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Natural convections in conjugated single and double enclosures

Freie Konvektion in Einzel- und Doppelhohlräumen

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Abstract

The natural convection in single and double conjugated enclosures are numerically investigated. The single and double enclosures are formed by low conductance walls with finite thickness. The outside vertical surfaces of the conducting walls are of the third kind of boundary condition while the top and bottom outside surfaces are adiabatic. The problem studied is characterized by a dominant horizontal temperature gradient and the thermal boundary conditions at the cavity surfaces can not be specified in priori. Numerical results reveal the characteristics in such kind of enclosures and show the importance of the thermal boundary conditions on the natural convection in enclosures. It is also found that the natural convections in the conjugated double enclosures are basically the same, with a major difference in their fluid temperature levels.

Zusammenfassung

Es wird der Wärmetransport durch freie Konvektion in Einzel- und Doppelhohlräumen numerisch untersucht, welche von Wänden endlicher Dicke und niedriger Wärmeleitfähigkeit gebildet werden. An deren vertikalen Außenseite soll die Randbedingung 3. Art herrschen, während Boden- und Deckenseite als adiabat vorausgesetzt seien. Das untersuchte Problem ist durch einen dominanten horizontalen Temperaturgradienten charakterisiert, sowie den Umstand, daß die Randbedigungen auf den Berandungen der Hohlräume nicht von vornherein festgelegt werden können. Numerische Ergebnisse lassen das charakteristische Übertragungsverhalten solcher Hohlräume erkennen und zeigen den Einfluß der thermischen Randbedingungen auf die natürliche innenseitige Konvektion. Ferner wurde gefunden, daß freie Konvektionsvorgänge in Doppelhohlräumen grundsätzlich nicht anders als in Einzelhohlräumen ablaufen, abgesehen davon, daß diese auf unterschiedlichen Temperaturniveaus stattfinden.

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Abbreviations

a :

thermal diffusivity

a E,W,N,S, aP :

coefficients in discretization equation

C p :

specific heat

g :

gravitational acceleration

G :

nominal flow rate in cavity,G=j ✓u✓π dy

h :

heat transfer coefficient

H :

cavity height

J :

radiosity

k :

thermal conductivity

Nu :

Nusselt number

p :

pressure

q :

heat flux

Q :

heat transfer rate

Ra :

Rayleigh number

S c,ad :

additional source term

S res :

mass residual in entire computation domain

T :

temperature

u, v :

velocity components inx- andy-direction

W :

cavity width

x, y, z :

Cartesian coordinates

β:

volume expansion coefficient

ϕx :

distance between interface to its neighbouring grid point

Δx, Δy :

dimensions of control volume

∈:

surface emmisivity

Ξ:

dimensionless temperature, Ξ=(T−T 2)/(T 1)/(T 1−T2)

μ:

dynamic viscosity

π:

density

b :

bottom

e :

eastern

f :

fluid

h :

horizontal

r :

radiative

s :

solid

t :

top, total

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Authors and Affiliations

  1. School of Energy and Power Engineering, Xi'an Jiaotong University, 710049, Xi'an, Shaaxi, PRC

    C. Y. Zhao &  W. Q. Tao

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  1. C. Y. Zhao
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  2. W. Q. Tao
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This work was supported by the National Natural Science Foundation of China.

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Zhao, C.Y., Tao, W.Q. Natural convections in conjugated single and double enclosures. Heat and Mass Transfer 30, 175–182 (1995). https://doi.org/10.1007/BF01476527

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  • DOI: https://doi.org/10.1007/BF01476527

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