Free convection boundary‐layer flow over horizontal plates and discs

Rotem, Zeev; Claassen, Lutz

doi:10.1002/cjce.5450470511

Cited by 21 publications

(3 citation statements)

References 10 publications

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“…There appears to be no experimental data for predominantly laminar flow in water. The data of Reilly, Tien & Adelman (1966) (used by Rotem & Claassen (19696) in comparisons with their laminar flow analyses) appear to have been obtained in the predominantly turbulent flow regime and agree closely with the experimental correlation for this type of flow obtained by Fishenden & Saunders (1950) in air. Apparently, predominantly turbulent flow is not markedly sensitive to Prandtl number changes, a t least in the range 0.72 < Pr < 10.…”

Section: Lam Inar Natural Convection Boundary Layers On Horizontal Plates 269supporting

confidence: 82%

Laminar natural convection boundary layers on near-horizontal plates

Ackroyd

1976

Proc. R. Soc. Lond. A

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The first order boundary-layer analysis for the laminar natural convection flow over a semi-infinite horizontal or near-horizontal heated plate has been extended to include variable properties effects. Detailed calculations are presented for air and water flows. It is shown further how these calculations can be extended to predict heat transfer rates on plates of rectangular planforms. Because of the lack of sufficiently detailed experimental data, a thorough comparison between the latter and the present calculations has not been possible. However, such comparisons as have been possible are encouraging and a significant improvement on previous theoretical predictions has been achieved. Although higher order corrections have not been discussed in detail, possible matching problems have been investigated briefly. Furthermore, it has been shown that stress work effects in the energy equation and the influence of pressure on density and temperature in the state relation are not only solely higher order effects but are of little significance at such orders.

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Section: Lam Inar Natural Convection Boundary Layers On Horizontal Plates 269supporting

confidence: 82%

Laminar natural convection boundary layers on near-horizontal plates

Ackroyd

1976

Proc. R. Soc. Lond. A

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“…Later Gill, extended Stewartson's solution to another type of wall-temperature variation and to Pr = 1 and 10. Gill et al (1965) and Rotem (1967) showed that the first of the two possible cases of flow was the only one for which boundary-layer solutions could be obtained. At first sight this seems to conflict with early photographs by Schmidt (1932), but this contradiction is only apparent: it can be shown that the flow below a heated plate facing downwards cannot be described by boundary-layer type equations.…”

Section: Introductionmentioning

confidence: 99%

Natural convection above unconfined horizontal surfaces

1969

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The paper discusses free convective flows above a horizontal plate, both theoretically and on the basis of experiments which yield quantitative data. The theory is applicable to the semi-infinite plate and is extended to cover the complete range of Prandtl number values including Pr → 0 and Pr → ∞. Experiments were carried out to demonstrate the existence of a laminar boundary layer above a horizontal plate at intermediate Grashof (respectively Rayleigh) numbers, and its extent along the plate. This layer breaks down into large-eddy instability some distance from the leading edge. The value of the critical Rayleigh number for this to occur, obtained experimentally using semi-focusing colour-Schlieren photography is in reasonable qualitative agreement with previously known data (Tritton 1963a,b).

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“…Heat is absorbed progressively as the fluid flows over the plate inducing a transverse pressure gradient and it is the variation of this favourable pressure gradient which drives the flow. Apart from a minor error in the sign of the gravity component, pointed out by Gill et al [2], the main features of Stewartson's solution have been supported by the experiments of Rotem and Claassen [3,4] and Pera and Gebhart [5]. Subsequent extensions to Stewartson's work were given by Jones [6], Clarke and Riley [7], Traughot [8] and Ackroyd [9].…”

Section: Introductionmentioning

confidence: 84%

Flow past a suddenly cooled horizontal plate

Ingham

Merkin

Pop

1986

Wärme- und Stoffübertragung

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Abstract. The problem of unsteady laminar, incompressible free convection above a horizontal semi-infinite flat plate is studied theoretically. It is assumed that for time t < 0 the plate is hotter than its surroundings and at time t = 0 the plate is suddenly cooled to the same temperature of its surroundings. Three solutions of the momentum and energy equations are obtained, namely (i) an analytical solution which is valid for small time, (ii) an asymptotic analytical solution which is valid for large time, and (iii) a numerical solution which matches these two limiting analytical solutions. It is found that the numerical solution matches the small and large time solutions accurately. Finally, the variation of the velocity, temperature, skin friction and heat transfer on the plate with time are discussed. Str6mung hinter einer pl6tzlich gekiihlten horizontalen PlatteZusammenfassung. In der Arbeit wird das Problem der freien, inkompressiblen, laminaren und nichtstation~ren Konvektion fiber eine halbunendliche waagerechte Platte theoretisch untersucht. Es wird vorausgesetzt, dab die Platte ffir t < 0 w~rmer als die sic umgebende Flfissigkeit ist und dann im Moment t = 0 pl6tzlich bis auf die Temperatur der Umgebung abgekiihlt wird. Es werden drei L6sungen ffir die Impulsgleichung und die Energiegleichung angegeben, und zwar:(i) eine analytische L6sung ffir kleine Werte des Zeitparameters, (ii) eine asymptotische analytische L6sung ftir grol3e Werte des Zeitparameters und (iii) eine numerische L6sung, die sich den beiden analytischen L6sungen anpal3t. Es wird gezeigt, dab sich die numerische L6sung den L6sun-gen for kleine bzw. grol3e Zeitwerte genau anpaBt. Zum Abschlul3 wird die Ver~inderung der Geschwindigkeit, Temperatur, Wandreibung und des W~rmefibergangs an der Platte in Abh~ngigkeit yon der Zeit behandelt.

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Free convection boundary‐layer flow over horizontal plates and discs

Cited by 21 publications

References 10 publications

Laminar natural convection boundary layers on near-horizontal plates

Laminar natural convection boundary layers on near-horizontal plates

Natural convection above unconfined horizontal surfaces

Flow past a suddenly cooled horizontal plate

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