Fully developed laminar buoyant flow in vertical 
cavities and ducts of bounded section

McBain, G. D.

doi:10.1017/s0022112099006783

Cited by 15 publications

(9 citation statements)

References 26 publications

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“…In a rectangular cavity with A y > 1.7, McBain [15] verified that the dynamical effects of the two vertical end walls on the flow within the cavity are practically negligible. In the experimental study, we supposed that all non-active walls are perfectly thermally insulated.…”

Section: Resultsmentioning

confidence: 96%

On the similarity between gravity and magneto-gravity convection within a non-electroconducting fluid in a differentially heated rectangular cavity

Khaldi¹,

Noudem²,

Gillon³

2005

International Journal of Heat and Mass Transfer

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Section: Resultsmentioning

confidence: 96%

On the similarity between gravity and magneto-gravity convection within a non-electroconducting fluid in a differentially heated rectangular cavity

Khaldi¹,

Noudem²,

Gillon³

2005

International Journal of Heat and Mass Transfer

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“…This is not an accident. It is has been proven elsewhere [12] that if a three-dimensional velocity field has zero gradient in some direction then the component of velocity in that direction is constant along vortex-lines (curves parallel to the curl of the velocity). And, indeed, the curl of any toroidal field is poloidal.…”

Section: Proof For the Scaloidal Subspacementioning

confidence: 99%

Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 1. Fields with divergence

McBain

2005

ANZIAM J.

Self Cite

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It is shown how to decompose a three-dimensional field periodic in two Cartesian coordinates into five parts, three of which are identically divergence-free and the other two orthogonal to all divergence-free fields. The three divergence-free parts coincide with the mean, poloidal and toroidal fields of Schmitt and Wahl; the present work, therefore, extends their decomposition from divergence-free fields to fields of arbitrary divergence. For the representation of known and unknown fields, each of the five subspaces is characterised by both a projection and a scalar representation. Use of Fourier components and wave coordinates reduces poloidal fields to the sum of two-dimensional poloidal fields, and toroidal fields to the sum of unidirectional toroidal fields.

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“…2019) and turbulent vertical boundary layer flows (Wei 2020) have been reported. Further, discussion on transient behaviours (Patterson & Imberger 1980; Xu, Patterson & Lei 2009), three-dimensional effects (McBain 1999), heating conditions (Sparrow & Gregg 1956; Nie & Xu 2019) and governing parameters (Lin & Armfield 2012) has been presented.…”

Section: Introductionmentioning

confidence: 99%

Effect of curvature on transient natural convection in a vertical circular pipe

Nie

2022

J. Fluid Mech.

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Natural convection adjacent to a curved vertical wall is widely present. Unfortunately, the effect of curvature on the transient thermal boundary layer (TBL) adjacent to the concave vertical wall has been neglected. In this study, dynamical evolution and thermal process of transient natural convection in a vertical circular pipe are discussed using scaling analysis, a boundary flow regime for the thin TBL without merging and a duct flow regime for the TBL with merging at the axis of the pipe are distinguished. The scaling laws quantifying the dependence of thickness, velocity and flow rate of the TBL of the fluid with the fixed Prandtl number in the vertical pipe on the Rayleigh number (RaT and Raq) and the ratio of height to radius of the pipe (A) are first reported for the isothermal and isoflux conditions. The curvature effect becomes stronger with the increase of the thickness of the TBL. Under the duct flow regime, the non-dimensional flow rate is scaled with $Ra_T^{1/2}{A^{ - 1}}$ for the isothermal condition and with $Ra_q^{1/2}{A^{ - 3/2}}$ for the isoflux condition. The scaling laws of the thickness, velocity and the flow rate of the TBL in the vertical pipe are validated based on the numerical results from direct numerical simulation (DNS) with good precision. The scaling coefficient is also presented under different regimes and conditions, which can serve as a design guide to determine natural convection in the vertical circular pipe.

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Fully developed laminar buoyant flow in vertical cavities and ducts of bounded section

Cited by 15 publications

References 26 publications

On the similarity between gravity and magneto-gravity convection within a non-electroconducting fluid in a differentially heated rectangular cavity

On the similarity between gravity and magneto-gravity convection within a non-electroconducting fluid in a differentially heated rectangular cavity

Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 1. Fields with divergence

Effect of curvature on transient natural convection in a vertical circular pipe

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