Time-dependent Rayleigh–Benard convection: Cell formation and Nusselt number

Moon, Je-Young; Chung, Bum-Jin

doi:10.1016/j.nucengdes.2014.04.017

Cited by 28 publications

(6 citation statements)

References 30 publications

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“…In nature, for example, this phenomenon can be found in large scales in the Earth's mantle [1] and the atmosphere of planets [2]. In engineering, for example, natural convection in enclosures can be used in microfluidic DNA analysis devices [3,4] and in temperaturecontrol strategies for solar-energy collectors [5] and nuclear reactors [6]. Therefore, there exists a great diversity of buoyancy-driven flows in enclosures that are of great interest in science and technology [7,8].…”

Section: Introductionmentioning

confidence: 99%

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

et al. 2015

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The transition from the complex Rayleigh-Bénard convection to the simple heated-from-the-sides configuration in a cubical cavity filled with a Newtonian fluid is numerically studied. The cavity is tilted by an angle θ around its lower horizontal edge and is heated and cooled from two opposite tilted sides. We first analyze the effect of a marginal inclination angle on quasi-Rayleigh-Bénard convection (θ≈0∘), which is a realistic physical approximation to the ideal Rayleigh-Bénard convection. We then yield the critical angles where multiple solutions that were initially found for θ≈0∘ disappear, eventually resulting in the single steady roll solution found in the heated-from-the-sides configuration (θ=90∘). We confirm the existence of critical angles during the transition θ:0∘→90∘, and we demonstrate that such angles are a consequence of either singularities or collisions of bifurcation points in the Rayleigh-number-θ parameter space. We finally derive the most important critical angles corresponding to any Newtonian fluid of Prandtl number greater than that of air.

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Section: Introductionmentioning

confidence: 99%

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

et al. 2015

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“…This instability appears in many scientific and industrial applications [12][13][14], and is still the subject of current research.…”

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confidence: 99%

Rayleigh-Bénard instability in graphene

et al. 2015

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Motivated by the observation that electrons in graphene, in the hydrodynamic regime of transport, can be treated as a two-dimensional ultrarelativistic gas with very low shear viscosity, we examine the existence of the Rayleigh-Bénard instability in a massless electron-hole plasma. First, we perform a linear stability analysis, derive the leading contributions to the relativistic Rayleigh number, and calculate the critical value above which the instability develops. By replacing typical values for graphene, such as thermal conductivity, shear viscosity, temperature, and sample sizes, we find that the instability might be experimentally observed in the near future. Additionally, we have performed simulations for vanishing reduced chemical potential and compare the measured critical Rayleigh number with the theoretical prediction, finding good agreement.

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“…When compared with temperature measurement, this technique is attractive as it provides a simple, cheap, and accurate measurement method through measurement of the electric current [11,12]. This technique was developed by several researchers [13][14][15][16] and the methodology has been tested to various flow conditions such as forced, natural, and mixed convection [17][18][19][20][21][22][23] and now is well-established. Nusselt number would depend on all three numbers: Pr, Re and Ra.…”

Section: Experiments Methodologymentioning

confidence: 99%

The influence of tip clearance and Prandtl number on turbulent forced convection heat transfer of rectangular fins

Park

Chung

2016

Heat Mass Transfer

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Mass transfer coefficient [m/s] H Fin height [m] I lim Limiting current density [A/m 2 ] K Thermal conductivity [W/m K] L Length of base plate [m] N Number of electrons in charge transfer reaction Nu Dh Nusselt number (h h D h /k) p Pressure [N/m 2 ] Pr Prandtl number (ν/α) Q Total heat transfer rate [W] Ra L Rayleigh number (Gr L Pr) Re Dh Reynolds number (VD h /ν) S Fin spacing [m] Sc Schmidt number (ν/D m ) t Fin thickness [m] t n Transference number T Temperature [K] U x Uncertainty of x V Mean velocity [m/s] W Width of the base plate [m] y Distance to nearest wall [m] y + Dimensionless wall distance (ρμ τ y/μ) Greek symbols α Thermal diffusivity [m 2 /s] β Volume expansion coefficient [1/K] μ Viscosity [kg/m s] ν Kinematic viscosity [m 2 /s] ρ Density [kg/m 3 ]

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Time-dependent Rayleigh–Benard convection: Cell formation and Nusselt number

Cited by 28 publications

References 30 publications

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

Rayleigh-Bénard instability in graphene

The influence of tip clearance and Prandtl number on turbulent forced convection heat transfer of rectangular fins

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