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Natural convection in a square enclosure with an internal isolated vertical plate

Natürliche Konvektion in einem quadratischen Horizontalschacht, der eine freistehende, senkrechte Platte enthält

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Abstract

Numerical computations were performed for the average Nusselt number at an internal vertical plate situated in a square enclosure, with the inner plate and the bounding wall of the enclosure maintained at uniform but different temperatures. Natural convection occurred in the air which occupied the enclosure space. The position of the inner vertical plate within the enclosure was varied parametrically. The plate height-cavity height ratio was 0.513. For narrow distance between the inner plate and the bounding wall the inner plate Nusselt number was enhanced. Aside from this, the plate average Nusselt number was remarkably insensitive to the plate position. The effect of the Rayleigh number on the velocity and temperature fields and local Nusselt numbers are also discussed. The agreement between the predicted flow pattern forRa=1.1×106 and the flow visualization result was reasonably good.

Zusammenfassung

Eine numerische Untersuchung liefert mittlere Nußelt-Zahlen an einer, in einem quadratischen Horizontalschacht freistehenden, senkrechten Platte, wobei deren Temperatur und die der umgebenden Wände jeweils konstant gehalten werden. Im Luftraum dazwischen stellte sich freie Konvektion ein. Die Position der Platte war veränderlich, ihre Höhe blieb mit 51.3% der Schachthöhe konstant. Rückte die Platte nahe an eine Schachtwand, so erhöhte sich die Nußelt-Zahl auf der dieser zugewandten Seite, während die Gesamt-Nußelt-Zahl bezüglich der Platte fast konstant bleibt. Es wird auch der Einfluß der Rayleigh-Zahl auf das Geschwindigkeitsund Temperaturfeld diskutiert. BeiRa=1.1·106 stimmten die Ergebnisse aus der Berechnung gut mit den experimentellen Befunden einer Strömungsvisualisation überein.

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Abbreviations

a :

distance between vertical plate and side-wall of enclosure thermal diffusivity (in definition ofu r)

b :

distance between vertical plate and bottom of enclosure

g :

gravitational acceleration

G :

characteristic flow rate

H :

height of vertical plate

k :

thermal conductivity

k f :

fluid thermal conductivity

K :

relative thermal conductivity,k/k f

L :

width of square enclosure

M res :

mass residual

Nu :

local Nusselt number

Nu m :

average Nusselt number

Nu L :

local Nusselt number of left side of vertical plate

Nu R :

local Nusselt number of right side of vertical plate

Nu B :

local Nusselt number of bottom side of vertical plate

Nu T :

local Nusselt number of top side of vertical plate

p′ :

effective pressure

P :

dimensionless pressure,P=p′/[ϱ(Ra Pr)(a/H)2]

Pr :

Prandtl number

Ra :

Rayleigh number,Ra=gβΔTH 3 Pr/ν 2

T :

temperature

T i :

temperature of internal plate

T o :

temperature of enclosure surface

u, v :

velocity components inx-, y-direction

U, V :

dimensionless velocities,U=u/u r, V=v/ur

u r :

reference velocity,u r=(Ra Pr)1/2/(a/H)

X, {iyY}:

dimensionless coordinates,X=x/H, Y=y/H

α :

heat transfer coefficient

β :

volume expansion coefficient

δ :

thickness of plate

ν :

kinematic viscosity

ϱ :

density

Φ :

dimensionless temperature, (T i−T)/(T i−To)

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Authors and Affiliations

  1. Department of Power Machinery Engineering, Xi'an Jiaotong University, 710049, Xi'an, Shaanxi, PRC

    Q. W. Wang & W. Q. Tao

  2. Department of Power Engineering, Northeast Institute of Electric Power Engineering, 132012, Jilin, Jilin, PRC

    M. Yang

Authors
  1. Q. W. Wang
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  2. M. Yang
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  3. W. Q. Tao
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Wang, Q.W., Yang, M. & Tao, W.Q. Natural convection in a square enclosure with an internal isolated vertical plate. Wärme- und Stoffübertragung 29, 161–169 (1994). https://doi.org/10.1007/BF01548600

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  • DOI: https://doi.org/10.1007/BF01548600

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