Transitions of natural convection in a horizontal annulus

Mizushima, Jiro; Hayashi, Sachiko; Adachi, Takahiro

doi:10.1016/s0017-9310(00)00188-5

Cited by 58 publications

(48 citation statements)

References 9 publications

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“…He observed dual steady solutions at Ra > Ra c ≈ 3800 for wide gap annuli (R = 2) by the vorticity-streamfunction method. Similar results were provided later by Mizushima et al, 20,21 xin et al 22 and Mercader et al 23 Petrone et al 24 performed a stability analysis of numerical steady-state solutions, and provided a detail of the bifurcation diagram near the imperfect bifurcation for different radius ratio R = 1.2, 1.4 and 2 at Pr = 0.7. Angeli et al 25 provided a critical review of buoyancy-induced flow transitions in horizontal annuli.…”

Section: Introductionsupporting

confidence: 68%

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Luo

Tan

2014

AIP Advances

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Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.

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Section: Introductionsupporting

confidence: 68%

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Luo

Tan

2014

AIP Advances

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“…In the light of the previous observations, what should be expected for large A is a consistent convective flow, with a fairly articulated streamline structure, as noticed in [9][10][11][12], associated with a consistent average Nusselt number, strongly depending on A, as noticed in [6]. All these properties occur even for very small Rayleigh numbers, so small that one would observe the fluid almost at rest if A were also small.…”

supporting

confidence: 59%

“…In (14), and can be either scalar-, vector-or tensor-valued functions and the dot between and denotes multiplication for scalar functions or the corresponding scalar product in case of vectors or tensors, respectively. Next, the norm of the difference between the gradients of solutions to problems (3)(4)(5) and (10)(11)(12), namely, the quantity ∇(v − w) 2 + ∇(τ − τ 0 ) 2 , is taken as a measure of the absolute error. Finally, an upper bound for the absolute error is found; such a bound essentially depends on Pr −1 (Ra/b) 2 .…”

Section: Mathematical Modelmentioning

confidence: 99%

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Natural convection in horizontal annuli: a lower bound for the energy

2007

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We study natural convection in the gap between two infinitely\ud long horizontal coaxial cylindrical surfaces, each of which is\ud maintained at constant temperature. If the inverse relative gap\ud width $\cA$ is large,\ud relevant steady convective flow and considerable heat transfer\ud are observed, even for extremely small Rayleigh numbers $\Ra$. A lower\ud bound for the norm of the velocity and of the temperature is\ud rigorously found by studying an approximation problem, which is a\ud good model in the parameter range where steady stable flow\ud occurs. The lower bound depends on $\cA$ only, and is an\ud increasing function of $\cA$. This means that the bound can be\ud arbitrarily increased via the geometry only - no matter how small\ud the temperature difference is, and independently of the Prandtl\ud number $\Pr$

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“…[10] studied natural convection flow in a horizontal annulus enclosure with a transversely oscillating inner cylinder. [11] investigated transition of natural convection in an annulus between horizontal concentric cylinders theoretically by assuming two-dimensional and incompressible flow fields.…”

mentioning

confidence: 99%

Transient Natural Convection in an Annulus with Thermal Radiation

Jha¹,

Yabo²,

Lin³

2017

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The interaction of transient fully developed natural convection flow with thermal radiation inside a vertical annulus is analyzed both analytically and numerically. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The mathematical model capturing the present physical situation is highly non-linear due to the presence of radiation effect. The solution of transient model is obtained by implicit finite difference method. To check accuracy of the numerical solution, steady state solution for energy and momentum equations are derived analytically using perturbation series method. Skin-friction and Nusselt number at the outer surface of inner cylinder as well as inner surface of the outer cylinder are obtained. Selected sets of graphical results illustrating the effects of various controlling parameters involved in the problem on flow formation are discussed.

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Transitions of natural convection in a horizontal annulus

Cited by 58 publications

References 9 publications

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Natural convection in horizontal annuli: a lower bound for the energy

Transient Natural Convection in an Annulus with Thermal Radiation

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