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Wärme - und Stoffübertragung

, Volume 22, Issue 1–2, pp 69–77 | Cite as

Natural convection in an inclined rectangular porous cavity with uniform heat flux from the side

  • P. Vasseur
  • L. Robillard
  • I. Anochiravani
Article

Abstract

The problem of natural convection in an inclined rectangular porous layer enclosure is studied numerically. The enclosure is heated from one side and cooled from the other by a constant heat flux while the two other walls are insulated. The effect of aspect ratio, inclination angle and Rayleigh number on heat transfer is studied. It is found that the enclosure orientation has a considerable effect on the heat transfer. The negative orientation sharply inhibits the convection and consequently the heat transfer and a positive orientation maximizes the energy transfer. The maximum temperature within the porous medium can be considerably higher than that induced by pure conduction when the cavity is negatively oriented. The peak of the average Nusselt number depends on the Rayleigh number and the aspect ratio. The heat transfer between the two thermally active boundaries is sensitive to the effect of aspect ratio. For an enclosure at high or low aspect ratio, the convection is considerably decreased and the heat transfer depends mainly on conduction.

Keywords

Heat Transfer Heat Flux Aspect Ratio Nusselt Number Natural Convection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A

aspect ratio of the cavity,H′/ L′

g

gravitational acceleration, m/s2

H

thickness of the cavity, m

k

effective thermal conductivity, W/m-°K

K

permeability of porous material, m2

L

length of the cavity, m

Nu

Nusselt number, (q′/ΔT′)L′/k

q′

heat flux, W/m2

Ra

Rayleigh number,g β KH′2 q′/α v k

t′

time, s

T′

temperature, °K

t′0

reference temperature, °K

ΔT′

characteristic temperature difference,q′ L′/k

u

horizontal dimensionless velocity

v

vertical dimensionless velocity

x

horizontal dimensionless coordinate

y

vertical dimensionless coordinate

Greek symbols

α

effective thermal diffusivity, m2/s

β

coefficient of thermal expansion, °K−1

v

kinematic viscosity, m2/s

ϕ

angle of inclination of enclosure, rad

ϱ

density, Kg/m3

ψ

dimensionless stream function

τ

dimensionless time

Superscripts

'

dimensional quantities

average value

Subscripts

max

maximum value

Naturkonvektion in einem geneigten, rechteckigen, porösen Hohlraum mit gleichmäßigem seitlichen Wärmefluß

Zusammenfassung

Numerisch wird das Problem der Naturkonvektion in einer geneigten, rechteckigen, porösen, eingeschlossenen Schicht studiert. Der Raum ist auf der einen Seite beheizt und auf der anderen durch konstanten Wärmeabzug gekühlt, während die beiden anderen Wände isoliert sind. Es wird der Einfluß des Längen-Seiten-Verhältnisses, des Neigungswinkels und der Rayleigh-Zahl auf den Wärmeübergang studiert. Es stellte sich heraus, daß die Neigung des Hohlraumes beträchtlichen Einfluß auf den Wärmeübergang hat. Negative Orientierung behindert die Konvektion stark — und damit auch den Wärmetransport — und eine positive Neigung führt zu einem Maximum im Wärmetransport. Bei negativer Orientierung kann die maximale Temperatur in dem porösen Medium beträchtlich höher sein als wie sie eine reine Wärmeleitung hervorrufen würde. Das Maximum in der über die Fläche gemittelten Nusselt-Zahl hängt von der Rayleigh-Zahl und dem Längen-Seiten-Verhältnis ab. Der Wärmetransport zwischen den beiden thermisch aktiven Grenzen ist empfindlich auf den Einfluß des Längen-Seiten-Verhältnisses. Für große oder kleine Seitenverhältnisse nimmt die Konvektion stark ab und der Wärmetransport beruht hauptsächlich auf Leitung.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • P. Vasseur
    • 1
  • L. Robillard
    • 1
  • I. Anochiravani
    • 1
  1. 1.Department of Mechanical EngineeringEcole PolytechniqueMontrealCanada

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