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An analysis of turbulent free convection about bodies of arbitrary geometrical configurations

Eine Analyse der freien Konvektion um Körper beliebiger geometrischer Gestalt

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Abstract

A general solution method is suggested for the prediction of the turbulent free convection heat transfer from curved surfaces. The method which may be viewed as a generalized version of the Eckert-Jackson method for the isothermal plate, is designed to deal with bodies of arbitrary geometrical configurations. The surface wall temperature is also allowed to vary in the streamwise direction in an arbitrary fashion. For the illustrative purpose, the calculations are carried out for the turbulent free convection about the horizontal circular cylinder, and the results are compared with the existing empirical formula. The flow transition from laminar to turbulent is also predicted by matching the laminar and turbulent solutions.

Zusammenfassung

Es wird eine allgemeine Lösungsmethode zur Vorhersage des Wärmeübergangs bei turbulenter, freier Konvektion um gekrümmte Flächen vorgeschlagen. Die Methode, die als generalisierte Version der Eckert-Jackson-Methode für die isotherme Platte angesehen werden kann, ist für Körper beliebiger geometrischer Gestalt gedacht. Auch die Oberflächentemperatur kann sich in Strömungsrichtung beliebig ändern. Zur Illustration für die Gültigkeit des Verfahrens werden die Rechnungen für turbulente, freie Konvektion um waagrechte, runde Zylinder durchgeführt und die Ergebnisse werden mit vorhandenen empirischen Formeln verglichen. Auch der Übergang von laminarer zu turbulenter Umströmung wird durch Anpassen der laminaren und turbulenten Lösungen vorhergesagt.

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Abbreviations

A, B, D :

shape factors

Cp :

specific heat

d :

diameter of cylinder

f :

function for velocity profile

fR :

Reynolds analogy factor

g :

acceleration due to gravity

g x :

tangential component ofg

Gr d :

Grashof number based ong andd

Gr x :

Grashof number based on gx andx

h :

local heat transfer coefficient

I, I t :

functions associated with deviation from unity

i :

integer associated with the coordinate system

j :

integer associated with the body shape at stagnation

k :

thermal conductivity

n :

exponent associated with the temperature difference

Nux :

local Nusselt number, hx/k

Nud :

=hd/k

Pr :

Prandtl number

r :

function representing wall geometry

T :

temperature

ΔT :

=T w-Te

u :

streamwise velocity component

u c :

characteristic velocity

x, y :

boundary layer coordinates

δ :

boundary layer thickness

ξ :

acceleration parameter

θ :

function for temperature profile

References

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shizuoka University, Hamamatsu, 432, Johoku, Japan

    A. Nakayama Ph.D. (Associate Professor) & H. Koyama Dr. Eng. (Professor)

Authors
  1. A. Nakayama Ph.D.
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  2. H. Koyama Dr. Eng.
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Additional information

The authors are grateful to Prof. E. R. G. Eckert for pointing out an error in the original manuscript.

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Nakayama, A., Koyama, H. An analysis of turbulent free convection about bodies of arbitrary geometrical configurations. Wärme- und Stoffübertragung 19, 263–268 (1985). https://doi.org/10.1007/BF01002280

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  • DOI: https://doi.org/10.1007/BF01002280

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