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Heat and Mass Transfer

, Volume 31, Issue 5, pp 313–321 | Cite as

Numerical analysis of natural convection around a vertical channel in a rectangular enclosure

  • J. P. Liu
  • W. Q. Tao
Originals

Abstract

Numerical computations were performed for the heat transfer and fluid flow characteristics of an internal vertical channel composed by a pair of parallel plates situated in a rectangular enclosure, with the inner plates 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 plates were symmetrically arranged. The dimensionless channel widthS was varied parametrically. The Rayleigh numbers ranged from 102 to 107. Static bifurcation was found in this configuration. The bifurcation is related to the flow pattern transition from single-vortex structure to double-vortex structure or vice versa. Comparison with the empirical correlations obtained for a vertical plate and a channel in an infinite space showed that the heat transfer process of the plates and the channel was deteriorated by the existence of the enclosure.

Keywords

Heat Transfer Natural Convection Rayleigh Number Empirical Correlation Vertical Plate 
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

thermal diffusivity

b

half width of the enclosure

B

dimensionless half width of the enclosure

Fl

dimensionless mass flow through half width of the channel

h

height of the channel plate

kf

fluid thermal conductivity

ks

solid thermal conductivity

K

relative thermal conductivity

l

distance from the top of the plate to the top wall of the enclosure, i.e., distance from the bottom of the plate to the bottom wall of the enclosure

L

dimensionless ofl

Mres

mass residual

NuCH

channel Nusselt number

NuCH

outside channel Nusselt number

Nui

local Nusselt number

NuI

average inside surface Nusselt number

NuO

average outside surface Nusselt number

p

effective pressure

P

dimensionless pressure, defined asP=p′/[(ρ(RaPr)/(a/h)2]

Pr

Prandtl number

Ra

Rayleigh number based on the height of the plate,h

RaCH

channel Rayleigh number

s

channel width

S

dimensionless channel width,s/h

t

time

T

temperature

Th

temperature of the internal plate

Tc

temperature of the enclosure surface

u,v

velocity components inx-,y-direction

U, V

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

ur

reference velocity, defined as (RaPr)1/2/(a/h)

x, y

coordinates

X, Y

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

Greek symbols

αi

heat transfer coefficient

β

volume expansion coefficient

δ

thickness of the plates

v

kinetic viscosity

ρ

density of the fluid

τ

dimensionless time, defined asu r t/h

φ

dimensionless temperature, defined as (T-T c )/(T h -T c )

Numerische Ermittlung der natürlichen Konvektion um einen vertikalen Kanal in einer rechteckigen Kammer

Zusammenfassung

Aus numerischen Berechnungen wurde das Wärmeübergangs- und Strömungsverhalten eines aus zwei parallelen Platten gebildeten Vertikalkanals ermittelt, der sich symmetrisch angeordnet in einer rechteckigen Kammer befindet. Kanal- und Kammerwände haben gleichförmige, jedoch unterschiedliche Temperaturen. In der luftgefüllten Kammer herrscht freie Konvektion. Die dimensionslose KanalbreiteS wurde als Parameter variiert, wobei die Rayleigh-Zahlen zwischen 102 und 107 lagen. Für die beschriebene Konfiguration wurde statische Bifurkation festgestellt, welche sich im Strömungsbild durch den Übergang von der Einzel-zur Doppelwirbelstruktur und umgekehrt dokumentiert. Der Vergleich mit empirischen Beziehungen für eine vertikale Platte und einen Kanal im umbegrenzten Raum ergab, daß der Wärmeaustausch an Platte und Kanal durch den Kammereinschluß behindert wird.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • J. P. Liu
    • 1
  • W. Q. Tao
    • 1
  1. 1.School of Energy and Power EngineeringXi'an jiaotong UniversityXi'anPRC

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