigh — Benard problem for Polymer Solution

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