Nonlinear convective stability problems of viscoelastic fluids in finite domains

Park, H. M.; Ryu, Dongsu

doi:10.1007/s00397-001-0223-x

Cited by 15 publications

(1 citation statement)

References 17 publications

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“…The first study on the Rayleigh-Bénard convection with viscoelastic fluids (VRBC) can be traced back to Green III 3 , who experimentally investigated heat transfer characteristics in VRBC and found the convective oscillating phenomena. His pioneering work was followed by a series of studies to gain a deeper understanding of several aspects of the VRBC [4][5][6][7] together with investigations on the flow reversal in turbulent flow 8 , overstability [9][10][11] , chaos 10 , properties of the RBC through linear and nonlinear stability analyses 12,13 , the effect of surfactants on the RBC 14 , experimental findings on the turbulent 15 and yield stress fluids VRBC 16,17 and on heat transfer properties in turbulent VRBC 18 . Direct numerical simulation (DNS) added much later to the tool kit for the study of both laminar and turbulent VRBC made possible remarkable contributions towards a thorough mapping of this flow [19][20][21] .…”

Section: Introductionmentioning

confidence: 99%

Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity

et al. 2023

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The oscillating onset of the Rayleigh-Bénard convection (RBC) with viscoelastic fluids in a slightly tilted 2-dimension (2D) rectangular cavity with aspect ratio Γ = 2 was investigated for the first time via direct numerical simulation. A series of simulations were conducted in the plane of the Rayleigh number (Ra) and the tilt angle (α ∈ [0◦,5◦]) with three Weissenberg numbers (Wi = (0.1,0.15,0.2)) at a fixed Prandtl number Pr = 7.0. The evolutionary path of the oscillating convection onset in the (Wi,α)-plane was determined and corresponding complex flow structures were observed. The inclination of the box delays the onset of the oscillations and the corresponding Rayleigh number Rac as compared to the horizontal configuration. Oscillating flow structures acquire the attributes of a traveling wave. A specific feature of the oscillating convection in the case of the horizontal cavity, the periodicity in space and time exists in the inclined box case as well. But, the evolution of the oscillatory flow structure is very different from the horizontal case in that the counter-clockwise cell assimilates the clockwise cell.

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Section: Introductionmentioning

confidence: 99%

Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity

et al. 2023

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Thermally-Driven Flows in Polymeric Liquids

Lappa

2022

Encyclopedia of Materials: Plastics and Polymers

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Within the vast array of problems related to the processing of plastic materials and polymeric liquids, the main focus of the present chapter is the illustration of the typical dynamics of thermally-driven flows in these fluids, i.e. 'natural' fluid motion induced by gravity or surfacetension effects. Experimental struggles with understanding the basic mechanisms of these fundamental types of convection in viscoelastic fluids have been mitigated over recent years by the development of relevant models and adequate numerical techniques. On the one hand, this progress has produced new fundamental knowledge; on the other hand, it has led to new questions, both general and system-specific (a relevant example being represented by the intriguing concept of "elastic turbulence"). This field continues to burgeon and bring surprises to this day. A synthetic review of the salient outcomes of past and recent studies is reported in this chapter (articulated in focused subsections) together with a critical discussion of some accompanying necessary definitions and paradigms used to reveal the intimate essence of these liquids. For the convenience of the reader, however, advanced formal discussions and mathematical arguments are stripped down to their essentials. In the same spirit, the use of jargon is kept at minimum and much of the available space is devoted to the description (both qualitative and quantitative) of the considered convective phenomena, the related thresholds in terms of characteristic numbers and the underlying "physics".

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Rayleigh–Bénard convection of viscoelastic fluids in arbitrary finite domains

Park

2004

International Journal of Heat and Mass Transfer

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Nonlinear convective stability problems of viscoelastic fluids in finite domains

Cited by 15 publications

References 17 publications

Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity

Oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted cavity

Thermally-Driven Flows in Polymeric Liquids

Rayleigh–Bénard convection of viscoelastic fluids in arbitrary finite domains

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