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Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli

Einfluß der Prandtl-Zahl auf den Wärmeübergang bei freier Konvektion in konzentrischen und exzentrischen horizontalen Ringspalten

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Abstract

The influence of various Prandtl numbers on the laminar convection flow between concentric and vertically eccentric cylinders is studied numerically. To overcome the difficulties associated with the complex physical domains a numerical transformation method is used to map this region on a rectangle. Although two independent computer programs which are based on different formulations of the governing equations were used, nearly identical results were obtained. Local heat transfer results are presented for a wide range of Rayleigh numbers for the first time. Local heat transfer rates are found to depend on the Prandtl number in addition to the Rayleigh number dependence.

Zusammenfassung

Anhand einer numerischen Studie wird der Einfluß der Prandtl-Zahl auf die laminare natürliche Konvektion im horizontalen konzentrischen und exzentrischen Ringspalt zwischen zwei Zylindern untersucht. Unter Verwendung einer numerischen Transformationsmethode können über körperkonforme Koordinatensysteme auch Vorgänge in komplexen Geometrien einer Lösung zugeführt werden. Obwohl von zwei unterschiedlichen Formulierungen der Erhaltungsgleichungen ausgegangen wird, ergeben sich nahezu identische Resultate. Die örtlichen Wärmestromdichten, die erstmals in einem weiten Bereich der Rayleigh-Zahl angegeben werden, weisen eine zusätzliche Abhängigkeit von der Prandtl-Zahl auf.

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Abbreviations

a :

thermal diffusivity

g :

acceleration of gravity

h :

film heat transfer coefficient

k :

thermal conductivity

L :

gap width (=R0−tRi)

n :

normal direction

Nu :

Nusselt number (=h Ri/k)

Pr :

Prandtl number (=v/a)

q″:

heat flux per unit area

R :

radius

Ra :

Rayleigh number (=gβΔTL3/va)

T :

temperature

β :

thermal expansion coefficient

ε :

eccentricity

θ :

dimensionless temperatureθ=T- T0/Ti-T0

ϕ :

angle

Λ :

equivalent conductivity

v :

kinematic viscosity

c :

conduction

i :

inner cylinder

o :

outer cylinder

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Authors and Affiliations

  1. Transnuklear GmbH, 645, Hanau

    U. Projahn

  2. Institut für Technische Thermodynamik Technische Hochschule Darmstadt, Petersenstraße 30, D-6100, Darmstadt

    H. Beer

Authors
  1. U. Projahn
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  2. H. Beer
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Projahn, U., Beer, H. Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli. Wärme- und Stoffübertragung 19, 249–254 (1985). https://doi.org/10.1007/BF01002278

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  • DOI: https://doi.org/10.1007/BF01002278

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